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+{
+ "2001_Adolescent_Pregnancy": {
+ "year": "2001",
+ "title": "Adolescent Pregnancy",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2001/HIMCM-A-2/index.html",
+ "question": "You are working temporarily for the Department of Health and Environmental Control. The director is concerned about the issue of teenage pregnancy in their region. You have decided that your team will analyze the situation and determine if it is really a problem in this region. You gather the following 2000 data. 2001-2.jpg\n\n### Image File: 2001-2.jpg\n\nThe image contains a table and some text data related to pregnancies and births across different age groups and counties.\n\n### Table Description:\n\nThe table is organized with the following columns:\n\n1. **County**: Numbered from 1 to 12.\n2. **Age 10-14 Pregnant**: Number of pregnancies in the 10-14 age group.\n3. **Age 15-17 Pregnant**: Number of pregnancies in the 15-17 age group.\n4. **Age 18-19 Pregnant**: Number of pregnancies in the 18-19 age group.\n5. **10-14 births**: Number of births in the 10-14 age group.\n6. **15-17 births**: Number of births in the 15-17 age group.\n7. **10-14 births-unmarried**: Number of births to unmarried individuals in the 10-14 age group.\n8. **15-17 births-unmarried**: Number of births to unmarried individuals in the 15-17 age group.\n9. **18-19 births-unmarried**: Number of births to unmarried individuals in the 18-19 age group.\n\nEach row corresponds to a different county, numbered from 1 to 12, with specific data for each category.\n\n### Text Data:\n\nBelow the table, there are two sections for the years 1998 and 1999, showing aggregated data for pregnancies and births by age group.\n\n#### 1998:\n- **Age 10-14**: \n - Pregnancies: 320\n - Births: 231\n- **Age 15-17**: \n - Pregnancies: 4041\n - Births: 3222\n- **Age 18-19**: \n - Pregnancies: 6387\n - Births: 5164\n\n#### 1999:\n- **Age 10-14**: \n - Pregnancies: 309\n - Births: 208\n- **Age 15-17**: \n - Pregnancies: 3882\n - Births: 3048\n- **Age 18-19**: \n - Pregnancies: 6714\n - Births: 5391\n\nThis data provides a detailed breakdown of pregnancies and births by age group and county, along with a summary for two consecutive years.",
+ "requirements": [
+ {
+ "category": "Data Analysis",
+ "description": "Evaluate the accuracy and completeness of the data analysis, including the calculation of pregnancy and birth rates for each age group and county."
+ },
+ {
+ "category": "Trend Analysis",
+ "description": "Assess the identification and analysis of trends over the years 1998 and 1999, including any significant changes in pregnancy and birth rates."
+ },
+ {
+ "category": "Comparative Analysis",
+ "description": "Grade the comparison of data across different counties to identify regions with higher or lower rates of teenage pregnancy and births."
+ },
+ {
+ "category": "Unmarried Births Analysis",
+ "description": "Evaluate the analysis of births to unmarried individuals and its implications on teenage pregnancy in the region."
+ },
+ {
+ "category": "Problem Identification",
+ "description": "Assess the determination of whether teenage pregnancy is a significant problem in the region based on the data analysis."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Evaluate the identification and discussion of any assumptions made during the analysis and the limitations of the data provided."
+ },
+ {
+ "category": "Recommendations",
+ "description": "Grade the quality and feasibility of recommendations provided to address teenage pregnancy in the region, based on the analysis."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves analyzing numerical data related to teenage pregnancies and births, which requires mathematical modeling to identify trends, correlations, and potential causative factors.",
+ "details": "You are a mathematician with expertise in statistical analysis and mathematical modeling. Your role is to ensure that the mathematical models used to analyze the data are robust and accurate. You should pay attention to the assumptions made in the models, the methods used to handle missing data, and the statistical significance of the results. Your expertise will help in identifying patterns and making predictions based on the data."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires processing and analyzing large datasets to extract meaningful insights, which is a core competency of data scientists.",
+ "details": "You are a data scientist skilled in data cleaning, transformation, and analysis. Your role is to ensure that the data is properly preprocessed and that the analytical methods used are appropriate for the dataset. You should focus on the use of machine learning techniques, if applicable, and the interpretation of the results. Your expertise will be crucial in visualizing the data and communicating findings to stakeholders."
+ },
+ {
+ "name": "Epidemiologist",
+ "thoughts": "The problem involves understanding the public health implications of teenage pregnancies, which is within the domain of epidemiology.",
+ "details": "You are an epidemiologist with expertise in studying the distribution and determinants of health-related states. Your role is to evaluate the public health impact of teenage pregnancies and to identify potential risk factors. You should pay attention to the demographic and socioeconomic variables that may influence the data. Your expertise will help in understanding the broader health implications and in formulating recommendations for intervention strategies."
+ },
+ {
+ "name": "Social Scientist",
+ "thoughts": "The problem involves understanding the social factors contributing to teenage pregnancies, which requires insights from social science.",
+ "details": "You are a social scientist with expertise in analyzing social behaviors and trends. Your role is to assess the social and cultural factors that may contribute to teenage pregnancies in the region. You should focus on the qualitative aspects of the data and consider how social norms, education, and family dynamics might influence the findings. Your expertise will be valuable in providing a comprehensive understanding of the issue and in suggesting socially informed interventions."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Data Analysis",
+ "description": "Evaluate the accuracy and completeness of the data analysis, including the calculation of pregnancy and birth rates for each age group and county."
+ },
+ {
+ "category": "Trend Analysis",
+ "description": "Assess the identification and analysis of trends over the years 1998 and 1999, including any significant changes in pregnancy and birth rates."
+ },
+ {
+ "category": "Comparative Analysis",
+ "description": "Grade the comparison of data across different counties to identify regions with higher or lower rates of teenage pregnancy and births."
+ },
+ {
+ "category": "Unmarried Births Analysis",
+ "description": "Evaluate the analysis of births to unmarried individuals and its implications on teenage pregnancy in the region."
+ },
+ {
+ "category": "Problem Identification",
+ "description": "Assess the determination of whether teenage pregnancy is a significant problem in the region based on the data analysis."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Evaluate the identification and discussion of any assumptions made during the analysis and the limitations of the data provided."
+ },
+ {
+ "category": "Recommendations",
+ "description": "Grade the quality and feasibility of recommendations provided to address teenage pregnancy in the region, based on the analysis."
+ }
+ ]
+ }
+ },
+ "2001_Design_of_an": {
+ "year": "2001",
+ "title": "Design of an Airline Terminal",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2001/HIMCM-A/index.html",
+ "question": "The design of airline terminals varies widely. The sketches below show airline terminals from several cities. The designs are quite dissimilar. Some involve circular arcs; others are rectangular; some are quite irregular. Which is optimal for operations? Develop a mathematical model for airport design and operation. Use your model to argue for the optimality of your specified design. Explain how it would operate.\n\n2011.jpg\n\n### Image File: 2011.jpg\n\nThe image shows five black silhouettes of airport terminal layouts, each labeled with the name of the airport it represents. Here is a detailed description:\n\n1. **Top Left:**\n - **Silhouette:** A compact, blocky shape with a main structure and several protruding sections.\n - **Label:** \"Boston-Logan International\"\n\n2. **Top Right:**\n - **Silhouette:** A long, narrow shape with a series of small extensions along its length.\n - **Label:** \"Munich International\"\n\n3. **Middle Left:**\n - **Silhouette:** A more complex shape with multiple branching sections, resembling a tree with several limbs.\n - **Label:** \"Charlotte/Douglas International\"\n\n4. **Middle Right:**\n - **Silhouette:** A curved main structure with several perpendicular extensions.\n - **Label:** \"Ronald Reagan Washington National\"\n\n5. **Bottom Center:**\n - **Silhouette:** A Y-shaped structure with additional smaller sections branching off.\n - **Label:** \"Pittsburgh International\"\n\nEach silhouette represents the layout of the respective airport's terminal, highlighting the unique design and structure of each location.",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "The mathematical model should be clearly defined, including assumptions, variables, and parameters relevant to airport terminal design and operation."
+ },
+ {
+ "category": "Operational Efficiency",
+ "description": "The model should evaluate the operational efficiency of different terminal designs, considering factors such as passenger flow, aircraft movement, and service accessibility."
+ },
+ {
+ "category": "Design Adaptability",
+ "description": "The model should be adaptable to various terminal designs, including circular, rectangular, and irregular shapes, and should provide a method for comparing these designs."
+ },
+ {
+ "category": "Optimal Design Justification",
+ "description": "The solution should include a well-reasoned argument for the optimality of the specified design, supported by results from the mathematical model."
+ },
+ {
+ "category": "Operational Explanation",
+ "description": "The solution should explain how the optimal terminal design would operate in practice, detailing the interaction between design elements and operational processes."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "The solution should clearly state any assumptions made in the model and discuss potential limitations or areas for improvement."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a deep understanding of geometric principles and optimization techniques to develop a mathematical model that can evaluate different airport terminal designs.",
+ "details": "As a mathematician, you are skilled in formulating mathematical models that can represent complex structures and operations. You should focus on the geometric aspects of the terminal designs, using your expertise in calculus, linear algebra, and optimization to assess the efficiency and functionality of each layout. Pay attention to how different shapes and configurations can impact operational flow and passenger movement."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to airport operations, such as passenger flow, aircraft movements, and logistical efficiency, to inform the model and determine optimal design.",
+ "details": "As a data scientist, you are adept at handling large datasets and extracting meaningful insights through statistical analysis and machine learning techniques. You should focus on gathering and analyzing data on airport operations, such as passenger traffic patterns and turnaround times, to evaluate how different terminal designs affect efficiency. Your expertise will be crucial in identifying trends and correlations that can guide the optimization process."
+ },
+ {
+ "name": "Architect",
+ "thoughts": "The problem requires architectural expertise to understand the practical implications of different terminal designs and how they can be implemented effectively.",
+ "details": "As an architect, you have a keen eye for design and functionality, ensuring that the terminal layout is not only optimal in theory but also feasible in practice. You should evaluate the structural integrity, aesthetic appeal, and spatial organization of each design, considering factors such as passenger comfort, accessibility, and safety. Your insights will be vital in bridging the gap between mathematical models and real-world applications."
+ },
+ {
+ "name": "Operations Manager",
+ "thoughts": "The problem requires an understanding of airport operations to assess how different terminal designs impact day-to-day activities and overall efficiency.",
+ "details": "As an operations manager, you are experienced in overseeing the logistical aspects of airport management, including passenger flow, baggage handling, and aircraft scheduling. You should evaluate how each terminal design affects operational efficiency, focusing on factors such as ease of navigation, turnaround times, and resource allocation. Your practical knowledge will be essential in determining which design offers the best balance between functionality and efficiency."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "The mathematical model should be clearly defined, including assumptions, variables, and parameters relevant to airport terminal design and operation."
+ },
+ {
+ "category": "Operational Efficiency",
+ "description": "The model should evaluate the operational efficiency of different terminal designs, considering factors such as passenger flow, aircraft movement, and service accessibility."
+ },
+ {
+ "category": "Design Adaptability",
+ "description": "The model should be adaptable to various terminal designs, including circular, rectangular, and irregular shapes, and should provide a method for comparing these designs."
+ },
+ {
+ "category": "Optimal Design Justification",
+ "description": "The solution should include a well-reasoned argument for the optimality of the specified design, supported by results from the mathematical model."
+ },
+ {
+ "category": "Operational Explanation",
+ "description": "The solution should explain how the optimal terminal design would operate in practice, detailing the interaction between design elements and operational processes."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "The solution should clearly state any assumptions made in the model and discuss potential limitations or areas for improvement."
+ }
+ ]
+ }
+ },
+ "2001_Forest_Service": {
+ "year": "2001",
+ "title": "Forest Service",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2001/HIMCM-B/index.html",
+ "question": "Your team has been approached by the Forest Service to help allocate resources to fight wildfires. In particular, the Forest Service is concerned about wildfires in a wilderness area consisting of small trees and brush in a park shaped like a square with dimensions 80 km on a side. Several years ago, the Forest Service constructed a network of north-south and east-west firebreaks that form a rectangular grid across the interior of the entire wilderness area. The firebreaks were built at 5 km intervals. Wildfires are most likely to occur during the dry season, which extends from July through September in this particular region. During this season, there is a prevailing westerly wind throughout the day. There are frequent lightning bursts that cause wildfires. The Forest Service wants to deploy four fire-fighting units to control fires during the next dry season. Each unit consists of 10 firefighters, one pickup truck, one dump truck, one water truck (50,000 liters), and one bulldozer (w/ truck and trailer). The unit has chainsaws, hand tools, and other fire-fighting equipment. The people can be quickly moved by helicopter within the wilderness area, but all the equipment must be driven via the existing firebreaks. One helicopter is on standby at all times throughout the dry season. Your task is to determine the best distribution of fire-fighting units within the wilderness area. The Forest Service is able to set up base camps for those units at sites anywhere within the area. In addition, you are asked to prepare a damage assessment forecast. This forecast will be used to estimate the amount of wilderness likely to be burned by fire as well as acting as a mechanism for helping the Service determine when additional fire-fighting units need to be brought in from elsewhere.",
+ "requirements": [
+ {
+ "category": "Resource Allocation Strategy",
+ "description": "Evaluate the strategy for distributing the four fire-fighting units across the wilderness area, considering factors such as accessibility, coverage, and response time."
+ },
+ {
+ "category": "Grid Utilization",
+ "description": "Assess how effectively the existing network of firebreaks is utilized for equipment movement and strategic placement of base camps."
+ },
+ {
+ "category": "Wind and Weather Considerations",
+ "description": "Analyze how the prevailing westerly wind and dry season conditions are factored into the placement and movement of fire-fighting units."
+ },
+ {
+ "category": "Helicopter Deployment",
+ "description": "Examine the plan for helicopter use in rapidly deploying personnel, ensuring optimal response times and coverage."
+ },
+ {
+ "category": "Damage Assessment Forecast",
+ "description": "Evaluate the methodology used to predict the extent of wilderness likely to be burned, including assumptions and data sources."
+ },
+ {
+ "category": "Additional Resource Needs",
+ "description": "Determine how the model identifies when additional fire-fighting units are required, based on the damage assessment forecast."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Review the assumptions made in the model, such as fire spread rates and resource effectiveness, and how limitations are addressed."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves complex spatial modeling and optimization to allocate resources effectively across the wilderness area. Mathematical expertise is crucial to develop models that can predict fire spread and optimize the placement of fire-fighting units.",
+ "details": "As a mathematician, you are skilled in spatial modeling, optimization techniques, and differential equations. You should focus on reviewing the mathematical models used to predict fire spread and resource allocation. Pay attention to the assumptions made in the models, the accuracy of the equations, and the robustness of the optimization algorithms. Your expertise will ensure that the models are mathematically sound and can effectively guide decision-making."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing historical wildfire data, weather patterns, and resource allocation data to inform the modeling process. Data science expertise is essential to process and interpret these datasets accurately.",
+ "details": "As a data scientist, you are proficient in data analysis, machine learning, and statistical methods. You should review the data-driven aspects of the modeling solutions, ensuring that the data is clean, relevant, and correctly interpreted. Focus on the use of predictive analytics to forecast wildfire occurrences and assess damage. Your role is to validate the data inputs and outputs, ensuring they are reliable and contribute to effective decision-making."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "Understanding the ecological impact of wildfires and the effectiveness of firebreaks is crucial. An environmental scientist can provide insights into the environmental factors that influence fire behavior and the potential ecological consequences of different firefighting strategies.",
+ "details": "As an environmental scientist, you are knowledgeable about ecosystems, fire ecology, and environmental impact assessments. You should evaluate the environmental assumptions in the modeling solutions, such as the impact of prevailing winds and vegetation types on fire spread. Your expertise will help ensure that the models consider ecological factors and that firefighting strategies minimize environmental damage."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem involves optimizing the logistics of deploying fire-fighting units and equipment efficiently. An operations research analyst can apply optimization techniques to improve resource allocation and logistics planning.",
+ "details": "As an operations research analyst, you specialize in optimization, logistics, and decision analysis. You should review the logistical models used to determine the best distribution of fire-fighting units and equipment. Focus on the efficiency of resource allocation, the feasibility of transportation routes, and the effectiveness of base camp locations. Your expertise will ensure that the solutions are practical and optimize the use of available resources."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Resource Allocation Strategy",
+ "description": "Evaluate the strategy for distributing the four fire-fighting units across the wilderness area, considering factors such as accessibility, coverage, and response time."
+ },
+ {
+ "category": "Grid Utilization",
+ "description": "Assess how effectively the existing network of firebreaks is utilized for equipment movement and strategic placement of base camps."
+ },
+ {
+ "category": "Wind and Weather Considerations",
+ "description": "Analyze how the prevailing westerly wind and dry season conditions are factored into the placement and movement of fire-fighting units."
+ },
+ {
+ "category": "Helicopter Deployment",
+ "description": "Examine the plan for helicopter use in rapidly deploying personnel, ensuring optimal response times and coverage."
+ },
+ {
+ "category": "Damage Assessment Forecast",
+ "description": "Evaluate the methodology used to predict the extent of wilderness likely to be burned, including assumptions and data sources."
+ },
+ {
+ "category": "Additional Resource Needs",
+ "description": "Determine how the model identifies when additional fire-fighting units are required, based on the damage assessment forecast."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Review the assumptions made in the model, such as fire spread rates and resource effectiveness, and how limitations are addressed."
+ }
+ ]
+ }
+ },
+ "2001_Skyscrapers": {
+ "year": "2001",
+ "title": "Skyscrapers",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2001/HIMCM-B-2/index.html",
+ "question": "Skyscrapers vary in height, size (square footage), occupancy rates, and usage. They adorn the skyline of our major cities. But as we have seen several times in history, the height of the building might preclude escape during a catastrophe either human or natural (earthquake, tornado, hurricane, etc). Let's consider the following scenario. A building (a skyscraper) needs to be evacuated. Power has been lost so the elevator banks are inoperative except for use by firefighters and rescue personnel with special keys. Build a mathematical model to clear the building within X minutes. Use this mathematical model to state the height of the building, maximum occupation, and type of evacuation methods used. Solve your model for X = 15 minutes, 30 minutes, and 60 minutes.",
+ "requirements": [
+ {
+ "category": "Model Formulation",
+ "description": "The mathematical model should clearly define variables such as building height, maximum occupancy, and evacuation methods, and how they interact to achieve evacuation within the specified time limits."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and justify any assumptions made regarding building structure, occupancy distribution, evacuation speed, and external conditions affecting evacuation."
+ },
+ {
+ "category": "Evacuation Methods",
+ "description": "Evaluate the selection and implementation of evacuation methods, including stair usage, emergency exits, and any innovative solutions proposed."
+ },
+ {
+ "category": "Scenario Analysis",
+ "description": "The model should be tested for different evacuation times (15, 30, and 60 minutes) and demonstrate adaptability and effectiveness in each scenario."
+ },
+ {
+ "category": "Model Validation",
+ "description": "Provide evidence or reasoning to validate the model's predictions, possibly through simulations or comparisons with real-world data."
+ },
+ {
+ "category": "Complexity and Feasibility",
+ "description": "Assess the complexity of the model and its feasibility in practical applications, ensuring it is not overly simplistic or impractical."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct sensitivity analysis to determine how changes in key parameters (e.g., occupancy rate, evacuation speed) affect the model's outcomes."
+ },
+ {
+ "category": "Result Interpretation",
+ "description": "Interpret the results of the model clearly, explaining how the evacuation times are achieved and any limitations or potential improvements."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires the formulation of a mathematical model to simulate evacuation scenarios, which involves complex calculations and optimization techniques.",
+ "details": "You are a mathematician with expertise in creating and analyzing mathematical models. Your role is crucial in ensuring that the model accurately represents the dynamics of evacuating a skyscraper under various constraints. You should pay attention to the assumptions made in the model, the equations used to represent evacuation processes, and the optimization methods applied to achieve evacuation within the specified time frames. Your deep understanding of mathematical principles will help in evaluating the robustness and validity of the model."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves processing and analyzing data related to building occupancy, evacuation times, and methods, which are essential for validating the model.",
+ "details": "You are a data scientist skilled in handling large datasets and extracting meaningful insights. Your expertise is vital in reviewing the data inputs used in the model, such as occupancy rates and evacuation statistics. You should focus on the accuracy and relevance of the data, the statistical methods used to analyze it, and how these insights are integrated into the model. Your proficiency in data analysis and machine learning can help in refining the model to better predict evacuation outcomes."
+ },
+ {
+ "name": "Structural Engineer",
+ "thoughts": "The problem involves understanding the physical structure of skyscrapers, which affects evacuation routes and methods.",
+ "details": "You are a structural engineer with knowledge of building design and safety protocols. Your role is to assess how the model accounts for the physical characteristics of skyscrapers, such as stairwell capacity, floor layout, and emergency exits. You should evaluate whether the model realistically represents the constraints imposed by the building's architecture and how these impact evacuation strategies. Your expertise in structural integrity and safety standards is crucial for ensuring the model's practical applicability."
+ },
+ {
+ "name": "Emergency Management Specialist",
+ "thoughts": "The problem requires expertise in emergency evacuation procedures and planning to ensure the model's effectiveness in real-world scenarios.",
+ "details": "You are an emergency management specialist with experience in planning and executing evacuation strategies during crises. Your role is to review the evacuation methods proposed in the model, considering factors like human behavior, communication systems, and coordination with rescue personnel. You should assess the feasibility and efficiency of the evacuation plans within the given time constraints. Your insights into emergency response protocols and crisis management will help in evaluating the model's ability to facilitate safe and timely evacuations."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Formulation",
+ "description": "The mathematical model should clearly define variables such as building height, maximum occupancy, and evacuation methods, and how they interact to achieve evacuation within the specified time limits."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and justify any assumptions made regarding building structure, occupancy distribution, evacuation speed, and external conditions affecting evacuation."
+ },
+ {
+ "category": "Evacuation Methods",
+ "description": "Evaluate the selection and implementation of evacuation methods, including stair usage, emergency exits, and any innovative solutions proposed."
+ },
+ {
+ "category": "Scenario Analysis",
+ "description": "The model should be tested for different evacuation times (15, 30, and 60 minutes) and demonstrate adaptability and effectiveness in each scenario."
+ },
+ {
+ "category": "Model Validation",
+ "description": "Provide evidence or reasoning to validate the model's predictions, possibly through simulations or comparisons with real-world data."
+ },
+ {
+ "category": "Complexity and Feasibility",
+ "description": "Assess the complexity of the model and its feasibility in practical applications, ensuring it is not overly simplistic or impractical."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct sensitivity analysis to determine how changes in key parameters (e.g., occupancy rate, evacuation speed) affect the model's outcomes."
+ },
+ {
+ "category": "Result Interpretation",
+ "description": "Interpret the results of the model clearly, explaining how the evacuation times are achieved and any limitations or potential improvements."
+ }
+ ]
+ }
+ },
+ "2001_The_Bicycle_Wheel": {
+ "year": "2001",
+ "title": "The Bicycle Wheel Problem",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2001/MCM-A/index.html",
+ "question": "Cyclists have different types of wheels they can use on their bicycles. The two basic types of wheels are those constructed using wire spokes and those constructed of a solid disk (see Figure 1). The spoked wheels are lighter, but the solid wheels are more aerodynamic. A solid wheel is never used on the front for a road race but can be used on the rear of the bike.\n\nProfessional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used. The decision is based on the number and steepness of the hills, the weather, wind speed, the competition, and other considerations. The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used for a given course.\n\nimage001.png\n\nFigure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right.\n\nThe director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below. For each of the tasks assume that the same spoked wheel will always be used on the front but there is a choice of wheels for the rear.\n\nTask 1. Provide a table giving the wind speed at which the power required for a solid rear wheel is less than for a spoked rear wheel. The table should include the wind speeds for different road grades starting from zero percent to ten percent in one percent increments. (Road grade is defined to be the ratio of the total rise of a hill divided by the length of the road. If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.) A rider starts at the bottom of the hill at a speed of 45 kph, and the deceleration of the rider is proportional to the road grade. A rider will lose about 8 kph for a five percent grade over 100 meters.\n\nTask 2. Provide an example of how the table could be used for a specific time trial course.\n\nTask 3. Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.\n\n### Image File: image001.png\n\nThe image contains two circular diagrams side by side.\n\n1. **Left Circle:**\n - The circle is filled with a gradient of gray shades, transitioning smoothly from light gray on the left side to dark gray on the right side.\n - There is a small, solid gray dot located at the center of the circle.\n\n2. **Right Circle:**\n - This circle resembles a bicycle wheel with spokes.\n - It has a central black dot, representing the hub.\n - Multiple straight black lines (spokes) radiate outward from the central dot to the circumference of the circle.\n - The circle's outline is a solid black line.\n\nThere is no text present in the image.",
+ "requirements": [
+ {
+ "category": "Modeling Accuracy",
+ "description": "Evaluate the mathematical model used to calculate the power required for solid versus spoked rear wheels under varying wind speeds and road grades. Ensure the model accurately reflects the physics of cycling and the impact of wheel type on performance."
+ },
+ {
+ "category": "Data Presentation",
+ "description": "Assess the clarity and comprehensiveness of the table provided in Task 1, ensuring it includes wind speeds for road grades from zero to ten percent in one percent increments, and correctly identifies conditions where solid wheels require less power."
+ },
+ {
+ "category": "Application Example",
+ "description": "Examine the example provided in Task 2, checking if it effectively demonstrates how to use the table for a specific time trial course, and whether it includes relevant course details and decision-making criteria."
+ },
+ {
+ "category": "Decision Adequacy",
+ "description": "Evaluate the analysis in Task 3 regarding the adequacy of the table as a decision-making tool, including any additional suggestions for improving wheel configuration decisions based on other factors like weather, competition, and rider preferences."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Identify and assess any assumptions made in the modeling process, such as the proportional deceleration related to road grade, and discuss potential limitations or areas for improvement in the model."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves complex calculations related to road grades, wind speeds, and power requirements, which are fundamentally mathematical in nature. A mathematician can help formulate the equations needed to model these relationships accurately.",
+ "details": "You are a mathematician with expertise in mathematical modeling and analysis. Your role is crucial in developing the equations that describe the power dynamics between different wheel types under varying conditions. You should pay attention to the accuracy of the mathematical formulations and ensure that the models are robust and can handle the range of variables presented in the problem. Your expertise in calculus and differential equations will be particularly valuable in understanding the deceleration effects and optimizing the model."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing data related to wind speeds, road grades, and cycling performance. A data scientist can help process this data to identify patterns and make predictions about wheel performance.",
+ "details": "You are a data scientist skilled in data analysis, machine learning, and statistical modeling. Your role involves collecting and analyzing data to inform the decision-making process for wheel selection. You should focus on ensuring the data is clean, accurate, and representative of real-world conditions. Your ability to use predictive modeling and data visualization will be essential in creating a user-friendly table and providing insights into how different variables affect wheel performance."
+ },
+ {
+ "name": "Mechanical Engineer",
+ "thoughts": "The problem involves understanding the physical properties and performance characteristics of different wheel types, which is within the domain of mechanical engineering. A mechanical engineer can provide insights into the aerodynamic and structural aspects of the wheels.",
+ "details": "You are a mechanical engineer with expertise in the design and performance of bicycle components. Your role is to evaluate the aerodynamic efficiency and structural integrity of both spoked and solid wheels. You should focus on how these physical characteristics translate into performance under different conditions, such as varying wind speeds and road grades. Your understanding of material science and fluid dynamics will be crucial in assessing the real-world implications of the mathematical and data models."
+ },
+ {
+ "name": "Sports Scientist",
+ "thoughts": "The problem involves optimizing cycling performance, which is a key area of sports science. A sports scientist can provide insights into how different wheel configurations affect a cyclist's performance and energy expenditure.",
+ "details": "You are a sports scientist with expertise in human performance and biomechanics. Your role is to assess how different wheel types impact a cyclist's efficiency and fatigue levels during a race. You should focus on the physiological effects of using different wheels, considering factors such as energy expenditure, muscle fatigue, and overall performance. Your knowledge of exercise physiology and biomechanics will be essential in interpreting the data and providing recommendations that align with the athlete's capabilities and race strategy."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Modeling Accuracy",
+ "description": "Evaluate the mathematical model used to calculate the power required for solid versus spoked rear wheels under varying wind speeds and road grades. Ensure the model accurately reflects the physics of cycling and the impact of wheel type on performance."
+ },
+ {
+ "category": "Data Presentation",
+ "description": "Assess the clarity and comprehensiveness of the table provided in Task 1, ensuring it includes wind speeds for road grades from zero to ten percent in one percent increments, and correctly identifies conditions where solid wheels require less power."
+ },
+ {
+ "category": "Application Example",
+ "description": "Examine the example provided in Task 2, checking if it effectively demonstrates how to use the table for a specific time trial course, and whether it includes relevant course details and decision-making criteria."
+ },
+ {
+ "category": "Decision Adequacy",
+ "description": "Evaluate the analysis in Task 3 regarding the adequacy of the table as a decision-making tool, including any additional suggestions for improving wheel configuration decisions based on other factors like weather, competition, and rider preferences."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Identify and assess any assumptions made in the modeling process, such as the proportional deceleration related to road grade, and discuss potential limitations or areas for improvement in the model."
+ }
+ ]
+ }
+ },
+ "2002_Airline_Overbooking": {
+ "year": "2002",
+ "title": "Airline Overbooking",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2002/MCM-B/index.html",
+ "question": "You're all packed and ready to go on a trip to visit your best friend in New York City. After you check in at the ticket counter, the airline clerk announces that your flight has been overbooked. Passengers need to check in immediately to determine if they still have a seat.\n\nHistorically, airlines know that only a certain percentage of passengers who have made reservations on a particular flight will actually take that flight. Consequently, most airlines overbook\u2014that is, they take more reservations than the capacity of the aircraft. Occasionally, more passengers will want to take a flight than the capacity of the plane, leading to one or more passengers being bumped and thus unable to take the flight for which they had reservations.\n\nAirlines deal with bumped passengers in various ways. Some are given nothing, some are booked on later flights on other airlines, and some are given some kind of cash or airline ticket incentive.\n\nConsider the overbooking issue in light of the current situation: Less flights by airlines from point A to point B, heightened security at and around airports, passengers' fear, and loss of billions of dollars in revenue by airlines to date.\n\nBuild a mathematical model that examines the effects that different overbooking schemes have on the revenue received by an airline company in order to find an optimal overbooking strategy, i.e., the number of people by which an airline should overbook a particular flight so that the company's revenue is maximized. Ensure that your model reflects the issues above, and consider alternatives for handling \"bumped\" passengers. Additionally, write a short memorandum to the airline's CEO summarizing your findings and analysis.",
+ "requirements": [
+ {
+ "category": "Objective Identification",
+ "description": "Clearly identify the main objective of maximizing airline revenue through optimal overbooking strategies."
+ },
+ {
+ "category": "Model Development",
+ "description": "Develop a mathematical model that accurately represents the relationship between overbooking strategies and airline revenue."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and justify assumptions made regarding passenger behavior, flight capacity, and overbooking percentages."
+ },
+ {
+ "category": "Handling Bumped Passengers",
+ "description": "Evaluate different methods for handling bumped passengers and incorporate these into the model to assess their impact on revenue."
+ },
+ {
+ "category": "Revenue Analysis",
+ "description": "Analyze how different overbooking schemes affect the airline's revenue, considering factors such as passenger fear and security concerns."
+ },
+ {
+ "category": "Optimization Strategy",
+ "description": "Determine the optimal number of passengers to overbook to maximize revenue, supported by model results."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct sensitivity analysis to understand how changes in key parameters affect the model outcomes."
+ },
+ {
+ "category": "Memorandum to CEO",
+ "description": "Write a concise memorandum summarizing findings, analysis, and recommendations for the airline's CEO."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a strong foundation in mathematical modeling to develop equations that can predict the optimal overbooking strategy. This involves understanding probability, optimization, and statistical analysis to accurately model passenger behavior and airline revenue.",
+ "details": "As a mathematician, you are adept at constructing and analyzing mathematical models. Your expertise in probability and optimization is crucial for developing a model that predicts the optimal number of overbooked seats. You should focus on ensuring the model's assumptions are valid and that the mathematical techniques used are appropriate for the problem. Pay attention to the accuracy of the equations and the logical consistency of the model."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing historical data on passenger behavior and flight overbooking to inform the model. A data scientist's skills in data analysis, machine learning, and statistical methods are essential for extracting insights from the data and validating the model.",
+ "details": "As a data scientist, your role is to analyze historical flight data to identify patterns and trends in passenger behavior. You should use statistical methods and machine learning techniques to validate the model's predictions and ensure its robustness. Focus on data quality, feature selection, and the interpretability of the model's outputs. Your insights will help refine the model and improve its predictive accuracy."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem involves optimizing airline operations, which is a classic operations research problem. An operations research analyst can apply techniques such as linear programming, simulation, and decision analysis to find the best overbooking strategy.",
+ "details": "As an operations research analyst, you specialize in optimizing complex systems. Your expertise in linear programming and simulation is vital for evaluating different overbooking strategies and their impact on airline operations. You should focus on the efficiency and feasibility of the proposed solutions, ensuring they align with operational constraints and business objectives. Your analysis will help identify the most effective strategies for maximizing revenue while minimizing passenger inconvenience."
+ },
+ {
+ "name": "Airline Revenue Management Specialist",
+ "thoughts": "The problem directly impacts airline revenue management, which involves balancing supply and demand to maximize revenue. A specialist in this field can provide insights into pricing strategies, demand forecasting, and customer compensation policies.",
+ "details": "As an airline revenue management specialist, you have a deep understanding of the airline industry's pricing and demand dynamics. Your role is to evaluate how different overbooking strategies affect revenue and customer satisfaction. You should consider factors such as pricing elasticity, customer compensation, and competitive positioning. Your expertise will ensure that the model aligns with industry practices and effectively balances revenue maximization with customer experience."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Objective Identification",
+ "description": "Clearly identify the main objective of maximizing airline revenue through optimal overbooking strategies."
+ },
+ {
+ "category": "Model Development",
+ "description": "Develop a mathematical model that accurately represents the relationship between overbooking strategies and airline revenue."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and justify assumptions made regarding passenger behavior, flight capacity, and overbooking percentages."
+ },
+ {
+ "category": "Handling Bumped Passengers",
+ "description": "Evaluate different methods for handling bumped passengers and incorporate these into the model to assess their impact on revenue."
+ },
+ {
+ "category": "Revenue Analysis",
+ "description": "Analyze how different overbooking schemes affect the airline's revenue, considering factors such as passenger fear and security concerns."
+ },
+ {
+ "category": "Optimization Strategy",
+ "description": "Determine the optimal number of passengers to overbook to maximize revenue, supported by model results."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct sensitivity analysis to understand how changes in key parameters affect the model outcomes."
+ },
+ {
+ "category": "Memorandum to CEO",
+ "description": "Write a concise memorandum summarizing findings, analysis, and recommendations for the airline's CEO."
+ }
+ ]
+ }
+ },
+ "2002_School_Busing": {
+ "year": "2002",
+ "title": "School Busing",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2002/HIMCM-A/index.html",
+ "question": "Consider a school where most of the students are from rural areas, so they must be bused. The buses might pick up all the students and go to the elementary school and then continue from that school to pick up more students for the high school. A clear alternative would be to have separate buses for each school, even though they would need to trace over the same routes. There are, of course, restrictions on time (no student should be in the bus more than an hour), drivers, equipment, money, and so forth. How can you set up school bus routes to optimize budget dollars while balancing the time on the bus for various school groups? Build a mathematical model that could be used by various rural and perhaps urban school districts. How would you test the model prior to implementation? Prepare a short article to the school board explaining your model, its assumptions, and its results.",
+ "requirements": [
+ {
+ "category": "Objective Identification",
+ "description": "Clearly identify the main objectives of the model, such as minimizing costs and ensuring no student spends more than an hour on the bus."
+ },
+ {
+ "category": "Model Formulation",
+ "description": "Develop a mathematical model that accurately represents the bus routing problem, including variables, constraints, and objective functions."
+ },
+ {
+ "category": "Constraint Handling",
+ "description": "Address all explicit constraints such as time limits, driver availability, equipment limitations, and budget restrictions within the model."
+ },
+ {
+ "category": "Implicit Assumptions",
+ "description": "Identify and justify any implicit assumptions made in the model, such as student distribution, bus capacity, and route overlap."
+ },
+ {
+ "category": "Generalizability",
+ "description": "Ensure the model is adaptable for use in various rural and urban school districts, considering different geographical and demographic factors."
+ },
+ {
+ "category": "Testing Methodology",
+ "description": "Outline a clear plan for testing the model prior to implementation, including validation techniques and potential scenarios."
+ },
+ {
+ "category": "Communication",
+ "description": "Prepare a concise article for the school board that explains the model, its assumptions, results, and potential impact on the school district."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires the development of a mathematical model to optimize bus routes, which involves complex mathematical concepts such as optimization, graph theory, and possibly linear programming.",
+ "details": "You are a mathematician with expertise in optimization and mathematical modeling. Your role is to ensure that the mathematical framework of the proposed solution is sound and efficient. You should pay attention to the assumptions made in the model, the formulation of the objective function, and the constraints. Your expertise in mathematical principles will be crucial in evaluating the robustness and feasibility of the model."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves handling and analyzing data related to student locations, bus routes, and time constraints, which is essential for building a data-driven model.",
+ "details": "You are a data scientist skilled in data analysis, statistical methods, and machine learning. Your role is to ensure that the data used in the model is accurate and effectively processed. You should focus on data collection methods, data cleaning, and the integration of data into the model. Your expertise will help in validating the model's predictions and ensuring that it can be generalized to different school districts."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem is essentially an optimization problem that requires expertise in operations research to find the most efficient bus routes while considering various constraints.",
+ "details": "You are an operations research analyst with expertise in optimization techniques and decision-making processes. Your role is to evaluate the efficiency of the proposed bus routing model. You should focus on the optimization algorithms used, the handling of constraints such as time and budget, and the overall effectiveness of the solution. Your insights will be valuable in ensuring that the model provides practical and cost-effective solutions."
+ },
+ {
+ "name": "Transportation Planner",
+ "thoughts": "The problem involves planning and logistics of transportation systems, which requires expertise in transportation planning to ensure practical implementation.",
+ "details": "You are a transportation planner with expertise in designing and managing transportation systems. Your role is to assess the practicality and feasibility of the proposed bus routes. You should consider factors such as route efficiency, student safety, and compliance with transportation regulations. Your experience in transportation logistics will be crucial in evaluating whether the model can be successfully implemented in real-world scenarios."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Objective Identification",
+ "description": "Clearly identify the main objectives of the model, such as minimizing costs and ensuring no student spends more than an hour on the bus."
+ },
+ {
+ "category": "Model Formulation",
+ "description": "Develop a mathematical model that accurately represents the bus routing problem, including variables, constraints, and objective functions."
+ },
+ {
+ "category": "Constraint Handling",
+ "description": "Address all explicit constraints such as time limits, driver availability, equipment limitations, and budget restrictions within the model."
+ },
+ {
+ "category": "Implicit Assumptions",
+ "description": "Identify and justify any implicit assumptions made in the model, such as student distribution, bus capacity, and route overlap."
+ },
+ {
+ "category": "Generalizability",
+ "description": "Ensure the model is adaptable for use in various rural and urban school districts, considering different geographical and demographic factors."
+ },
+ {
+ "category": "Testing Methodology",
+ "description": "Outline a clear plan for testing the model prior to implementation, including validation techniques and potential scenarios."
+ },
+ {
+ "category": "Communication",
+ "description": "Prepare a concise article for the school board that explains the model, its assumptions, results, and potential impact on the school district."
+ }
+ ]
+ }
+ },
+ "2002_Wind_and_Waterspray": {
+ "year": "2002",
+ "title": "Wind and Waterspray",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2002/MCM-A/index.html",
+ "question": "An ornamental fountain in a large open plaza surrounded by buildings squirts water high into the air. On gusty days, the wind blows spray from the fountain onto passersby. The water-flow from the fountain is controlled by a mechanism linked to an anemometer (which measures wind speed and direction) located on top of an adjacent building. The objective of this control is to provide passersby with an acceptable balance between an attractive spectacle and a soaking: The harder the wind blows, the lower the water volume and height to which the water is squirted, hence the less spray falls outside the pool area. Your task is to devise an algorithm which uses data provided by the anemometer to adjust the water-flow from the fountain as the wind conditions change.",
+ "requirements": [
+ {
+ "category": "Understanding of Wind Data",
+ "description": "Evaluate the ability to interpret and utilize wind speed and direction data from the anemometer effectively."
+ },
+ {
+ "category": "Modeling of Fountain Water Flow",
+ "description": "Assess the development of a mathematical model that accurately represents the relationship between wind conditions and the fountain's water flow, volume, and height."
+ },
+ {
+ "category": "Algorithm Design",
+ "description": "Examine the design of the algorithm that adjusts the fountain's water flow in real-time based on changing wind conditions."
+ },
+ {
+ "category": "Balance Between Spectacle and Safety",
+ "description": "Evaluate how well the solution balances the visual appeal of the fountain with minimizing water spray on passersby."
+ },
+ {
+ "category": "Adaptability and Responsiveness",
+ "description": "Assess the algorithm's ability to quickly and effectively respond to changes in wind conditions."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Identify and evaluate any assumptions made in the model and their impact on the solution's effectiveness."
+ },
+ {
+ "category": "Validation and Testing",
+ "description": "Evaluate the methods used to validate and test the algorithm's performance under various wind conditions."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to understand the relationship between wind speed/direction and the fountain's water flow. This involves formulating equations that can predict the optimal water height and volume based on varying wind conditions.",
+ "details": "You are a mathematician with expertise in differential equations and dynamic systems. Your role is to ensure that the mathematical models used in the algorithm accurately represent the physical phenomena involved. Pay attention to the assumptions made in the model and verify that they are reasonable given the real-world context. Your evaluation should focus on the robustness and accuracy of the mathematical formulations and their ability to adapt to changing wind conditions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves processing and analyzing data from the anemometer to inform the algorithm's decisions. This requires expertise in data handling, statistical analysis, and possibly machine learning to predict wind patterns and adjust the fountain's settings accordingly.",
+ "details": "You are a data scientist skilled in data analysis and predictive modeling. Your role is to review the data processing methods and ensure that the algorithm effectively uses the anemometer data to make real-time adjustments. Pay attention to the data quality, preprocessing steps, and the statistical methods used to derive insights. Your evaluation should focus on the algorithm's ability to handle noisy data and its effectiveness in predicting wind changes to optimize fountain performance."
+ },
+ {
+ "name": "Control Systems Engineer",
+ "thoughts": "The problem involves designing a control system that dynamically adjusts the fountain's water flow based on real-time wind data. This requires expertise in control theory and systems engineering to ensure the mechanism responds accurately and efficiently to changing conditions.",
+ "details": "You are a control systems engineer with expertise in designing and implementing automated systems. Your role is to review the control algorithm and ensure it is capable of real-time adjustments with minimal delay. Pay attention to the feedback loop design, the responsiveness of the system, and the integration of the anemometer data into the control mechanism. Your evaluation should focus on the system's stability, reliability, and ability to maintain the desired balance between spectacle and safety."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem involves understanding the environmental impact of the fountain's operation, particularly how wind patterns affect water dispersion. This requires expertise in environmental science to assess the broader implications of the fountain's spray on the surrounding area.",
+ "details": "You are an environmental scientist with expertise in atmospheric conditions and their effects on urban environments. Your role is to review the environmental considerations of the algorithm, ensuring it minimizes negative impacts on passersby and the surrounding area. Pay attention to the wind pattern analysis and the potential for water wastage or unintended soaking. Your evaluation should focus on the sustainability of the fountain's operation and its alignment with environmental best practices."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Understanding of Wind Data",
+ "description": "Evaluate the ability to interpret and utilize wind speed and direction data from the anemometer effectively."
+ },
+ {
+ "category": "Modeling of Fountain Water Flow",
+ "description": "Assess the development of a mathematical model that accurately represents the relationship between wind conditions and the fountain's water flow, volume, and height."
+ },
+ {
+ "category": "Algorithm Design",
+ "description": "Examine the design of the algorithm that adjusts the fountain's water flow in real-time based on changing wind conditions."
+ },
+ {
+ "category": "Balance Between Spectacle and Safety",
+ "description": "Evaluate how well the solution balances the visual appeal of the fountain with minimizing water spray on passersby."
+ },
+ {
+ "category": "Adaptability and Responsiveness",
+ "description": "Assess the algorithm's ability to quickly and effectively respond to changes in wind conditions."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Identify and evaluate any assumptions made in the model and their impact on the solution's effectiveness."
+ },
+ {
+ "category": "Validation and Testing",
+ "description": "Evaluate the methods used to validate and test the algorithm's performance under various wind conditions."
+ }
+ ]
+ }
+ },
+ "2003_Aviation_Baggage_Screening": {
+ "year": "2003",
+ "title": "Aviation Baggage Screening Strategies: To Screen or Not to Screen, that is the Question",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2003/ICM-C/index.html",
+ "question": "ICM_2003.pdf ICM_2003.pdf Aviation Baggage Screening Strategies: To Screen or Not to Screen, that is the Question\n\n### Text in the PDF File: ICM_2003.pdf\n\n**Aviation Baggage Screening Strategies**\n\n**Overview:**\nThe Transportation Security Administration (TSA) is implementing a mandate for 100% screening of all checked bags at 429 passenger airports using Explosive Detection Systems (EDSs). These systems use computed tomography (CT) technology to create 3D images of bag contents, identifying potential explosives. EDSs are operational 92% of the time and can process 160-210 bags per hour. Each EDS costs nearly $1 million and requires significant installation costs.\n\n**Challenges:**\n- Limited production of EDSs to meet federal mandates.\n- High costs and space requirements for EDS deployment.\n- Emerging technologies may offer more cost-effective solutions in the future.\n\n**Tasks:**\n\n1. **Model Development for EDS Requirements:**\n - Develop a model to determine the number of EDSs needed at Airports A & B.\n - Use data from Table 1 in the Technical Information Sheet (TIS) to inform the model.\n - Consider assumptions such as flight occupancy rates and baggage check patterns.\n\n2. **Position Paper:**\n - Outline security objectives and constraints for airlines based on flight data in Table 1.\n\n3. **Scheduling Model:**\n - Create a model to help airlines schedule flight departures during peak hours at Airports A & B.\n - Use assumptions and data from Table 1 to produce a schedule.\n\n4. **Recommendations:**\n - Provide recommendations to Mr. Sheldon and airlines regarding baggage screening during peak hours.\n\n5. **National Impact Memo:**\n - Explain how models can be adapted for all 193 airports in the Midwest Region.\n - Address potential national implementation.\n\n6. **Incorporating ETD Machines:**\n - Modify EDS models to include Explosive Trace Detection (ETD) machines.\n - Determine the number of ETD machines needed and assess schedule changes.\n - Evaluate the cost-effectiveness of this enhanced screening policy.\n\n7. **Future Research Recommendations:**\n - Analyze the impact of changes in device technology, cost, accuracy, speed, and reliability.\n - Recommend STEM research areas to improve security system performance.\n\n**Technical Information Sheet (TIS) - Table 1: Peak Hour Flight Departures**\n\n| Flight Type | Seats per Flight | Airport A Flights | Airport B Flights |\n|-------------|------------------|-------------------|-------------------|\n| 1 | 34 | 10 | 8 |\n| 2 | 46 | 4 | 6 |\n| 3 | 85 | 3 | 7 |\n| 4 | 128 | 3 | 5 |\n| 5 | 142 | 19 | 9 |\n| 6 | 194 | 5 | 10 |\n| 7 | 215 | 1 | 2 |\n| 8 | 350 | 1 | 1 |\n\n**Additional Notes:**\n- Flights with 85 or fewer seats have 70%-100% occupancy.\n- Flights with 128-215 seats have 60%-100% occupancy.\n- Flights with 350 seats have 50%-100% occupancy.\n- Passenger arrival times range from 45 minutes to 2 hours before departure.\n- 20% of passengers do not check luggage, 20% check one bag, and the rest check two bags.\n- Installation costs for EDS: $100,000 at Airport A and $80,000 at Airport B.",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the accuracy and feasibility of the model developed to determine the number of EDSs needed at Airports A & B, considering flight occupancy rates and baggage check patterns."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Assess the validity and impact of assumptions made in the model, such as flight occupancy rates and passenger baggage check patterns."
+ },
+ {
+ "category": "Position Paper",
+ "description": "Grade the clarity and comprehensiveness of the security objectives and constraints outlined for airlines based on flight data."
+ },
+ {
+ "category": "Scheduling Model",
+ "description": "Evaluate the effectiveness of the scheduling model in optimizing flight departures during peak hours at Airports A & B."
+ },
+ {
+ "category": "Recommendations",
+ "description": "Assess the practicality and relevance of recommendations provided to Mr. Sheldon and airlines regarding baggage screening during peak hours."
+ },
+ {
+ "category": "National Impact Memo",
+ "description": "Evaluate the adaptability and scalability of the models for implementation across all 193 airports in the Midwest Region, considering national impact."
+ },
+ {
+ "category": "Incorporating ETD Machines",
+ "description": "Grade the modifications made to include ETD machines in the EDS models, including the determination of ETD machine requirements and schedule changes."
+ },
+ {
+ "category": "Cost-effectiveness",
+ "description": "Assess the evaluation of the cost-effectiveness of the enhanced screening policy incorporating ETD machines."
+ },
+ {
+ "category": "Future Research Recommendations",
+ "description": "Evaluate the analysis of potential changes in device technology, cost, accuracy, speed, and reliability, and the recommendations for STEM research areas to improve security system performance."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves developing mathematical models to determine the number of EDSs required, scheduling flight departures, and assessing cost-effectiveness. This requires expertise in mathematical modeling, optimization, and statistical analysis.",
+ "details": "As a mathematician, you are skilled in formulating and solving complex equations that underpin the models needed for this problem. You should focus on ensuring the mathematical rigor and validity of the models, paying attention to assumptions and constraints. Your expertise in optimization techniques will be crucial in developing efficient solutions for scheduling and resource allocation."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing flight data, passenger patterns, and baggage check statistics to inform the models. This involves data processing, statistical analysis, and possibly machine learning techniques to predict trends and optimize solutions.",
+ "details": "As a data scientist, you are adept at handling large datasets and extracting meaningful insights. You should focus on the accuracy and reliability of the data used in the models, ensuring that the statistical methods applied are appropriate. Your ability to visualize data and interpret results will be essential in communicating findings and recommendations effectively."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem involves optimizing the deployment and scheduling of EDSs and ETD machines, which is a classic operations research challenge. This requires expertise in linear programming, queuing theory, and simulation modeling.",
+ "details": "As an operations research analyst, you are skilled in applying mathematical and analytical methods to help make better decisions. You should focus on developing models that optimize the use of resources, minimize costs, and improve efficiency. Your expertise in simulation modeling will be valuable in testing different scenarios and assessing the impact of various strategies."
+ },
+ {
+ "name": "Security Systems Engineer",
+ "thoughts": "The problem involves assessing the effectiveness and integration of security technologies like EDS and ETD machines. This requires expertise in security systems design, technology evaluation, and risk assessment.",
+ "details": "As a security systems engineer, you are knowledgeable about the latest security technologies and their applications. You should focus on evaluating the technical feasibility and reliability of the proposed solutions, ensuring they meet security objectives. Your ability to assess risks and recommend improvements will be crucial in enhancing the overall security strategy."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the accuracy and feasibility of the model developed to determine the number of EDSs needed at Airports A & B, considering flight occupancy rates and baggage check patterns."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Assess the validity and impact of assumptions made in the model, such as flight occupancy rates and passenger baggage check patterns."
+ },
+ {
+ "category": "Position Paper",
+ "description": "Grade the clarity and comprehensiveness of the security objectives and constraints outlined for airlines based on flight data."
+ },
+ {
+ "category": "Scheduling Model",
+ "description": "Evaluate the effectiveness of the scheduling model in optimizing flight departures during peak hours at Airports A & B."
+ },
+ {
+ "category": "Recommendations",
+ "description": "Assess the practicality and relevance of recommendations provided to Mr. Sheldon and airlines regarding baggage screening during peak hours."
+ },
+ {
+ "category": "National Impact Memo",
+ "description": "Evaluate the adaptability and scalability of the models for implementation across all 193 airports in the Midwest Region, considering national impact."
+ },
+ {
+ "category": "Incorporating ETD Machines",
+ "description": "Grade the modifications made to include ETD machines in the EDS models, including the determination of ETD machine requirements and schedule changes."
+ },
+ {
+ "category": "Cost-effectiveness",
+ "description": "Assess the evaluation of the cost-effectiveness of the enhanced screening policy incorporating ETD machines."
+ },
+ {
+ "category": "Future Research Recommendations",
+ "description": "Evaluate the analysis of potential changes in device technology, cost, accuracy, speed, and reliability, and the recommendations for STEM research areas to improve security system performance."
+ }
+ ]
+ }
+ },
+ "2003_Gamma_Knife_Treatment": {
+ "year": "2003",
+ "title": "Gamma Knife Treatment Planning",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2003/MCM-B/index.html",
+ "question": "Stereotactic radiosurgery delivers a single high dose of ionizing radiation to a radiographically well-defined, small intracranial 3D brain tumor without delivering any significant fraction of the prescribed dose to the surrounding brain tissue. Three modalities are commonly used in this area; they are the gamma knife unit, heavy charged particle beams, and external high-energy photon beams from linear accelerators. The gamma knife unit delivers a single high dose of ionizing radiation emanating from 201 cobalt-60 unit sources through a heavy helmet. All 201 beams simultaneously intersect at the isocenter, resulting in a spherical (approximately) dose distribution at the effective dose levels. Irradiating the isocenter to deliver dose is termed a \u201cshot.\u201d Shots can be represented as different spheres. Four interchangeable outer collimator helmets with beam channel diameters of 4, 8, 14, and 18 mm are available for irradiating different size volumes. For a target volume larger than one shot, multiple shots can be used to cover the entire target. In practice, most target volumes are treated with 1 to 15 shots. The target volume is a bounded, three-dimensional digital image that usually consists of millions of points. The goal of radiosurgery is to deplete tumor cells while preserving normal structures. Since there are physical limitations and biological uncertainties involved in this therapy process, a treatment plan needs to account for all those limitations and uncertainties. In general, an optimal treatment plan is designed to meet the following requirements.\n\nMinimize the dose gradient across the target volume. Match specified isodose contours to the target volumes. Match specified dose-volume constraints of the target and critical organ. Minimize the integral dose to the entire volume of normal tissues or organs. Constrain dose to specified normal tissue points below tolerance doses. Minimize the maximum dose to critical volumes.\n\nProhibit shots from protruding outside the target. Prohibit shots from overlapping (to avoid hot spots). Cover the target volume with effective dosage as much as possible. But at least 90% of the target volume must be covered by shots. Use as few shots as possible.",
+ "requirements": [
+ {
+ "category": "Dose Distribution",
+ "description": "Evaluate the minimization of the dose gradient across the target volume to ensure uniform treatment."
+ },
+ {
+ "category": "Isodose Contours",
+ "description": "Assess how well the specified isodose contours match the target volumes, ensuring precise targeting."
+ },
+ {
+ "category": "Dose-Volume Constraints",
+ "description": "Check the adherence to specified dose-volume constraints for both the target and critical organs."
+ },
+ {
+ "category": "Integral Dose Minimization",
+ "description": "Evaluate the minimization of the integral dose to the entire volume of normal tissues or organs."
+ },
+ {
+ "category": "Normal Tissue Dose Constraints",
+ "description": "Ensure that the dose to specified normal tissue points is constrained below tolerance doses."
+ },
+ {
+ "category": "Maximum Dose Minimization",
+ "description": "Assess the minimization of the maximum dose to critical volumes to prevent damage."
+ },
+ {
+ "category": "Shot Prohibition",
+ "description": "Verify that shots do not protrude outside the target volume, maintaining precision."
+ },
+ {
+ "category": "Shot Overlap",
+ "description": "Ensure that shots do not overlap to avoid creating hot spots in the treatment area."
+ },
+ {
+ "category": "Target Volume Coverage",
+ "description": "Evaluate the coverage of the target volume with effective dosage, ensuring at least 90% coverage."
+ },
+ {
+ "category": "Shot Minimization",
+ "description": "Assess the use of as few shots as possible while maintaining effective coverage."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves complex geometric and optimization challenges that require mathematical expertise to model the dose distribution and ensure the constraints are met effectively.",
+ "details": "As a mathematician, you are skilled in geometric modeling, optimization techniques, and mathematical analysis. You should focus on reviewing the mathematical formulation of the dose distribution model, ensuring that the constraints such as minimizing dose gradients and prohibiting shot overlap are mathematically sound. Pay attention to the accuracy of the mathematical representation of the target volume and the optimization algorithms used to achieve the treatment goals."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing large datasets of 3D digital images and optimizing treatment plans based on statistical and machine learning methods.",
+ "details": "As a data scientist, you are adept at handling large volumes of data, applying statistical analysis, and using machine learning techniques to optimize treatment plans. You should review the data processing methods used to analyze the 3D images of the target volume, ensuring that the data is accurately represented and utilized in the modeling process. Evaluate the use of data-driven approaches to optimize the treatment plan and ensure that the model effectively balances the constraints and objectives."
+ },
+ {
+ "name": "Medical Physicist",
+ "thoughts": "The problem involves understanding the physical principles of radiation therapy and ensuring that the treatment plan adheres to safety and efficacy standards.",
+ "details": "As a medical physicist, you have expertise in the physical aspects of radiation therapy, including dose calculation and radiation safety. You should review the modeling solutions to ensure that the physical principles of radiation delivery are accurately represented and that the treatment plan adheres to safety standards. Pay attention to the accuracy of dose calculations and the effectiveness of the proposed treatment plan in achieving the desired therapeutic outcomes while minimizing risks to normal tissues."
+ },
+ {
+ "name": "Radiation Oncologist",
+ "thoughts": "The problem requires clinical expertise to ensure that the treatment plan is effective in depleting tumor cells while preserving normal structures.",
+ "details": "As a radiation oncologist, you have clinical expertise in the treatment of brain tumors using radiosurgery. You should review the modeling solutions to ensure that the treatment plan is clinically viable and aligns with therapeutic goals. Focus on the clinical implications of the proposed dose distribution and the effectiveness of the plan in achieving tumor control while minimizing side effects. Evaluate the model's ability to meet clinical constraints and ensure patient safety and treatment efficacy."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Dose Distribution",
+ "description": "Evaluate the minimization of the dose gradient across the target volume to ensure uniform treatment."
+ },
+ {
+ "category": "Isodose Contours",
+ "description": "Assess how well the specified isodose contours match the target volumes, ensuring precise targeting."
+ },
+ {
+ "category": "Dose-Volume Constraints",
+ "description": "Check the adherence to specified dose-volume constraints for both the target and critical organs."
+ },
+ {
+ "category": "Integral Dose Minimization",
+ "description": "Evaluate the minimization of the integral dose to the entire volume of normal tissues or organs."
+ },
+ {
+ "category": "Normal Tissue Dose Constraints",
+ "description": "Ensure that the dose to specified normal tissue points is constrained below tolerance doses."
+ },
+ {
+ "category": "Maximum Dose Minimization",
+ "description": "Assess the minimization of the maximum dose to critical volumes to prevent damage."
+ },
+ {
+ "category": "Shot Prohibition",
+ "description": "Verify that shots do not protrude outside the target volume, maintaining precision."
+ },
+ {
+ "category": "Shot Overlap",
+ "description": "Ensure that shots do not overlap to avoid creating hot spots in the treatment area."
+ },
+ {
+ "category": "Target Volume Coverage",
+ "description": "Evaluate the coverage of the target volume with effective dosage, ensuring at least 90% coverage."
+ },
+ {
+ "category": "Shot Minimization",
+ "description": "Assess the use of as few shots as possible while maintaining effective coverage."
+ }
+ ]
+ }
+ },
+ "2003_The_Stunt_Person": {
+ "year": "2003",
+ "title": "The Stunt Person",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2003/MCM-A/index.html",
+ "question": "An exciting action scene in a movie is going to be filmed, and you are the stunt coordinator! A stunt person on a motorcycle will jump over an elephant and land in a pile of cardboard boxes to cushion their fall. You need to protect the stunt person, and also use relatively few cardboard boxes (lower cost, not seen by camera, etc.). Your job is to: determine what size boxes to use determine how many boxes to use determine how the boxes will be stacked determine if any modifications to the boxes would help generalize to different combined weights (stunt person & motorcycle) and different jump heights",
+ "requirements": [
+ {
+ "category": "Safety",
+ "description": "Evaluate the solution's effectiveness in ensuring the stunt person's safety during the jump and landing."
+ },
+ {
+ "category": "Cost-efficiency",
+ "description": "Assess the solution's ability to minimize the number of cardboard boxes used while maintaining safety."
+ },
+ {
+ "category": "Box Size Determination",
+ "description": "Grade the method used to determine the optimal size of the cardboard boxes for cushioning the fall."
+ },
+ {
+ "category": "Box Quantity Calculation",
+ "description": "Evaluate the accuracy and rationale behind the calculation of the number of boxes needed."
+ },
+ {
+ "category": "Box Stacking Strategy",
+ "description": "Assess the proposed strategy for stacking the boxes to maximize safety and minimize visibility."
+ },
+ {
+ "category": "Adaptability",
+ "description": "Evaluate the solution's ability to generalize to different combined weights and jump heights."
+ },
+ {
+ "category": "Box Modification Suggestions",
+ "description": "Grade the creativity and feasibility of any proposed modifications to the boxes to enhance performance."
+ },
+ {
+ "category": "Mathematical Rigor",
+ "description": "Assess the mathematical modeling techniques used to solve the problem, including assumptions and calculations."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves calculating trajectories, forces, and impacts, which are fundamentally mathematical concepts. A mathematician can help model the jump and landing to ensure safety and efficiency.",
+ "details": "You are a mathematician with expertise in physics-based modeling and optimization. You should focus on the equations governing motion, impact forces, and structural integrity of the boxes. Your role is crucial in ensuring that the calculations are accurate and that the model accounts for all variables, such as weight and height, to predict the safest landing scenario."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing data related to previous stunts, box durability, and material properties to make informed decisions about box selection and arrangement.",
+ "details": "You are a data scientist skilled in data analysis and predictive modeling. You should review the data on box materials, past stunt performances, and impact resistance. Your expertise will help in identifying patterns and making data-driven decisions about the number and arrangement of boxes, ensuring both safety and cost-effectiveness."
+ },
+ {
+ "name": "Mechanical Engineer",
+ "thoughts": "The problem involves understanding the mechanical properties of the boxes and the forces exerted during the stunt. A mechanical engineer can provide insights into the structural integrity and modifications needed for the boxes.",
+ "details": "You are a mechanical engineer with expertise in materials science and structural analysis. You should evaluate the design and material of the boxes to ensure they can withstand the impact. Your role is to suggest any modifications to the boxes that could enhance their performance, such as reinforcing certain areas or using different materials to better absorb the impact."
+ },
+ {
+ "name": "Safety Expert",
+ "thoughts": "The problem is centered around ensuring the safety of the stunt person, which requires a thorough understanding of safety protocols and risk assessment.",
+ "details": "You are a safety expert with a focus on risk management and accident prevention. You should review the entire stunt setup, including the box arrangement and jump parameters, to identify potential hazards. Your expertise will help in developing safety measures and contingency plans to protect the stunt person during the jump, ensuring that all safety standards are met."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Safety",
+ "description": "Evaluate the solution's effectiveness in ensuring the stunt person's safety during the jump and landing."
+ },
+ {
+ "category": "Cost-efficiency",
+ "description": "Assess the solution's ability to minimize the number of cardboard boxes used while maintaining safety."
+ },
+ {
+ "category": "Box Size Determination",
+ "description": "Grade the method used to determine the optimal size of the cardboard boxes for cushioning the fall."
+ },
+ {
+ "category": "Box Quantity Calculation",
+ "description": "Evaluate the accuracy and rationale behind the calculation of the number of boxes needed."
+ },
+ {
+ "category": "Box Stacking Strategy",
+ "description": "Assess the proposed strategy for stacking the boxes to maximize safety and minimize visibility."
+ },
+ {
+ "category": "Adaptability",
+ "description": "Evaluate the solution's ability to generalize to different combined weights and jump heights."
+ },
+ {
+ "category": "Box Modification Suggestions",
+ "description": "Grade the creativity and feasibility of any proposed modifications to the boxes to enhance performance."
+ },
+ {
+ "category": "Mathematical Rigor",
+ "description": "Assess the mathematical modeling techniques used to solve the problem, including assumptions and calculations."
+ }
+ ]
+ }
+ },
+ "2004_Motel_Cleaning_Problem": {
+ "year": "2004",
+ "title": "Motel Cleaning Problem",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2004/HIMCM-A/index.html",
+ "question": "Motels and hotels hire people to clean the rooms after each evening's use. Develop a mathematical model for the cleaning schedule and use of cleaning resources. Your model should include consideration of such things as stay-overs, costs, number of rooms, number of rooms per floor, etc. Draft a letter to the manager of a major motel or hotel complex that recommends your model to help them in the management of their operation.",
+ "requirements": [
+ {
+ "category": "Objective clarity",
+ "description": "The model should clearly define the objectives, such as minimizing costs, optimizing cleaning schedules, and efficient resource allocation."
+ },
+ {
+ "category": "Incorporation of constraints",
+ "description": "The model must consider constraints like stay-overs, number of rooms, number of rooms per floor, and cleaning resource limitations."
+ },
+ {
+ "category": "Cost analysis",
+ "description": "The model should include a detailed analysis of costs associated with cleaning, including labor, materials, and any other relevant expenses."
+ },
+ {
+ "category": "Scalability",
+ "description": "The model should be scalable to accommodate different sizes of hotel or motel complexes, with varying numbers of rooms and floors."
+ },
+ {
+ "category": "Practical applicability",
+ "description": "The model should be practical and implementable in real-world scenarios, providing actionable insights for hotel management."
+ },
+ {
+ "category": "Assumptions",
+ "description": "The model should clearly state any assumptions made, such as average cleaning time per room or standard resource availability."
+ },
+ {
+ "category": "Deliverable requirements",
+ "description": "The solution should include a draft letter to the manager, effectively communicating the benefits and implementation of the model."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a solid understanding of mathematical modeling to create an efficient cleaning schedule that optimizes resources and minimizes costs.",
+ "details": "As a mathematician, you are adept at formulating mathematical models that can handle complex variables such as stay-overs, costs, and room distribution. You should focus on ensuring the model accurately represents the relationships between these variables and can be solved efficiently. Pay attention to the assumptions made in the model and verify that they are realistic and applicable to real-world scenarios. Your expertise in optimization techniques will be crucial in evaluating the effectiveness of the proposed schedule."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to room occupancy, cleaning times, and resource allocation to inform the model.",
+ "details": "As a data scientist, your role is to ensure that the model is grounded in accurate and comprehensive data analysis. You should evaluate the data sources used in the model, checking for completeness and reliability. Your skills in statistical analysis and machine learning can help identify patterns and trends that may influence the cleaning schedule. Pay attention to how data is integrated into the model and whether it supports the decision-making process effectively. Your ability to interpret data insights will be key in assessing the model's practicality and scalability."
+ },
+ {
+ "name": "Operations Manager",
+ "thoughts": "The problem requires practical insights into the day-to-day operations of a hotel or motel, including cleaning logistics and resource management.",
+ "details": "As an operations manager, you have firsthand experience with the challenges of managing cleaning schedules and resources. You should review the model to ensure it aligns with operational realities, such as staff availability, equipment constraints, and time management. Your understanding of workflow efficiency and cost control will be vital in assessing whether the model can be implemented successfully. Pay attention to the feasibility of the proposed schedule and its impact on staff productivity and guest satisfaction."
+ },
+ {
+ "name": "Hospitality Consultant",
+ "thoughts": "The problem benefits from expertise in the hospitality industry, including guest expectations and service quality.",
+ "details": "As a hospitality consultant, you bring a strategic perspective to the model, focusing on how it can enhance the overall guest experience. You should evaluate the model's ability to maintain high standards of cleanliness while optimizing resource use. Your insights into industry trends and best practices will help ensure the model is competitive and innovative. Pay attention to how the model addresses guest needs and expectations, and consider its potential to improve service quality and operational efficiency. Your expertise will be crucial in recommending the model to hotel management as a valuable tool for enhancing their operations."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Objective clarity",
+ "description": "The model should clearly define the objectives, such as minimizing costs, optimizing cleaning schedules, and efficient resource allocation."
+ },
+ {
+ "category": "Incorporation of constraints",
+ "description": "The model must consider constraints like stay-overs, number of rooms, number of rooms per floor, and cleaning resource limitations."
+ },
+ {
+ "category": "Cost analysis",
+ "description": "The model should include a detailed analysis of costs associated with cleaning, including labor, materials, and any other relevant expenses."
+ },
+ {
+ "category": "Scalability",
+ "description": "The model should be scalable to accommodate different sizes of hotel or motel complexes, with varying numbers of rooms and floors."
+ },
+ {
+ "category": "Practical applicability",
+ "description": "The model should be practical and implementable in real-world scenarios, providing actionable insights for hotel management."
+ },
+ {
+ "category": "Assumptions",
+ "description": "The model should clearly state any assumptions made, such as average cleaning time per room or standard resource availability."
+ },
+ {
+ "category": "Deliverable requirements",
+ "description": "The solution should include a draft letter to the manager, effectively communicating the benefits and implementation of the model."
+ }
+ ]
+ }
+ },
+ "2004_To_Be_Secure": {
+ "year": "2004",
+ "title": "To Be Secure or Not to Be?",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2004/ICM-C/index.html",
+ "question": "ICM_2004.pdf ICM_2004.pdf To Be Secure or Not to Be?\n\n### Text in the PDF File: ICM_2004.pdf\n\n**IT Security Risk Assessment for a New University Campus**\n\n**Overview:**\nThe creation of a new university campus requires a comprehensive IT security risk assessment to protect against potential threats such as hackers and viruses. This involves implementing multiple layers of defenses, including both policies and technologies, to safeguard personal information and software.\n\n**Preventative Defensive Measures:**\n1. **Management and Usage Policies:**\n - Password requirements\n - Formal security audits\n - Usage tracking\n - Wireless device usage\n - Removable media concerns\n - Personal use limitations\n - User training\n\n2. **Technological Solutions:**\n - Intrusion Detection Systems (IDS)\n - Firewalls\n - Anti-virus systems\n - Vulnerability scanners\n - Redundancy\n\n**Risk Categories:**\n1. **Confidentiality:** Protecting data from unauthorized access.\n2. **Integrity:** Ensuring data remains unaltered.\n3. **Availability:** Ensuring resources are accessible to authorized users.\n\n**Opportunity Costs:**\n- Litigation damages\n- Loss of proprietary data\n- Consumer confidence\n- Loss of direct revenue\n- Data and service reconstruction\n\n**Task 1: Model Development**\nDevelop a model to determine the optimal mix of preventive defensive measures that minimize potential opportunity costs and associated costs (procurement, maintenance, training) for the new university.\n\n**University System Specifications:**\n- 10 academic departments\n- Intercollegiate athletics department\n- Admissions office, bookstore, registrar\u2019s office, dormitory complex\n- 600 staff and faculty\n- 21 computer labs with 30 computers each\n- 600 staff and faculty computers\n- Dormitory network connections for 15,000 students\n- Online bookstore and registrar services\n\n**Task 2: Flexible Model Creation**\nCreate a flexible model adaptable to changing technologies and applicable to different organizations. Include assumptions and an example of how the university can use and update the model.\n\n**Task 3: Position Paper**\nPrepare a position paper for the university President detailing the model's strengths, weaknesses, and flexibility, and explain what can and cannot be inferred from the model.\n\n**Task 4: Commercial Company Comparison**\nAnalyze differences in risk category contributions if modeling IT security for a commercial search engine company. Assess the model's applicability to such organizations.\n\n**Task 5: Honeynet Consideration**\nAdvise on the use of honeynets for gathering IT security threat information for a university or search engine company.\n\n**Task 6: Future IT Security**\nWrite a memo to Rite-On Consulting's President on the future of IT security and how the model can anticipate and respond to future security risks.\n\n**Current Opportunity Costs and Risk Contributions:**\n\n| Opportunity Cost | Amount | Risk Category Contribution |\n|--------------------------|------------|-------------------------------------|\n| Litigation | $3,800,000 | Confidentiality (55%), Integrity (45%) |\n| Proprietary Data Loss | $1,500,000 | Confidentiality (70%), Integrity (30%) |\n| Consumer Confidence | $2,900,000 | Confidentiality (40%), Integrity (30%), Availability (30%) |\n| Data Reconstruction | $400,000 | Integrity (100%) |\n| Service Reconstruction | $80,000 | Integrity (100%) |\n| Direct Revenue Loss | $250,000 | Integrity (30%), Availability (70%) |\n\n**Technical Specifications:**\n- Detailed technical data sheets for defensive measures are available in Enclosures A and B.\n- Costs and effectiveness of various defensive measures are provided, including procurement, maintenance, and training costs.\n\n**Conclusion:**\nThe proposed model and tasks aim to establish a robust IT security framework for the new university campus, balancing security needs with cost-effectiveness and adaptability to future technological advancements.",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the effectiveness of the model in determining the optimal mix of preventive defensive measures that minimize opportunity costs and associated costs such as procurement, maintenance, and training."
+ },
+ {
+ "category": "Risk Categories",
+ "description": "Assess how well the model addresses the risk categories of confidentiality, integrity, and availability, and their contributions to opportunity costs."
+ },
+ {
+ "category": "Flexible Model Creation",
+ "description": "Grade the adaptability of the model to changing technologies and its applicability to different organizations, including the clarity of assumptions and example usage."
+ },
+ {
+ "category": "Position Paper",
+ "description": "Evaluate the position paper's analysis of the model's strengths, weaknesses, and flexibility, and its explanation of what can and cannot be inferred from the model."
+ },
+ {
+ "category": "Commercial Company Comparison",
+ "description": "Assess the analysis of differences in risk category contributions when applying the model to a commercial search engine company, and the model's applicability to such organizations."
+ },
+ {
+ "category": "Honeynet Consideration",
+ "description": "Evaluate the advice on the use of honeynets for gathering IT security threat information for a university or search engine company."
+ },
+ {
+ "category": "Future IT Security",
+ "description": "Grade the memo's insights on the future of IT security and how the model can anticipate and respond to future security risks."
+ },
+ {
+ "category": "Opportunity Costs Analysis",
+ "description": "Assess the accuracy and comprehensiveness of the analysis of current opportunity costs and their risk category contributions."
+ },
+ {
+ "category": "Technical Specifications",
+ "description": "Evaluate the use of detailed technical data sheets for defensive measures, including the consideration of costs and effectiveness in the model."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves developing mathematical models to optimize IT security measures, which requires a strong understanding of mathematical principles and techniques.",
+ "details": "As a mathematician, you are adept at formulating and solving complex equations that can help determine the optimal mix of preventive defensive measures. You should focus on ensuring the mathematical models are robust, accurate, and capable of handling the various constraints and variables involved in IT security risk assessment. Your expertise in optimization and statistical analysis will be crucial in evaluating the effectiveness of the proposed models."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing large datasets related to IT security risks and opportunity costs, which is a key area of expertise for data scientists.",
+ "details": "As a data scientist, you are skilled in data analysis, machine learning, and statistical methods, which are essential for processing and interpreting the data associated with IT security risks. You should focus on ensuring the data-driven models are accurate and can adapt to changing technologies and organizational needs. Your ability to handle big data and extract meaningful insights will be vital in assessing the model's applicability and effectiveness."
+ },
+ {
+ "name": "IT Security Specialist",
+ "thoughts": "The problem is centered around IT security risk assessment, which directly aligns with the expertise of an IT security specialist.",
+ "details": "As an IT security specialist, you have a deep understanding of the various technological solutions and policies required to protect against security threats. You should focus on evaluating the effectiveness and practicality of the proposed defensive measures, such as intrusion detection systems, firewalls, and anti-virus systems. Your knowledge of current security technologies and trends will be crucial in assessing the model's ability to address potential threats and vulnerabilities."
+ },
+ {
+ "name": "Systems Analyst",
+ "thoughts": "The problem involves assessing the IT infrastructure and systems of a new university campus, which is a key responsibility of a systems analyst.",
+ "details": "As a systems analyst, you are skilled in evaluating and designing IT systems to meet organizational needs. You should focus on ensuring the proposed models are compatible with the university's existing systems and can be integrated effectively. Your expertise in system design and analysis will be essential in assessing the model's flexibility and adaptability to different organizational contexts and technological advancements."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the effectiveness of the model in determining the optimal mix of preventive defensive measures that minimize opportunity costs and associated costs such as procurement, maintenance, and training."
+ },
+ {
+ "category": "Risk Categories",
+ "description": "Assess how well the model addresses the risk categories of confidentiality, integrity, and availability, and their contributions to opportunity costs."
+ },
+ {
+ "category": "Flexible Model Creation",
+ "description": "Grade the adaptability of the model to changing technologies and its applicability to different organizations, including the clarity of assumptions and example usage."
+ },
+ {
+ "category": "Position Paper",
+ "description": "Evaluate the position paper's analysis of the model's strengths, weaknesses, and flexibility, and its explanation of what can and cannot be inferred from the model."
+ },
+ {
+ "category": "Commercial Company Comparison",
+ "description": "Assess the analysis of differences in risk category contributions when applying the model to a commercial search engine company, and the model's applicability to such organizations."
+ },
+ {
+ "category": "Honeynet Consideration",
+ "description": "Evaluate the advice on the use of honeynets for gathering IT security threat information for a university or search engine company."
+ },
+ {
+ "category": "Future IT Security",
+ "description": "Grade the memo's insights on the future of IT security and how the model can anticipate and respond to future security risks."
+ },
+ {
+ "category": "Opportunity Costs Analysis",
+ "description": "Assess the accuracy and comprehensiveness of the analysis of current opportunity costs and their risk category contributions."
+ },
+ {
+ "category": "Technical Specifications",
+ "description": "Evaluate the use of detailed technical data sheets for defensive measures, including the consideration of costs and effectiveness in the model."
+ }
+ ]
+ }
+ },
+ "2005_Flood_Planning": {
+ "year": "2005",
+ "title": "Flood Planning",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2005/MCM-A/index.html",
+ "question": "Lake Murray in central South Carolina is formed by a large earthen dam, which was completed in 1930 for power production. Model the flooding downstream in the event there is a catastrophic earthquake that breaches the dam. Two particular questions: Rawls Creek is a year-round stream that flows into the Saluda River a short distance downriver from the dam. How much flooding will occur in Rawls Creek from a dam failure, and how far back will it extend? Could the flood be so massive downstream that water would reach up to the S.C. State Capitol Building, which is on a hill overlooking the Congaree River?",
+ "requirements": [
+ {
+ "category": "Flood Modeling",
+ "description": "Develop a mathematical model to simulate the flooding downstream from the dam breach, including hydrodynamic equations and boundary conditions."
+ },
+ {
+ "category": "Rawls Creek Flood Analysis",
+ "description": "Analyze the extent of flooding in Rawls Creek, including the volume of water, flow rate, and how far the floodwaters will extend upstream."
+ },
+ {
+ "category": "Downstream Impact Assessment",
+ "description": "Evaluate the potential for floodwaters to reach the S.C. State Capitol Building, considering topography, distance, and floodwater dynamics."
+ },
+ {
+ "category": "Assumptions and Simplifications",
+ "description": "Identify and justify any assumptions made in the model, such as soil saturation, dam breach size, and earthquake magnitude."
+ },
+ {
+ "category": "Data Utilization",
+ "description": "Utilize relevant data such as historical flood records, topographical maps, and hydrological data to support the model."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct sensitivity analysis to determine how changes in key parameters affect the flood model outcomes."
+ },
+ {
+ "category": "Validation and Verification",
+ "description": "Validate the model against known flood events or simulations to ensure accuracy and reliability."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to simulate the dynamics of water flow and flooding scenarios. A mathematician can develop and solve the differential equations that describe the flow of water from the dam breach and predict the extent of flooding.",
+ "details": "You are a mathematician with expertise in fluid dynamics and differential equations. Your role is to ensure that the mathematical models accurately represent the physical processes involved in the dam breach and subsequent flooding. Pay attention to the assumptions made in the model, the boundary conditions, and the numerical methods used for solving the equations. Your evaluation should focus on the mathematical rigor and validity of the model."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing geographical and hydrological data to predict flooding patterns. A data scientist can process and analyze large datasets to inform the model and validate its predictions.",
+ "details": "You are a data scientist skilled in data analysis, statistical methods, and machine learning. Your task is to review the data inputs used in the model, such as topographical maps, historical flood data, and seismic activity records. Ensure that the data is accurate, relevant, and properly integrated into the model. Your evaluation should focus on the data quality, the methods used for data processing, and the model's predictive accuracy."
+ },
+ {
+ "name": "Hydrologist",
+ "thoughts": "The problem involves understanding the behavior of water systems and the impact of a dam breach on downstream areas. A hydrologist can provide insights into the hydrological processes and validate the model's predictions about flooding.",
+ "details": "You are a hydrologist with expertise in water flow, river systems, and flood risk assessment. Your role is to evaluate the hydrological aspects of the model, including the representation of river channels, floodplains, and water flow dynamics. Pay attention to the model's ability to simulate real-world hydrological processes and its predictions about flood extent and impact. Your evaluation should focus on the hydrological accuracy and realism of the model."
+ },
+ {
+ "name": "Civil Engineer",
+ "thoughts": "The problem involves assessing the structural integrity of the dam and the potential impact of its failure on infrastructure. A civil engineer can evaluate the model's assumptions about the dam's response to an earthquake and the resulting flood impact on downstream structures.",
+ "details": "You are a civil engineer with expertise in structural analysis and infrastructure resilience. Your task is to review the model's assumptions about the dam's structural behavior during an earthquake and the potential consequences of its failure. Pay attention to the engineering principles applied in the model and the predicted impact on downstream infrastructure, such as bridges and buildings. Your evaluation should focus on the structural soundness and practical implications of the model's predictions."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Flood Modeling",
+ "description": "Develop a mathematical model to simulate the flooding downstream from the dam breach, including hydrodynamic equations and boundary conditions."
+ },
+ {
+ "category": "Rawls Creek Flood Analysis",
+ "description": "Analyze the extent of flooding in Rawls Creek, including the volume of water, flow rate, and how far the floodwaters will extend upstream."
+ },
+ {
+ "category": "Downstream Impact Assessment",
+ "description": "Evaluate the potential for floodwaters to reach the S.C. State Capitol Building, considering topography, distance, and floodwater dynamics."
+ },
+ {
+ "category": "Assumptions and Simplifications",
+ "description": "Identify and justify any assumptions made in the model, such as soil saturation, dam breach size, and earthquake magnitude."
+ },
+ {
+ "category": "Data Utilization",
+ "description": "Utilize relevant data such as historical flood records, topographical maps, and hydrological data to support the model."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct sensitivity analysis to determine how changes in key parameters affect the flood model outcomes."
+ },
+ {
+ "category": "Validation and Verification",
+ "description": "Validate the model against known flood events or simulations to ensure accuracy and reliability."
+ }
+ ]
+ }
+ },
+ "2005_Nonrenewable_Resources": {
+ "year": "2005",
+ "title": "Nonrenewable Resources",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2005/ICM-C/index.html",
+ "question": "Select a vital nonrenewable or exhaustible resource (water, mineral, energy, food, etc.) for which your team can find appropriate worldwide historic data on its endowment, discovery, annual consumption, and price. The modeling tasks are:\n\nUsing the endowment, discoveries, and consumption data, model the depletion or degradation of the commodity over a long horizon using resource modeling principles. Adjust the model to account for future economic, demographic, political, and environmental factors. Be sure to reveal the details of your model, provide visualizations of the model's output, and explain limitations of the model. Create a fair, practical \"harvesting/management\" policy that may include economic incentives or disincentives, which sustain the usage over a long period of time while avoiding severe disruption of consumption, degradation, or rapid exhaustion of the resource. Develop a \"security\" policy that protects the resource against theft, misuse, disruption, and unnecessary degradation or destruction of the resource. Other issues that may need to be addressed are political and security management alternatives associated with these policies. Develop policies to control any short- or long-term \"environmental effects\" of the harvesting. Be sure to include issues such as pollutants, increased susceptibility to natural disasters, waste handling and storage, and other factors you deem appropriate. Compare this resource with any other alternatives for its purpose. What new science or technologies could be developed to mitigate the use and potential exhaustion of this resource? Develop a research policy to advance these new areas.",
+ "requirements": [
+ {
+ "category": "Data Collection and Analysis",
+ "description": "Evaluate the appropriateness and comprehensiveness of the historical data on endowment, discovery, annual consumption, and price of the selected resource."
+ },
+ {
+ "category": "Resource Depletion Modeling",
+ "description": "Assess the accuracy and robustness of the model used to predict the depletion or degradation of the resource over a long horizon, including the incorporation of resource modeling principles."
+ },
+ {
+ "category": "Future Adjustments",
+ "description": "Examine how well the model accounts for future economic, demographic, political, and environmental factors affecting resource depletion."
+ },
+ {
+ "category": "Model Details and Visualization",
+ "description": "Check the clarity and detail in the explanation of the model, including the quality and effectiveness of visualizations provided."
+ },
+ {
+ "category": "Model Limitations",
+ "description": "Evaluate the identification and explanation of the limitations of the model."
+ },
+ {
+ "category": "Harvesting/Management Policy",
+ "description": "Assess the fairness and practicality of the proposed policy for sustaining resource usage, including economic incentives or disincentives."
+ },
+ {
+ "category": "Security Policy",
+ "description": "Evaluate the effectiveness of the proposed security policy in protecting the resource against theft, misuse, disruption, and unnecessary degradation."
+ },
+ {
+ "category": "Environmental Effects Policy",
+ "description": "Examine the policies developed to control short- or long-term environmental effects of resource harvesting, including handling pollutants and waste."
+ },
+ {
+ "category": "Comparison with Alternatives",
+ "description": "Assess the comparison of the selected resource with alternatives for its purpose, including the evaluation of new science or technologies to mitigate resource exhaustion."
+ },
+ {
+ "category": "Research Policy",
+ "description": "Evaluate the development of a research policy aimed at advancing new areas of science or technology to mitigate resource use and potential exhaustion."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to understand the dynamics of resource depletion and to predict future trends based on historical data. Mathematical principles are essential for formulating equations that describe the resource's endowment, discovery rates, and consumption patterns.",
+ "details": "As a mathematician, you are skilled in developing and analyzing mathematical models that describe complex systems. You should focus on ensuring the accuracy and robustness of the equations used in the model, considering factors such as non-linear dynamics and stochastic processes. Pay attention to the assumptions made in the model and evaluate their validity. Your expertise in differential equations, optimization, and statistical analysis will be crucial in reviewing the modeling solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves handling large datasets related to resource endowment, discovery, consumption, and price. Data scientists are essential for processing, analyzing, and visualizing this data to inform the model and provide insights into trends and patterns.",
+ "details": "As a data scientist, you are adept at managing and analyzing complex datasets. You should focus on the quality and completeness of the data used in the model, ensuring that it is representative and reliable. Your skills in data cleaning, statistical analysis, and machine learning will be vital in identifying patterns and making predictions. Pay attention to the visualizations provided in the modeling solutions, ensuring they effectively communicate the model's outputs and insights."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem requires understanding the environmental impacts of resource depletion and the development of policies to mitigate these effects. Environmental scientists are crucial for assessing the ecological consequences and proposing sustainable management practices.",
+ "details": "As an environmental scientist, you are knowledgeable about the interactions between human activities and natural ecosystems. You should focus on evaluating the environmental implications of the resource management policies proposed in the model. Your expertise in ecology, environmental impact assessment, and sustainability will be essential in reviewing the solutions. Pay attention to the proposed measures for pollution control, waste management, and disaster susceptibility, ensuring they are practical and effective."
+ },
+ {
+ "name": "Economist",
+ "thoughts": "The problem involves economic factors such as pricing, incentives, and disincentives related to resource management. Economists are vital for analyzing the economic implications of the model and developing policies that balance resource sustainability with economic growth.",
+ "details": "As an economist, you are skilled in evaluating the economic aspects of resource management. You should focus on the economic models and policies proposed in the solutions, ensuring they are feasible and equitable. Your expertise in cost-benefit analysis, market dynamics, and policy development will be crucial in reviewing the solutions. Pay attention to the proposed economic incentives and disincentives, assessing their potential impact on resource consumption and sustainability."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Data Collection and Analysis",
+ "description": "Evaluate the appropriateness and comprehensiveness of the historical data on endowment, discovery, annual consumption, and price of the selected resource."
+ },
+ {
+ "category": "Resource Depletion Modeling",
+ "description": "Assess the accuracy and robustness of the model used to predict the depletion or degradation of the resource over a long horizon, including the incorporation of resource modeling principles."
+ },
+ {
+ "category": "Future Adjustments",
+ "description": "Examine how well the model accounts for future economic, demographic, political, and environmental factors affecting resource depletion."
+ },
+ {
+ "category": "Model Details and Visualization",
+ "description": "Check the clarity and detail in the explanation of the model, including the quality and effectiveness of visualizations provided."
+ },
+ {
+ "category": "Model Limitations",
+ "description": "Evaluate the identification and explanation of the limitations of the model."
+ },
+ {
+ "category": "Harvesting/Management Policy",
+ "description": "Assess the fairness and practicality of the proposed policy for sustaining resource usage, including economic incentives or disincentives."
+ },
+ {
+ "category": "Security Policy",
+ "description": "Evaluate the effectiveness of the proposed security policy in protecting the resource against theft, misuse, disruption, and unnecessary degradation."
+ },
+ {
+ "category": "Environmental Effects Policy",
+ "description": "Examine the policies developed to control short- or long-term environmental effects of resource harvesting, including handling pollutants and waste."
+ },
+ {
+ "category": "Comparison with Alternatives",
+ "description": "Assess the comparison of the selected resource with alternatives for its purpose, including the evaluation of new science or technologies to mitigate resource exhaustion."
+ },
+ {
+ "category": "Research Policy",
+ "description": "Evaluate the development of a research policy aimed at advancing new areas of science or technology to mitigate resource use and potential exhaustion."
+ }
+ ]
+ }
+ },
+ "2006_A_South_Sea": {
+ "year": "2006",
+ "title": "A South Sea Island Resort",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2006/HIMCM-B/index.html",
+ "question": "A South Sea island chain has decided to transform one of their islands into a resort. This roughly circular island, about 5 kilometers across, contains a mountain that covers the entire island. The mountain is approximately conical, is about 1000 meters high at the center, appears to be sandy, and has little vegetation on it. It has been proposed to lease some fire-fighting ships and wash the mountain into the harbor. It is desired to accomplish this as quickly as possible. Build a mathematical model for washing away the mountain. Use your model to respond to the questions below.\n\nHow should the stream of water be directed at the mountain, as a function of time? How long will it take using a single fire-fighting ship? Could the use of 2 (or 3, 4, etc.) fire-fighting ships decrease the time by more than a factor of 2 (or 3, 4, etc.)? Make a recommendation to the resort committee about what to do.",
+ "requirements": [
+ {
+ "category": "Modeling Approach",
+ "description": "Evaluate the mathematical model used to simulate the erosion of the mountain by water streams, including assumptions made about the mountain's structure and material properties."
+ },
+ {
+ "category": "Water Stream Direction",
+ "description": "Assess the strategy for directing the water stream at the mountain over time, including any dynamic adjustments based on erosion progress."
+ },
+ {
+ "category": "Time Estimation",
+ "description": "Analyze the accuracy of the time estimation for washing away the mountain using a single fire-fighting ship, considering factors like water pressure and erosion rate."
+ },
+ {
+ "category": "Resource Optimization",
+ "description": "Evaluate the model's analysis on the impact of using multiple fire-fighting ships, including whether the time reduction is proportional to the number of ships used."
+ },
+ {
+ "category": "Recommendation",
+ "description": "Review the practical recommendations made to the resort committee, including cost-benefit analysis and feasibility of the proposed solution."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Identify and assess the assumptions made in the model, such as the conical shape of the mountain and its sandy composition, and discuss any limitations these may impose."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to understand the dynamics of erosion and fluid mechanics involved in washing away the mountain. Formulating equations to describe the rate of erosion and the impact of water streams is crucial.",
+ "details": "You are a mathematician with expertise in fluid dynamics and erosion modeling. You should focus on developing equations that describe the interaction between the water streams and the mountain's surface. Pay attention to the geometric properties of the conical mountain and how they affect the erosion rate. Your skills in differential equations and calculus will be essential in predicting how the mountain will erode over time and in optimizing the water stream direction."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to the mountain's erosion rate and the effectiveness of different water stream strategies. Data analysis will be key in validating the model and making recommendations.",
+ "details": "You are a data scientist with expertise in data analysis and machine learning. You should focus on collecting and analyzing data from simulations or real-world tests to validate the mathematical model. Pay attention to patterns in erosion rates and how they correlate with different water stream strategies. Your skills in statistical analysis and predictive modeling will be crucial in assessing the effectiveness of using multiple fire-fighting ships and in making data-driven recommendations to the resort committee."
+ },
+ {
+ "name": "Environmental Engineer",
+ "thoughts": "The problem involves environmental considerations, such as the impact of washing away the mountain on the surrounding ecosystem and harbor. An environmental engineer can assess these impacts and ensure sustainable practices.",
+ "details": "You are an environmental engineer with expertise in assessing the environmental impact of engineering projects. You should focus on evaluating the potential consequences of washing the mountain into the harbor, such as sedimentation and water quality changes. Pay attention to the sustainability of the proposed methods and the long-term effects on the island's ecosystem. Your skills in environmental impact assessment and sustainable engineering practices will be essential in ensuring that the resort development is environmentally responsible."
+ },
+ {
+ "name": "Hydrologist",
+ "thoughts": "The problem involves understanding the behavior of water streams and their interaction with the mountain's surface. A hydrologist can provide insights into the optimal use of water resources and erosion processes.",
+ "details": "You are a hydrologist with expertise in water resource management and erosion processes. You should focus on analyzing how the water streams can be optimized to maximize erosion while minimizing water usage. Pay attention to the hydrodynamic properties of the water streams and how they affect the erosion rate. Your skills in hydrology and erosion modeling will be crucial in determining the most efficient way to direct the water streams and in assessing the feasibility of using multiple fire-fighting ships."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Modeling Approach",
+ "description": "Evaluate the mathematical model used to simulate the erosion of the mountain by water streams, including assumptions made about the mountain's structure and material properties."
+ },
+ {
+ "category": "Water Stream Direction",
+ "description": "Assess the strategy for directing the water stream at the mountain over time, including any dynamic adjustments based on erosion progress."
+ },
+ {
+ "category": "Time Estimation",
+ "description": "Analyze the accuracy of the time estimation for washing away the mountain using a single fire-fighting ship, considering factors like water pressure and erosion rate."
+ },
+ {
+ "category": "Resource Optimization",
+ "description": "Evaluate the model's analysis on the impact of using multiple fire-fighting ships, including whether the time reduction is proportional to the number of ships used."
+ },
+ {
+ "category": "Recommendation",
+ "description": "Review the practical recommendations made to the resort committee, including cost-benefit analysis and feasibility of the proposed solution."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Identify and assess the assumptions made in the model, such as the conical shape of the mountain and its sandy composition, and discuss any limitations these may impose."
+ }
+ ]
+ }
+ },
+ "2006_Inflation_of_the": {
+ "year": "2006",
+ "title": "Inflation of the Parachute",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2006/HIMCM-A/index.html",
+ "question": "HiMCM2006ProblemA.pdf HiMCM2006ProblemA.pdf Inflation of the Parachute\n\n### Text in the PDF File: HiMCM2006ProblemA.pdf\n\n**Problem A: Inflation of the Parachute**\n\n**Overview:**\nParachutes are made from lightweight fabric, support tapes, and suspension lines. They are deployed using systems like freefall or static line, and come in various types including round, ribbon, ring, and ram-air parachutes. Each type has unique characteristics affecting their deployment and inflation.\n\n**Types of Parachutes:**\n\n1. **Round Parachutes:**\n - Used in military, emergency, and cargo applications.\n - Dome-shaped canopies, often conical or parabolic for stability.\n - Some are steerable with \"T-U cut\" for limited forward speed.\n\n2. **Pull Down Apex Parachutes:**\n - A variation of round parachutes with a lenticular shape.\n - Features an annular geometry with a hole at the apex for air exit.\n - Provides forward speed up to 10 mph (15 km/h).\n\n3. **Ribbon and Ring Parachutes:**\n - Designed for high-speed deployment, up to Mach 2.\n - Ring-shaped canopy with large holes or ribbons to reduce stress.\n\n4. **Ram-air Parachutes:**\n - Modern parachutes with self-inflating \"ram-air\" airfoils.\n - Provide control of speed and direction, similar to paragliders.\n - Consist of two fabric layers connected by airfoil-shaped ribs.\n\n**Reserves:**\n- Paratroopers and sports parachutists carry a main and a reserve parachute.\n- Reserve parachutes are used if the main parachute fails.\n- Deployment systems include ripcord and hand-deployed pilot chutes.\n\n**Deployment Systems:**\n- **Ripcord System:** Releases a spring-loaded pilot chute to deploy the canopy.\n- **Hand Deployed Pilot Chute:** Uses air stream force to extract the deployment bag.\n- **Static Line:** Used for paratroopers and student skydivers, provides rapid and reliable deployment.\n\n**Modeling the Inflation Process:**\n- Develop a mathematical model to understand parachute inflation.\n- Consider how the geometry and folding of the parachute affect inflation.\n- Discuss methods to influence the rate of inflation.\n\n**Conclusion:**\nUnderstanding the deployment and inflation of different parachute types is crucial for optimizing their performance. The geometry and folding techniques play a significant role in the inflation process, and adjustments can be made to control the rate of inflation effectively.",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Develop a mathematical model that accurately represents the inflation process of parachutes, considering different types such as round, pull down apex, ribbon and ring, and ram-air parachutes."
+ },
+ {
+ "category": "Geometry and Folding",
+ "description": "Analyze how the geometry and folding techniques of parachutes affect their inflation process, and incorporate these factors into the model."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and justify any assumptions made in the model regarding parachute materials, deployment systems, and environmental conditions."
+ },
+ {
+ "category": "Influencing Inflation Rate",
+ "description": "Discuss and propose methods to influence the rate of inflation, considering factors such as deployment systems and parachute design."
+ },
+ {
+ "category": "Types of Parachutes",
+ "description": "Evaluate the unique characteristics of different parachute types and how these affect their deployment and inflation, ensuring the model accounts for these differences."
+ },
+ {
+ "category": "Deployment Systems",
+ "description": "Consider the impact of different deployment systems (ripcord, hand deployed pilot chute, static line) on the inflation process and incorporate these into the model."
+ },
+ {
+ "category": "Performance Optimization",
+ "description": "Assess how the model can be used to optimize parachute performance, including stability, speed, and reliability during inflation."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem of parachute inflation involves complex geometric and physical principles that require mathematical modeling to understand and optimize the inflation process.",
+ "details": "You are a mathematician with expertise in geometric modeling and differential equations. Your role is to analyze the mathematical formulations related to the parachute's geometry and inflation dynamics. You should pay attention to the accuracy of the equations used to model the inflation process and ensure that they correctly represent the physical phenomena involved. Your evaluation should focus on the mathematical rigor and the applicability of the models to real-world scenarios."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to parachute deployment and inflation, which requires data-driven insights to optimize performance.",
+ "details": "You are a data scientist skilled in data analysis and machine learning. Your role is to review the data used in the modeling solutions, ensuring that it is accurately processed and interpreted. You should focus on the statistical methods used to analyze the deployment and inflation data, and evaluate how well the model predictions align with empirical data. Your expertise will help in identifying patterns and trends that can inform improvements in parachute design and deployment strategies."
+ },
+ {
+ "name": "Aerodynamics Engineer",
+ "thoughts": "The inflation of parachutes is heavily influenced by aerodynamic principles, which are crucial for understanding the forces and airflow involved in the deployment process.",
+ "details": "You are an aerodynamics engineer with expertise in fluid dynamics and airflow analysis. Your role is to evaluate the modeling solutions from an aerodynamic perspective, ensuring that the models accurately represent the airflow around and through the parachute during inflation. You should pay attention to the assumptions made about air resistance, drag, and lift, and assess how these factors are incorporated into the model. Your insights will be valuable in optimizing the parachute design for better performance and reliability."
+ },
+ {
+ "name": "Materials Scientist",
+ "thoughts": "The materials used in parachute construction play a significant role in their inflation characteristics, requiring an understanding of material properties and behavior.",
+ "details": "You are a materials scientist with expertise in fabric and textile engineering. Your role is to review the modeling solutions with a focus on the materials used in parachute construction. You should evaluate how the properties of the fabric, such as tensile strength, elasticity, and porosity, are considered in the model. Your expertise will help ensure that the material characteristics are accurately represented and that the model accounts for their impact on the inflation process. Your evaluation should also consider the durability and performance of the materials under different deployment conditions."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Develop a mathematical model that accurately represents the inflation process of parachutes, considering different types such as round, pull down apex, ribbon and ring, and ram-air parachutes."
+ },
+ {
+ "category": "Geometry and Folding",
+ "description": "Analyze how the geometry and folding techniques of parachutes affect their inflation process, and incorporate these factors into the model."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and justify any assumptions made in the model regarding parachute materials, deployment systems, and environmental conditions."
+ },
+ {
+ "category": "Influencing Inflation Rate",
+ "description": "Discuss and propose methods to influence the rate of inflation, considering factors such as deployment systems and parachute design."
+ },
+ {
+ "category": "Types of Parachutes",
+ "description": "Evaluate the unique characteristics of different parachute types and how these affect their deployment and inflation, ensuring the model accounts for these differences."
+ },
+ {
+ "category": "Deployment Systems",
+ "description": "Consider the impact of different deployment systems (ripcord, hand deployed pilot chute, static line) on the inflation process and incorporate these into the model."
+ },
+ {
+ "category": "Performance Optimization",
+ "description": "Assess how the model can be used to optimize parachute performance, including stability, speed, and reliability during inflation."
+ }
+ ]
+ }
+ },
+ "2006_Positioning_and_Moving": {
+ "year": "2006",
+ "title": "Positioning and Moving Sprinkler Systems for Irrigation",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2006/MCM-A/index.html",
+ "question": "There are a wide variety of techniques available for irrigating a field. The technologies range from advanced drip systems to periodic flooding. One of the systems that is used on smaller ranches is the use of \"hand move\" irrigation systems. Lightweight aluminum pipes with sprinkler heads are put in place across fields, and they are moved by hand at periodic intervals to ensure that the whole field receives an adequate amount of water. This type of irrigation system is cheaper and easier to maintain than other systems. It is also flexible, allowing for use on a wide variety of fields and crops. The disadvantage is that it requires a great deal of time and effort to move and set up the equipment at regular intervals. Given that this type of irrigation system is to be used, how can it be configured to minimize the amount of time required to irrigate a field that is 80 meters by 30 meters? For this task, you are asked to find an algorithm to determine how to irrigate the rectangular field that minimizes the amount of time required by a rancher to maintain the irrigation system. One pipe set is used in the field. You should determine the number of sprinklers and the spacing between sprinklers, and you should find a schedule to move the pipes, including where to move them. A pipe set consists of a number of pipes that can be connected together in a straight line. Each pipe has a 10 cm inner diameter with rotating spray nozzles that have a 0.6 cm inner diameter. When put together, the resulting pipe is 20 meters long. At the water source, the pressure is 420 Kilo-Pascals and has a flow rate of 150 liters per minute. No part of the field should receive more than 0.75 cm per hour of water, and each part of the field should receive at least 2 centimeters of water every 4 days. The total amount of water should be applied as uniformly as possible.",
+ "requirements": [
+ {
+ "category": "Algorithm Efficiency",
+ "description": "Evaluate the efficiency of the proposed algorithm in minimizing the time required to irrigate the field, considering the movement and setup of the irrigation system."
+ },
+ {
+ "category": "Water Distribution Constraints",
+ "description": "Assess whether the solution ensures no part of the field receives more than 0.75 cm per hour of water and at least 2 centimeters every 4 days."
+ },
+ {
+ "category": "Uniformity of Water Application",
+ "description": "Check the uniformity of water distribution across the field, ensuring that the total amount of water is applied as uniformly as possible."
+ },
+ {
+ "category": "Sprinkler Configuration",
+ "description": "Determine the adequacy of the number of sprinklers and their spacing to cover the entire field effectively."
+ },
+ {
+ "category": "Pipe Movement Schedule",
+ "description": "Evaluate the proposed schedule for moving the pipes, including the locations to move them, to ensure efficient coverage of the field."
+ },
+ {
+ "category": "Technical Feasibility",
+ "description": "Verify the technical feasibility of the solution, considering the specifications of the pipe set, water pressure, and flow rate."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to optimize the configuration and scheduling of the irrigation system. This involves calculating the optimal number of sprinklers, their spacing, and the movement schedule to ensure uniform water distribution while minimizing time and effort.",
+ "details": "As a mathematician, you are skilled in formulating and solving optimization problems. You should focus on the mathematical aspects of the irrigation system configuration, such as calculating the optimal sprinkler spacing and movement schedule. Pay attention to constraints like water distribution uniformity and maximum water application rates. Your expertise in mathematical modeling and problem-solving will be crucial in evaluating the proposed solutions for efficiency and feasibility."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to water flow rates, pressure, and field dimensions to inform the irrigation model. A data-driven approach can help optimize the irrigation schedule and configuration.",
+ "details": "As a data scientist, you are adept at handling and analyzing complex datasets. You should focus on the data aspects of the problem, such as analyzing water flow rates and pressure to determine the optimal irrigation configuration. Use statistical methods and machine learning techniques to model and predict the best irrigation schedule. Your expertise in data analysis will be essential in reviewing solutions for accuracy and effectiveness in achieving uniform water distribution."
+ },
+ {
+ "name": "Agricultural Engineer",
+ "thoughts": "The problem involves practical considerations of irrigation technology and field conditions. An agricultural engineer can provide insights into the feasibility and efficiency of different irrigation configurations and schedules.",
+ "details": "As an agricultural engineer, you have expertise in irrigation systems and agricultural practices. You should evaluate the practicality of the proposed irrigation configurations and schedules, considering factors like ease of setup and maintenance. Pay attention to the physical constraints of the field and the equipment, ensuring that the solutions are not only theoretically sound but also practically implementable. Your knowledge of irrigation technology will be vital in assessing the solutions for real-world applicability."
+ },
+ {
+ "name": "Hydrologist",
+ "thoughts": "The problem involves understanding water distribution and flow dynamics, which are crucial for ensuring uniform irrigation across the field. A hydrologist can provide insights into water movement and distribution patterns.",
+ "details": "As a hydrologist, you specialize in the study of water movement and distribution. You should focus on the hydrological aspects of the problem, such as ensuring uniform water application and preventing over-irrigation. Evaluate the solutions for their effectiveness in achieving the desired water distribution across the field. Your expertise in hydrology will be important in reviewing the solutions for their ability to meet the water application constraints and maintain uniformity in irrigation."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Algorithm Efficiency",
+ "description": "Evaluate the efficiency of the proposed algorithm in minimizing the time required to irrigate the field, considering the movement and setup of the irrigation system."
+ },
+ {
+ "category": "Water Distribution Constraints",
+ "description": "Assess whether the solution ensures no part of the field receives more than 0.75 cm per hour of water and at least 2 centimeters every 4 days."
+ },
+ {
+ "category": "Uniformity of Water Application",
+ "description": "Check the uniformity of water distribution across the field, ensuring that the total amount of water is applied as uniformly as possible."
+ },
+ {
+ "category": "Sprinkler Configuration",
+ "description": "Determine the adequacy of the number of sprinklers and their spacing to cover the entire field effectively."
+ },
+ {
+ "category": "Pipe Movement Schedule",
+ "description": "Evaluate the proposed schedule for moving the pipes, including the locations to move them, to ensure efficient coverage of the field."
+ },
+ {
+ "category": "Technical Feasibility",
+ "description": "Verify the technical feasibility of the solution, considering the specifications of the pipe set, water pressure, and flow rate."
+ }
+ ]
+ }
+ },
+ "2006_Wheel_Chair_Access": {
+ "year": "2006",
+ "title": "Wheel Chair Access at Airports",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2006/MCM-B/index.html",
+ "question": "One of the frustrations with air travel is the need to fly through multiple airports, and each stop generally requires each traveler to change to a different airplane. This can be especially difficult for people who are not able to easily walk to a different flight's waiting area. One of the ways that an airline can make the transition easier is to provide a wheelchair and an escort to those people who ask for help. It is generally known well in advance which passengers require help, but it is not uncommon to receive notice when a passenger first registers at the airport. In rare instances, an airline may not receive notice from a passenger until just prior to landing. Airlines are under constant pressure to keep their costs down. Wheelchairs wear out and are expensive and require maintenance. There is also a cost for making the escorts available. Moreover, wheelchairs and their escorts must be constantly moved around the airport so that they are available to people when their flight lands. In some large airports, the time required to move across the airport is nontrivial. The wheelchairs must be stored somewhere, but space is expensive and severely limited in an airport terminal. Also, wheelchairs left in high traffic areas represent a liability risk as people try to move around them. Finally, one of the biggest costs is the cost of holding a plane if someone must wait for an escort and becomes late for their flight. The latter cost is especially troubling because it can affect the airline's average flight delay, which can lead to fewer ticket sales as potential customers may choose to avoid an airline. Epsilon Airlines has decided to ask a third party to help them obtain a detailed analysis of the issues and costs of keeping and maintaining wheelchairs and escorts available for passengers. The airline needs to find a way to schedule the movement of wheelchairs throughout each day in a cost-effective way. They also need to find and define the costs for budget planning in both the short and long term. Epsilon Airlines has asked your consultant group to put together a bid to help them solve their problem. Your bid should include an overview and analysis of the situation to help them decide if you fully understand their problem. They require a detailed description of an algorithm that you would like to implement which can determine where the escorts and wheelchairs should be and how they should move throughout each day. The goal is to keep the total costs as low as possible. Your bid is one of many that the airline will consider. You must make a strong case as to why your solution is the best and show that it will be able to handle a wide range of airports under a variety of circumstances. Your bid should also include examples of how the algorithm would work for a large (at least 4 concourses), a medium (at least two concourses), and a small airport (one concourse) under high and low traffic loads. You should determine all potential costs and balance their respective weights. Finally, as populations begin to include a higher percentage of older people who have more time to travel but may require more aid, your report should include projections of potential costs and needs in the future with recommendations to meet future needs.",
+ "requirements": [
+ {
+ "category": "Problem Understanding",
+ "description": "Demonstrates a comprehensive understanding of the logistical challenges and cost factors associated with managing wheelchairs and escorts in airports."
+ },
+ {
+ "category": "Algorithm Design",
+ "description": "Provides a detailed description of an algorithm to schedule the movement of wheelchairs and escorts, ensuring availability while minimizing costs."
+ },
+ {
+ "category": "Cost Analysis",
+ "description": "Identifies and quantifies all potential costs involved, including maintenance, storage, liability, and flight delays, and balances their respective weights."
+ },
+ {
+ "category": "Adaptability",
+ "description": "Shows how the proposed solution can handle different airport sizes and traffic loads, with examples for large, medium, and small airports."
+ },
+ {
+ "category": "Future Projections",
+ "description": "Includes projections of potential costs and needs as the population ages, with recommendations to meet future demands."
+ },
+ {
+ "category": "Justification of Solution",
+ "description": "Makes a strong case for why the proposed solution is the best, considering a wide range of airports and circumstances."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves complex optimization and scheduling, which requires a strong foundation in mathematical modeling to develop efficient algorithms for minimizing costs and maximizing resource utilization.",
+ "details": "As a mathematician, you are adept at formulating mathematical models that can address the scheduling and optimization challenges presented by Epsilon Airlines. You should focus on developing algorithms that can efficiently allocate wheelchairs and escorts across different airport concourses, taking into account constraints such as time, space, and cost. Your expertise in linear programming, combinatorial optimization, and queuing theory will be crucial in creating models that can predict and manage the flow of resources in real-time. Pay attention to the scalability of your solutions to ensure they can be applied to airports of varying sizes and traffic loads."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing large datasets to forecast demand for wheelchairs and escorts, as well as to evaluate the effectiveness of different scheduling strategies.",
+ "details": "As a data scientist, your role is to leverage data analytics and machine learning techniques to predict passenger needs and optimize resource allocation. You should focus on developing predictive models that can anticipate the demand for wheelchairs and escorts based on historical data, flight schedules, and passenger demographics. Your skills in data mining, statistical analysis, and predictive modeling will be essential in identifying patterns and trends that can inform decision-making. Ensure that your models are robust and adaptable to changes in passenger behavior and airport operations, and consider the integration of real-time data to enhance the accuracy of your predictions."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem involves optimizing operational processes and resource allocation, which is a key area of expertise for operations research analysts.",
+ "details": "As an operations research analyst, you are skilled in applying advanced analytical methods to help make better decisions. Your focus should be on developing strategies that optimize the movement and availability of wheelchairs and escorts, minimizing costs while ensuring passenger satisfaction. You should evaluate different operational scenarios and use simulation techniques to test the effectiveness of your proposed solutions. Pay attention to the constraints and variables that impact the scheduling and movement of resources, and ensure that your models can adapt to varying airport sizes and traffic conditions."
+ },
+ {
+ "name": "Transportation Planner",
+ "thoughts": "The problem involves planning and managing the logistics of moving resources within an airport, which is a key responsibility of transportation planners.",
+ "details": "As a transportation planner, your expertise lies in designing efficient systems for the movement of people and goods. You should focus on developing logistical plans that ensure the timely availability of wheelchairs and escorts, minimizing delays and improving passenger experience. Your skills in spatial analysis, route optimization, and infrastructure planning will be crucial in addressing the challenges of resource allocation within the airport environment. Consider the physical layout of airports and the impact of traffic patterns on resource movement, and ensure that your plans are flexible enough to accommodate future changes in passenger demographics and needs."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Problem Understanding",
+ "description": "Demonstrates a comprehensive understanding of the logistical challenges and cost factors associated with managing wheelchairs and escorts in airports."
+ },
+ {
+ "category": "Algorithm Design",
+ "description": "Provides a detailed description of an algorithm to schedule the movement of wheelchairs and escorts, ensuring availability while minimizing costs."
+ },
+ {
+ "category": "Cost Analysis",
+ "description": "Identifies and quantifies all potential costs involved, including maintenance, storage, liability, and flight delays, and balances their respective weights."
+ },
+ {
+ "category": "Adaptability",
+ "description": "Shows how the proposed solution can handle different airport sizes and traffic loads, with examples for large, medium, and small airports."
+ },
+ {
+ "category": "Future Projections",
+ "description": "Includes projections of potential costs and needs as the population ages, with recommendations to meet future demands."
+ },
+ {
+ "category": "Justification of Solution",
+ "description": "Makes a strong case for why the proposed solution is the best, considering a wide range of airports and circumstances."
+ }
+ ]
+ }
+ },
+ "2007_Gerrymandering": {
+ "year": "2007",
+ "title": "Gerrymandering",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2007/MCM-A/index.html",
+ "question": "The United States Constitution provides that the House of Representatives shall be composed of some number (currently 435) of individuals who are elected from each state in proportion to the state's population relative to that of the country as a whole. While this provides a way of determining how many representatives each state will have, it says nothing about how the district represented by a particular representative shall be determined geographically. This oversight has led to egregious (at least some people think so, usually not the incumbent) district shapes that look \"unnatural\" by some standards. Hence the following question: Suppose you were given the opportunity to draw congressional districts for a state. How would you do so as a purely \"baseline\" exercise to create the \"simplest\" shapes for all the districts in a state? The rules include only that each district in the state must contain the same population. The definition of \"simple\" is up to you; but you need to make a convincing argument to voters in the state that your solution is fair. As an application of your method, draw geographically simple congressional districts for the state of New York.",
+ "requirements": [
+ {
+ "category": "Definition of Simplicity",
+ "description": "Evaluate how the solution defines 'simple' shapes for districts and the rationale behind this definition."
+ },
+ {
+ "category": "Population Equality",
+ "description": "Assess the method used to ensure each district contains the same population, including data sources and calculations."
+ },
+ {
+ "category": "Geographical Modeling",
+ "description": "Examine the approach used to draw districts geographically, including algorithms or techniques employed."
+ },
+ {
+ "category": "Fairness Argument",
+ "description": "Evaluate the argument made to convince voters that the solution is fair, including any metrics or criteria used."
+ },
+ {
+ "category": "Application to New York",
+ "description": "Review the specific application of the method to draw districts in New York, including any state-specific considerations."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and assess any implicit assumptions made in the modeling process, such as geographical constraints or population data accuracy."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem of drawing congressional districts involves geometric and spatial considerations, which are inherently mathematical. A mathematician can help define what \"simple\" shapes mean in a rigorous way, using concepts from geometry and topology.",
+ "details": "You are a mathematician with expertise in geometric modeling and spatial analysis. You should focus on evaluating the mathematical definitions of \"simplicity\" used in the proposed solutions, ensuring they are logically sound and applicable. Your skills in optimization and spatial partitioning will be crucial in assessing whether the districts are drawn in a way that minimizes complexity while adhering to population equality."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing population data to ensure each district contains the same number of people. A data scientist can handle large datasets and apply statistical methods to verify the fairness and accuracy of the districting.",
+ "details": "You are a data scientist with expertise in data analysis and statistical modeling. You should focus on reviewing the population data used in the solutions, ensuring it is accurate and up-to-date. Your skills in data visualization and geographic information systems (GIS) will be essential in evaluating how well the proposed districts reflect population distribution and whether they meet the criteria of equal population."
+ },
+ {
+ "name": "Geographer",
+ "thoughts": "The problem involves geographic considerations, such as the natural layout of the land and existing political boundaries. A geographer can provide insights into how these factors should influence district shapes.",
+ "details": "You are a geographer with expertise in spatial analysis and geographic information systems (GIS). You should focus on reviewing how the proposed district shapes align with natural and political boundaries, ensuring they make sense geographically. Your understanding of human geography and spatial patterns will be crucial in assessing whether the districts are drawn in a way that respects the state's physical and cultural landscape."
+ },
+ {
+ "name": "Political Scientist",
+ "thoughts": "The problem has political implications, as district shapes can affect electoral outcomes. A political scientist can evaluate the fairness and potential biases in the proposed districting solutions.",
+ "details": "You are a political scientist with expertise in electoral systems and political geography. You should focus on reviewing the potential political impacts of the proposed district shapes, ensuring they do not unfairly advantage any party or group. Your understanding of gerrymandering and electoral fairness will be crucial in assessing whether the districts are drawn in a way that promotes fair representation and democratic principles."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Definition of Simplicity",
+ "description": "Evaluate how the solution defines 'simple' shapes for districts and the rationale behind this definition."
+ },
+ {
+ "category": "Population Equality",
+ "description": "Assess the method used to ensure each district contains the same population, including data sources and calculations."
+ },
+ {
+ "category": "Geographical Modeling",
+ "description": "Examine the approach used to draw districts geographically, including algorithms or techniques employed."
+ },
+ {
+ "category": "Fairness Argument",
+ "description": "Evaluate the argument made to convince voters that the solution is fair, including any metrics or criteria used."
+ },
+ {
+ "category": "Application to New York",
+ "description": "Review the specific application of the method to draw districts in New York, including any state-specific considerations."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and assess any implicit assumptions made in the modeling process, such as geographical constraints or population data accuracy."
+ }
+ ]
+ }
+ },
+ "2007_Organ_Transplant:_The": {
+ "year": "2007",
+ "title": "Organ Transplant: The Kidney Exchange Problem",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2007/ICM-C/index.html",
+ "question": "2007-ICM.pdf 2007-ICM.pdf Organ Transplant: The Kidney Exchange Problem\n\n### Text in the PDF File: 2007-ICM.pdf\n\n# 2007 ICM Problem C: Organ Transplant - The Kidney Exchange Problem\n\n## Overview\nThe demand for organ transplants, particularly kidneys, far exceeds the supply. The US Organ Procurement and Transplantation Network (OPTN) was established to address this issue, but challenges remain, including long waiting lists and inefficiencies in organ matching.\n\n## Tasks\n\n### Task 1: US Transplant Network Model\n- **Objective**: Develop a mathematical model for the US transplant network to identify bottlenecks and improve efficiency.\n- **Considerations**: \n - Potential bottlenecks in organ matching.\n - Allocation of additional resources.\n - Impact of dividing the network into smaller units (e.g., state-level).\n - Policy changes to enhance system effectiveness.\n\n### Task 2: International Policy Comparison\n- **Objective**: Compare US policies with those of another country and assess potential improvements.\n- **Deliverable**: A one-page report to Congress with findings and recommendations based on the model from Task 1.\n\n### Task 3: Maximizing Kidney Exchanges\n- **Objective**: Create a procedure to maximize the number and quality of kidney exchanges.\n- **Considerations**: \n - Medical and psychological factors.\n - Estimation of increased annual transplants and impact on waiting lists.\n\n### Task 4: Patient Decision Strategy\n- **Objective**: Develop a strategy for patients to decide on accepting a kidney offer or participating in an exchange.\n- **Considerations**: \n - Risks, alternatives, and probabilities.\n - Differences between cadaver and live donor kidneys.\n\n### Task 5: Policy Recommendations\n- **Objective**: Recommend changes to current criteria and policies.\n- **Considerations**: \n - Ethical dimensions of exchange procedures and patient strategies.\n - Criteria for priority and placement.\n - Discussion on organ sales.\n\n### Task 6: Donor Perspective\n- **Objective**: Analyze risks and factors influencing donor decisions.\n- **Considerations**: \n - Success probability for recipients.\n - Donor survival and health risks.\n - Influence of personal issues and network size on donor decisions.\n - Strategies to recruit more altruistic donors.\n\n## Key Data\n- **Waiting List**: Nearly 94,000 candidates, expected to exceed 100,000.\n- **Kidney Transplants**: 68,000 patients waiting; 10,000 from cadavers and 6,000 from living donors annually.\n- **Age Distribution of Waiting Patients**:\n - Under 18: 748\n - 18 to 34: 8,033\n - 35 to 49: 20,553\n - 50 to 64: 28,530\n - 65 and over: 10,628\n\n## Ethical and Political Considerations\n- **Ethical Issues**: Fairness in waiting list criteria, age priority, and organ allocation.\n- **Political Issues**: Regionalization effects, proficiency of local doctors, and potential centralization of transplants.\n- **Policy Debates**: Presumed consent, financial compensation for donors, and national policy changes.\n\n## Conclusion\nThe problem requires a comprehensive approach involving mathematical modeling, policy analysis, and ethical considerations to improve the kidney exchange system and address the organ shortage crisis.",
+ "requirements": [
+ {
+ "category": "Mathematical Modeling",
+ "description": "Evaluate the mathematical model developed for the US transplant network, focusing on its ability to identify bottlenecks and improve efficiency."
+ },
+ {
+ "category": "Resource Allocation",
+ "description": "Assess how the model addresses the allocation of additional resources and the impact of dividing the network into smaller units."
+ },
+ {
+ "category": "Policy Analysis",
+ "description": "Grade the comparison of US policies with those of another country, including the thoroughness of the analysis and the feasibility of recommended improvements."
+ },
+ {
+ "category": "Procedure Development",
+ "description": "Evaluate the procedure created to maximize kidney exchanges, considering medical and psychological factors and the estimation of increased transplants."
+ },
+ {
+ "category": "Patient Strategy",
+ "description": "Assess the strategy developed for patients deciding on accepting a kidney offer or participating in an exchange, focusing on risk analysis and decision-making criteria."
+ },
+ {
+ "category": "Ethical Considerations",
+ "description": "Grade the recommendations for policy changes, particularly the ethical dimensions of exchange procedures and patient strategies."
+ },
+ {
+ "category": "Donor Analysis",
+ "description": "Evaluate the analysis of risks and factors influencing donor decisions, including strategies to recruit more altruistic donors."
+ },
+ {
+ "category": "Data Utilization",
+ "description": "Assess how effectively the provided data (e.g., waiting list statistics, age distribution) is utilized in the modeling and analysis."
+ },
+ {
+ "category": "Ethical and Political Considerations",
+ "description": "Evaluate the discussion on ethical and political issues, such as fairness in waiting list criteria and regionalization effects."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The kidney exchange problem requires sophisticated mathematical modeling to optimize the matching process and identify bottlenecks within the transplant network. A mathematician can develop algorithms and models to improve efficiency and resource allocation.",
+ "details": "As a mathematician, you are adept at formulating complex mathematical models that can simulate the dynamics of the US transplant network. You should focus on identifying potential bottlenecks and inefficiencies in organ matching, and propose mathematical solutions to optimize the allocation of resources. Your expertise in mathematical principles and modeling methods will be crucial in developing strategies to enhance system effectiveness."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets related to organ transplants, waiting lists, and donor-recipient matching. A data scientist can leverage statistical methods and machine learning to extract insights and inform policy recommendations.",
+ "details": "As a data scientist, your role is to analyze complex datasets to uncover patterns and trends that can inform the kidney exchange model. You should focus on processing data related to waiting lists, donor-recipient matches, and transplant outcomes. Your skills in data analysis, statistical methods, and machine learning will be essential in developing data-driven strategies to maximize kidney exchanges and improve the efficiency of the transplant network."
+ },
+ {
+ "name": "Health Policy Analyst",
+ "thoughts": "The kidney exchange problem is deeply intertwined with health policies and regulations. A health policy analyst can assess current policies, compare international practices, and recommend changes to improve the system's effectiveness.",
+ "details": "As a health policy analyst, you are skilled in evaluating and comparing health policies related to organ transplantation. You should focus on analyzing the US policies and comparing them with those of other countries to identify potential improvements. Your expertise in policy analysis will be crucial in developing recommendations for Congress that address ethical dimensions, criteria for priority and placement, and potential policy changes to enhance the kidney exchange system."
+ },
+ {
+ "name": "Bioethicist",
+ "thoughts": "The kidney exchange problem involves significant ethical considerations, such as fairness in organ allocation and the implications of organ sales. A bioethicist can provide insights into the ethical dimensions of the problem and guide policy recommendations.",
+ "details": "As a bioethicist, your role is to analyze the ethical issues surrounding organ transplantation and kidney exchanges. You should focus on evaluating the fairness of waiting list criteria, age priority, and organ allocation procedures. Your expertise in ethical analysis will be essential in addressing the ethical dimensions of exchange procedures, patient strategies, and donor recruitment, ensuring that policy recommendations are ethically sound and socially responsible."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Mathematical Modeling",
+ "description": "Evaluate the mathematical model developed for the US transplant network, focusing on its ability to identify bottlenecks and improve efficiency."
+ },
+ {
+ "category": "Resource Allocation",
+ "description": "Assess how the model addresses the allocation of additional resources and the impact of dividing the network into smaller units."
+ },
+ {
+ "category": "Policy Analysis",
+ "description": "Grade the comparison of US policies with those of another country, including the thoroughness of the analysis and the feasibility of recommended improvements."
+ },
+ {
+ "category": "Procedure Development",
+ "description": "Evaluate the procedure created to maximize kidney exchanges, considering medical and psychological factors and the estimation of increased transplants."
+ },
+ {
+ "category": "Patient Strategy",
+ "description": "Assess the strategy developed for patients deciding on accepting a kidney offer or participating in an exchange, focusing on risk analysis and decision-making criteria."
+ },
+ {
+ "category": "Ethical Considerations",
+ "description": "Grade the recommendations for policy changes, particularly the ethical dimensions of exchange procedures and patient strategies."
+ },
+ {
+ "category": "Donor Analysis",
+ "description": "Evaluate the analysis of risks and factors influencing donor decisions, including strategies to recruit more altruistic donors."
+ },
+ {
+ "category": "Data Utilization",
+ "description": "Assess how effectively the provided data (e.g., waiting list statistics, age distribution) is utilized in the modeling and analysis."
+ },
+ {
+ "category": "Ethical and Political Considerations",
+ "description": "Evaluate the discussion on ethical and political issues, such as fairness in waiting list criteria and regionalization effects."
+ }
+ ]
+ }
+ },
+ "2007_The_Airplane_Seating": {
+ "year": "2007",
+ "title": "The Airplane Seating Problem",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2007/MCM-B/index.html",
+ "question": "Airlines are free to seat passengers waiting to board an aircraft in any order whatsoever. It has become customary to seat passengers with special needs first, followed by first-class passengers (who sit at the front of the plane). Then coach and business-class passengers are seated by groups of rows, beginning with the row at the back of the plane and proceeding forward. Apart from consideration of the passengers' wait time, from the airline's point of view, time is money, and boarding time is best minimized. The plane makes money for the airline only when it is in motion, and long boarding times limit the number of trips that a plane can make in a day. The development of larger planes, such as the Airbus A380 (800 passengers), accentuate the problem of minimizing boarding (and deboarding) time. Devise and compare procedures for boarding and deboarding planes with varying numbers of passengers: small (85-210), midsize (210-330), and large (450-800). Prepare an executive summary, not to exceed two single-spaced pages, in which you set out your conclusions to an audience of airline executives, gate agents, and flight crews. Note: The 2 page executive summary is to be included IN ADDITION to the reports required by the contest guidelines. An article appeared in the NY Times Nov 14, 2006 addressing procedures currently being followed and the importance to the airline of finding better solutions.",
+ "requirements": [
+ {
+ "category": "Objective Clarity",
+ "description": "Clearly define the objective of minimizing boarding and deboarding time and its importance to airline operations."
+ },
+ {
+ "category": "Procedure Development",
+ "description": "Develop and describe procedures for boarding and deboarding that are applicable to small, midsize, and large aircraft."
+ },
+ {
+ "category": "Comparative Analysis",
+ "description": "Compare the effectiveness of different procedures in terms of time efficiency and adaptability to varying numbers of passengers."
+ },
+ {
+ "category": "Passenger Class Consideration",
+ "description": "Address the boarding order of different passenger classes (special needs, first-class, coach, business-class) and its impact on time efficiency."
+ },
+ {
+ "category": "Assumptions and Constraints",
+ "description": "Identify and justify any assumptions made regarding passenger behavior, aircraft layout, and boarding/deboarding logistics."
+ },
+ {
+ "category": "Quantitative Analysis",
+ "description": "Provide quantitative analysis or simulations to support the proposed procedures and their expected time savings."
+ },
+ {
+ "category": "Scalability",
+ "description": "Evaluate the scalability of the proposed procedures for different aircraft sizes and passenger numbers."
+ },
+ {
+ "category": "Real-world Applicability",
+ "description": "Discuss the practicality and potential implementation challenges of the proposed procedures in real-world scenarios."
+ },
+ {
+ "category": "Executive Summary",
+ "description": "Prepare a concise executive summary that effectively communicates the conclusions and recommendations to airline executives, gate agents, and flight crews."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves optimizing boarding and deboarding procedures, which requires mathematical modeling to analyze and minimize time effectively.",
+ "details": "As a mathematician, you are skilled in formulating optimization problems and developing algorithms to solve them. You should focus on the mathematical models used to simulate boarding and deboarding processes, ensuring they are robust and accurately represent real-world scenarios. Pay attention to the assumptions made in the models and the validity of the solutions proposed. Your expertise in operations research and queuing theory will be crucial in evaluating the efficiency of different boarding strategies."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing data related to passenger boarding times and patterns to inform the development of efficient procedures.",
+ "details": "As a data scientist, you are adept at handling large datasets and extracting meaningful insights from them. You should review the data analysis methods used to assess boarding times and passenger flow, ensuring they are statistically sound and provide actionable insights. Your skills in machine learning and predictive analytics can help identify patterns and trends that may not be immediately apparent. Focus on the accuracy and reliability of the data used in the models and the conclusions drawn from it."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem is fundamentally about optimizing processes, which is the core focus of operations research.",
+ "details": "As an operations research analyst, you specialize in improving efficiency and effectiveness in complex systems. You should evaluate the proposed boarding and deboarding procedures from a process optimization perspective, considering factors such as time, cost, and resource allocation. Your expertise in linear programming, simulation, and decision analysis will be essential in assessing the feasibility and practicality of the solutions. Pay attention to how the models balance competing objectives and constraints."
+ },
+ {
+ "name": "Industrial Engineer",
+ "thoughts": "The problem involves designing efficient systems and processes, which is a key area of expertise for industrial engineers.",
+ "details": "As an industrial engineer, you focus on optimizing systems and processes to improve performance and productivity. You should review the boarding and deboarding strategies with an eye toward workflow efficiency and ergonomic considerations. Your skills in systems design, process improvement, and human factors engineering will be valuable in evaluating how the proposed solutions impact passenger experience and operational efficiency. Consider the practical implementation of the models and their scalability across different aircraft sizes."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Objective Clarity",
+ "description": "Clearly define the objective of minimizing boarding and deboarding time and its importance to airline operations."
+ },
+ {
+ "category": "Procedure Development",
+ "description": "Develop and describe procedures for boarding and deboarding that are applicable to small, midsize, and large aircraft."
+ },
+ {
+ "category": "Comparative Analysis",
+ "description": "Compare the effectiveness of different procedures in terms of time efficiency and adaptability to varying numbers of passengers."
+ },
+ {
+ "category": "Passenger Class Consideration",
+ "description": "Address the boarding order of different passenger classes (special needs, first-class, coach, business-class) and its impact on time efficiency."
+ },
+ {
+ "category": "Assumptions and Constraints",
+ "description": "Identify and justify any assumptions made regarding passenger behavior, aircraft layout, and boarding/deboarding logistics."
+ },
+ {
+ "category": "Quantitative Analysis",
+ "description": "Provide quantitative analysis or simulations to support the proposed procedures and their expected time savings."
+ },
+ {
+ "category": "Scalability",
+ "description": "Evaluate the scalability of the proposed procedures for different aircraft sizes and passenger numbers."
+ },
+ {
+ "category": "Real-world Applicability",
+ "description": "Discuss the practicality and potential implementation challenges of the proposed procedures in real-world scenarios."
+ },
+ {
+ "category": "Executive Summary",
+ "description": "Prepare a concise executive summary that effectively communicates the conclusions and recommendations to airline executives, gate agents, and flight crews."
+ }
+ ]
+ }
+ },
+ "2008_Creating_Sudoku_Puzzles": {
+ "year": "2008",
+ "title": "Creating Sudoku Puzzles",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2008/MCM-B/index.html",
+ "question": "Develop an algorithm to construct Sudoku puzzles of varying difficulty. Develop metrics to define a difficulty level. The algorithm and metrics should be extensible to a varying number of difficulty levels. You should illustrate the algorithm with at least 4 difficulty levels. Your algorithm should guarantee a unique solution. Analyze the complexity of your algorithm. Your objective should be to minimize the complexity of the algorithm and meet the above requirements.",
+ "requirements": [
+ {
+ "category": "Algorithm Development",
+ "description": "Evaluate the effectiveness of the algorithm in generating Sudoku puzzles across different difficulty levels."
+ },
+ {
+ "category": "Difficulty Metrics",
+ "description": "Assess the metrics used to define and differentiate the difficulty levels of the Sudoku puzzles."
+ },
+ {
+ "category": "Extensibility",
+ "description": "Examine how the algorithm and difficulty metrics can be extended to accommodate a varying number of difficulty levels."
+ },
+ {
+ "category": "Solution Uniqueness",
+ "description": "Verify that the algorithm guarantees a unique solution for each generated Sudoku puzzle."
+ },
+ {
+ "category": "Complexity Analysis",
+ "description": "Analyze the computational complexity of the algorithm and evaluate efforts to minimize it."
+ },
+ {
+ "category": "Illustration of Difficulty Levels",
+ "description": "Ensure that the algorithm is illustrated with at least four distinct difficulty levels."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a strong understanding of combinatorial mathematics and logic to ensure the Sudoku puzzles have a unique solution and to develop metrics for difficulty levels.",
+ "details": "You are a mathematician with expertise in combinatorial mathematics and logic. You should focus on the mathematical structure of Sudoku puzzles, ensuring that each puzzle has a unique solution. Pay attention to the logical consistency and the mathematical formulation of the difficulty metrics. Your evaluation should ensure that the algorithm adheres to mathematical principles and efficiently constructs puzzles with varying difficulty levels."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data patterns and developing metrics to quantify the difficulty of Sudoku puzzles, which requires data-driven insights and statistical analysis.",
+ "details": "You are a data scientist skilled in data analysis and statistical methods. You should focus on developing and validating metrics that accurately reflect the difficulty levels of Sudoku puzzles. Pay attention to the data patterns and statistical models used to define these metrics. Your evaluation should ensure that the metrics are robust, extensible, and effectively differentiate between difficulty levels."
+ },
+ {
+ "name": "Algorithm Designer",
+ "thoughts": "The problem requires designing an efficient algorithm to generate Sudoku puzzles with varying difficulty levels while minimizing complexity.",
+ "details": "You are an algorithm designer with expertise in creating efficient algorithms. You should focus on the design and implementation of the algorithm that constructs Sudoku puzzles. Pay attention to the algorithm's complexity and efficiency, ensuring it meets the requirement of generating puzzles with a unique solution. Your evaluation should ensure that the algorithm is optimized for performance and scalability across different difficulty levels."
+ },
+ {
+ "name": "Game Theorist",
+ "thoughts": "The problem involves understanding the strategic elements of puzzle design, which requires insights into game theory to ensure engaging and challenging puzzles.",
+ "details": "You are a game theorist with expertise in strategic game design. You should focus on the engagement and challenge aspects of the Sudoku puzzles. Pay attention to how the difficulty levels affect player experience and puzzle-solving strategies. Your evaluation should ensure that the puzzles are not only mathematically sound but also provide a satisfying challenge to players across all difficulty levels."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Algorithm Development",
+ "description": "Evaluate the effectiveness of the algorithm in generating Sudoku puzzles across different difficulty levels."
+ },
+ {
+ "category": "Difficulty Metrics",
+ "description": "Assess the metrics used to define and differentiate the difficulty levels of the Sudoku puzzles."
+ },
+ {
+ "category": "Extensibility",
+ "description": "Examine how the algorithm and difficulty metrics can be extended to accommodate a varying number of difficulty levels."
+ },
+ {
+ "category": "Solution Uniqueness",
+ "description": "Verify that the algorithm guarantees a unique solution for each generated Sudoku puzzle."
+ },
+ {
+ "category": "Complexity Analysis",
+ "description": "Analyze the computational complexity of the algorithm and evaluate efforts to minimize it."
+ },
+ {
+ "category": "Illustration of Difficulty Levels",
+ "description": "Ensure that the algorithm is illustrated with at least four distinct difficulty levels."
+ }
+ ]
+ }
+ },
+ "2008_Going_Green": {
+ "year": "2008",
+ "title": "Going Green",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2008/HIMCM-B/index.html",
+ "question": "The United States can address its national carbon footprint in two ways: by reducing carbon dioxide emissions or by increasing carbon dioxide consumption (sequestration). Assume that the total U.S. carbon dioxide emissions are capped at 2007-2008 levels indefinitely. What should the U.S. do to increase carbon dioxide consumption to achieve national carbon neutrality with minimal economic and cultural impact? Is it even possible to achieve neutrality? Model your solution to show feasibility, effectiveness, and costs. Prepare a short summary paper for the U.S. Congress to persuade them to adopt your plan.",
+ "requirements": [
+ {
+ "category": "Objective Clarity",
+ "description": "Clearly define the goal of achieving national carbon neutrality through increased carbon dioxide consumption."
+ },
+ {
+ "category": "Modeling Approach",
+ "description": "Develop a mathematical model that addresses carbon dioxide consumption and sequestration strategies."
+ },
+ {
+ "category": "Feasibility Analysis",
+ "description": "Evaluate the feasibility of achieving carbon neutrality under the given constraints."
+ },
+ {
+ "category": "Effectiveness Evaluation",
+ "description": "Assess the effectiveness of proposed strategies in increasing carbon dioxide consumption."
+ },
+ {
+ "category": "Cost Analysis",
+ "description": "Analyze the economic costs associated with implementing the proposed strategies."
+ },
+ {
+ "category": "Cultural Impact Assessment",
+ "description": "Evaluate the cultural impacts of the proposed strategies and how they can be minimized."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and justify any assumptions made in the model regarding emissions, consumption, and sequestration."
+ },
+ {
+ "category": "Data Utilization",
+ "description": "Use relevant data to support the model and analysis, ensuring accuracy and reliability."
+ },
+ {
+ "category": "Solution Feasibility",
+ "description": "Determine if achieving carbon neutrality is possible and provide evidence to support the conclusion."
+ },
+ {
+ "category": "Persuasiveness",
+ "description": "Prepare a compelling summary paper for the U.S. Congress that effectively communicates the plan and its benefits."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a strong foundation in mathematical modeling to develop equations and models that can predict the impact of various strategies on carbon dioxide consumption and sequestration.",
+ "details": "You are a mathematician with expertise in formulating and solving complex mathematical models. Your role involves developing equations that represent the carbon cycle, including emissions and sequestration processes. You should pay attention to the assumptions made in the models, the accuracy of the mathematical representations, and the feasibility of the solutions proposed. Your evaluation should focus on the logical consistency and mathematical soundness of the proposed strategies."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets related to carbon emissions, sequestration methods, and economic impacts, requiring expertise in data processing and statistical analysis.",
+ "details": "You are a data scientist skilled in handling and analyzing complex datasets. Your role is to evaluate the data-driven aspects of the modeling solutions, ensuring that the data used is accurate, relevant, and comprehensive. You should focus on the statistical methods employed, the validity of the data sources, and the robustness of the data analysis. Your evaluation should ensure that the conclusions drawn from the data are supported by sound statistical evidence."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem is deeply rooted in environmental science, requiring an understanding of ecological processes, carbon sequestration methods, and the environmental impact of proposed solutions.",
+ "details": "You are an environmental scientist with expertise in carbon cycles and sequestration techniques. Your role is to assess the environmental feasibility and impact of the proposed solutions. You should evaluate the ecological validity of the sequestration methods, the potential environmental benefits or harms, and the sustainability of the proposed strategies. Your evaluation should ensure that the solutions are environmentally sound and align with ecological principles."
+ },
+ {
+ "name": "Economist",
+ "thoughts": "The problem involves assessing the economic impact of carbon neutrality strategies, requiring expertise in economic modeling and cost-benefit analysis.",
+ "details": "You are an economist with expertise in evaluating the economic implications of environmental policies. Your role is to analyze the cost-effectiveness of the proposed solutions, considering both short-term and long-term economic impacts. You should focus on the economic models used, the assumptions regarding costs and benefits, and the potential economic trade-offs. Your evaluation should ensure that the proposed strategies are economically viable and minimize negative economic impacts."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Objective Clarity",
+ "description": "Clearly define the goal of achieving national carbon neutrality through increased carbon dioxide consumption."
+ },
+ {
+ "category": "Modeling Approach",
+ "description": "Develop a mathematical model that addresses carbon dioxide consumption and sequestration strategies."
+ },
+ {
+ "category": "Feasibility Analysis",
+ "description": "Evaluate the feasibility of achieving carbon neutrality under the given constraints."
+ },
+ {
+ "category": "Effectiveness Evaluation",
+ "description": "Assess the effectiveness of proposed strategies in increasing carbon dioxide consumption."
+ },
+ {
+ "category": "Cost Analysis",
+ "description": "Analyze the economic costs associated with implementing the proposed strategies."
+ },
+ {
+ "category": "Cultural Impact Assessment",
+ "description": "Evaluate the cultural impacts of the proposed strategies and how they can be minimized."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and justify any assumptions made in the model regarding emissions, consumption, and sequestration."
+ },
+ {
+ "category": "Data Utilization",
+ "description": "Use relevant data to support the model and analysis, ensuring accuracy and reliability."
+ },
+ {
+ "category": "Solution Feasibility",
+ "description": "Determine if achieving carbon neutrality is possible and provide evidence to support the conclusion."
+ },
+ {
+ "category": "Persuasiveness",
+ "description": "Prepare a compelling summary paper for the U.S. Congress that effectively communicates the plan and its benefits."
+ }
+ ]
+ }
+ },
+ "2009_Designing_a_Traffic": {
+ "year": "2009",
+ "title": "Designing a Traffic Circle",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2009/MCM-A/index.html",
+ "question": "Many cities and communities have traffic circles\u2014from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small ones with one or two lanes in the circle. Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority to traffic already in the circle; some position a yield sign in the circle at each incoming road to give priority to incoming traffic; and some position a traffic light on each incoming road (with no right turn allowed on a red light). Other designs may also be possible.\n\nThe goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle. State clearly the objective(s) you use in your model for making the optimal choice as well as the factors that affect this choice. Include a Technical Summary of not more than two double-spaced pages that explains to a Traffic Engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle. That is, summarize the conditions under which each type of traffic-control method should be used. When traffic lights are recommended, explain a method for determining how many seconds each light should remain green (which may vary according to the time of day and other factors). Illustrate how your model works with specific examples.",
+ "requirements": [
+ {
+ "category": "Objective Definition",
+ "description": "Clearly state the objective(s) of the model for optimizing traffic flow in circles."
+ },
+ {
+ "category": "Factors Consideration",
+ "description": "Identify and incorporate relevant factors that affect traffic flow and control method choice, such as traffic volume, circle size, and time of day."
+ },
+ {
+ "category": "Model Development",
+ "description": "Develop a mathematical model that effectively addresses the stated objectives and factors, providing a logical framework for decision-making."
+ },
+ {
+ "category": "Traffic Control Methods",
+ "description": "Evaluate different traffic control methods (stop signs, yield signs, traffic lights) and determine conditions under which each should be used."
+ },
+ {
+ "category": "Traffic Light Timing",
+ "description": "Provide a method for calculating optimal traffic light timing, considering variable factors like time of day and traffic patterns."
+ },
+ {
+ "category": "Technical Summary",
+ "description": "Create a concise technical summary that explains the model's application to a Traffic Engineer, including conditions for each control method."
+ },
+ {
+ "category": "Illustrative Examples",
+ "description": "Include specific examples to demonstrate how the model works in practice, enhancing understanding and applicability."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to analyze traffic flow dynamics and optimize control methods. A mathematician can develop equations and models to simulate different traffic scenarios and evaluate the effectiveness of various control strategies.",
+ "details": "You are a mathematician with expertise in traffic flow modeling. You should focus on formulating mathematical models that capture the dynamics of traffic circles, including vehicle interactions and flow rates. Pay attention to the assumptions made in the models and ensure they are realistic and applicable to real-world scenarios. Your evaluation should consider the mathematical rigor and the ability of the model to predict traffic behavior accurately."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing traffic data to inform the model and optimize traffic control strategies. A data scientist can process and interpret large datasets to identify patterns and trends in traffic flow, which are crucial for model validation and improvement.",
+ "details": "You are a data scientist with expertise in traffic data analysis. You should focus on extracting meaningful insights from traffic data, such as peak hours, average vehicle speed, and congestion patterns. Pay attention to the quality and completeness of the data used in the model. Your evaluation should consider how well the model incorporates data-driven insights and whether it can adapt to changes in traffic conditions."
+ },
+ {
+ "name": "Traffic Engineer",
+ "thoughts": "Traffic engineers have practical experience in designing and implementing traffic control systems. They can provide insights into the feasibility and effectiveness of different control methods in real-world settings.",
+ "details": "You are a traffic engineer with expertise in traffic circle design and control systems. You should focus on evaluating the practicality of the proposed traffic control methods, considering factors such as safety, cost, and ease of implementation. Pay attention to how the model addresses real-world constraints and the conditions under which each control method is recommended. Your evaluation should consider the model's applicability to various traffic circle designs and its ability to improve traffic flow and safety."
+ },
+ {
+ "name": "Urban Planner",
+ "thoughts": "Urban planners consider the broader context of traffic systems within city planning. They can provide insights into how traffic circle control methods fit into the overall transportation network and urban development goals.",
+ "details": "You are an urban planner with expertise in integrating traffic systems into urban environments. You should focus on evaluating how the proposed traffic control methods align with city planning objectives, such as reducing congestion and promoting sustainable transportation. Pay attention to the model's consideration of environmental and social factors, such as pedestrian access and public transportation integration. Your evaluation should consider the long-term impact of the model on urban mobility and development."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Objective Definition",
+ "description": "Clearly state the objective(s) of the model for optimizing traffic flow in circles."
+ },
+ {
+ "category": "Factors Consideration",
+ "description": "Identify and incorporate relevant factors that affect traffic flow and control method choice, such as traffic volume, circle size, and time of day."
+ },
+ {
+ "category": "Model Development",
+ "description": "Develop a mathematical model that effectively addresses the stated objectives and factors, providing a logical framework for decision-making."
+ },
+ {
+ "category": "Traffic Control Methods",
+ "description": "Evaluate different traffic control methods (stop signs, yield signs, traffic lights) and determine conditions under which each should be used."
+ },
+ {
+ "category": "Traffic Light Timing",
+ "description": "Provide a method for calculating optimal traffic light timing, considering variable factors like time of day and traffic patterns."
+ },
+ {
+ "category": "Technical Summary",
+ "description": "Create a concise technical summary that explains the model's application to a Traffic Engineer, including conditions for each control method."
+ },
+ {
+ "category": "Illustrative Examples",
+ "description": "Include specific examples to demonstrate how the model works in practice, enhancing understanding and applicability."
+ }
+ ]
+ }
+ },
+ "2010_Curbing_City_Violence": {
+ "year": "2010",
+ "title": "Curbing City Violence",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2010/HIMCM-B/index.html",
+ "question": "A regional city has had lots of problems with gangs and violence over the years. The mayor, chief of police, and city council need your help. Data are available for the following: Incidents of violence, Homicides, Assaults, Regional Population (Census data), Unemployment, Unemployment rate, High School enrollment, High school drop outs, Graduation rate, Drop out rate, Prison population, Released on parole, Parole violations, Percent of parole violations, and Juvenile Inmates. Analyze and model these data to give the city a plan to reduce violence. After you complete your analysis and model, prepare a news release for the mayor briefly outlining your proposals that recommend a campaign strategy to curb the violence. 2010_HiMCM_Problem_B_Data.pdf Click here to view the available Data.\n\n### Text in the PDF File: 2010_HiMCM_Problem_B_Data.pdf\n\n### Violence and Population Data (2000-2008)\n\n| Year | Incidence of Violence | Homicides | Assaults | County Population | City Population |\n|------|-----------------------|-----------|----------|-------------------|-----------------|\n| 2000 | 752 | 18 | 734 | 401,762 | 151,060 |\n| 2001 | 814 | 15 | 799 | 406,953 | 144,696 |\n| 2002 | 712 | 20 | 692 | 412,376 | 146,689 |\n| 2003 | 744 | 19 | 725 | 417,419 | 148,117 |\n| 2004 | 695 | 17 | 678 | 420,802 | 149,906 |\n| 2005 | 652 | 7 | 645 | 421,374 | 149,675 |\n| 2006 | 690 | 7 | 683 | 421,417 | 148,870 |\n| 2007 | 725 | 14 | 711 | 423,762 | 149,208 |\n| 2008 | 736 | 25 | 711 | 428,549 | 150,898 |\n\n### Unemployment Data (2000-2008)\n\n| Year | Unemployment | Unemployment Rate (%) |\n|------|--------------|-----------------------|\n| 2000 | 15,861.3 | 10.5 |\n| 2001 | 16,061.256 | 11.1 |\n| 2002 | 18,629.503 | 12.7 |\n| 2003 | 18,810.859 | 12.7 |\n| 2004 | 17,688.908 | 11.8 |\n| 2005 | 15,715.875 | 10.5 |\n| 2006 | 14,738.13 | 9.9 |\n| 2007 | 15,368.424 | 10.3 |\n| 2008 | 17,805.964 | 11.8 |\n\n### High School Data (2000-2008)\n\n| Year | HS Enrollment | HS Drop Outs | Graduation Rate | HS Drop Out Rate |\n|------|---------------|--------------|-----------------|------------------|\n| 2000 | 8,252 | 203 | 0.84 | 0.0246 |\n| 2001 | 8,695 | 225 | 0.836 | 0.0259 |\n| 2002 | 8,863 | 204 | 0.877 | 0.0230 |\n| 2003 | 9,253 | 75 | 0.9 | 0.0081 |\n| 2004 | 9,308 | 124 | 0.891 | 0.0133 |\n| 2005 | 9,492 | 85 | 0.898 | 0.0090 |\n| 2006 | 9,496 | 124 | 0.92 | 0.0131 |\n| 2007 | 9,482 | 180 | 0.884 | 0.0190 |\n| 2008 | 9,561 | 147 | 0.89 | 0.0154 |\n\n### Juvenile and Parole Data (2000-2007)\n\n| Year | Juvenile Inmates | Prison Population | Released on Parole | Parole Violation | % of Parole Violation |\n|------|------------------|-------------------|--------------------|------------------|-----------------------|\n| 2000 | 154,014 | 126,117 | 89,363 | - | 0.709 |\n| 2001 | 153,649 | 125,991 | 88,972 | - | 0.706 |\n| 2002 | 151,579 | 117,310 | 85,574 | - | 0.729 |\n| 2003 | 4,400 | 153,783 | 115,424 | 78,053 | 0.676 |\n| 2004 | 3,436 | 157,895 | 118,018 | 76,725 | 0.650 |\n| 2005 | 2,881 | 158,837 | 122,737 | 80,962 | 0.660 |\n| 2006 | 2,517 | 166,547 | 131,315 | 89,883 | 0.684 |\n| 2007 | 2,115 | 166,277 | 137,590 | 92,628 | 0.673 |",
+ "requirements": [
+ {
+ "category": "Data Analysis",
+ "description": "Evaluate the thoroughness and accuracy of the analysis of the provided data sets, including trends and correlations between violence and socio-economic factors."
+ },
+ {
+ "category": "Model Development",
+ "description": "Assess the mathematical model developed to predict or explain the relationship between the variables and violence, including the choice of modeling techniques and justification."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and evaluate the assumptions made in the model, ensuring they are reasonable and clearly stated."
+ },
+ {
+ "category": "Strategic Recommendations",
+ "description": "Grade the effectiveness and feasibility of the proposed strategies to reduce violence based on the model's findings."
+ },
+ {
+ "category": "Integration of Data",
+ "description": "Assess how well the solution integrates different data sets (e.g., unemployment, high school, juvenile and parole data) to provide a comprehensive analysis."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Evaluate whether the solution includes a sensitivity analysis to understand the impact of changes in key variables on the model's outcomes."
+ },
+ {
+ "category": "Communication",
+ "description": "Grade the clarity and conciseness of the news release prepared for the mayor, ensuring it effectively communicates the key findings and recommendations."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a deep understanding of mathematical modeling to identify patterns and relationships between various socio-economic factors and incidents of violence. A mathematician can help in formulating equations and models that can predict trends and outcomes based on the data provided.",
+ "details": "As a mathematician, you are skilled in creating and analyzing mathematical models that can help understand complex systems. You should focus on identifying correlations and causations within the data, using statistical methods and mathematical principles. Pay attention to the accuracy of the models and ensure they are robust enough to handle the variability in the data. Your expertise will be crucial in developing predictive models that can inform strategies to reduce violence."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets to extract meaningful insights that can inform policy decisions. A data scientist can leverage machine learning techniques and data analysis tools to uncover hidden patterns and trends in the data.",
+ "details": "As a data scientist, you are adept at handling and processing complex datasets. You should focus on cleaning and preprocessing the data to ensure its quality and reliability. Use your skills in statistical analysis and machine learning to identify key factors contributing to violence and evaluate the effectiveness of different intervention strategies. Your ability to visualize data and communicate findings will be essential in preparing a compelling news release for the mayor."
+ },
+ {
+ "name": "Sociologist",
+ "thoughts": "Understanding the social dynamics and cultural factors that contribute to gang violence and crime is crucial. A sociologist can provide insights into the societal influences and community structures that may be impacting the rates of violence.",
+ "details": "As a sociologist, you are skilled in analyzing social behaviors and community interactions. You should focus on interpreting the data in the context of social theories and frameworks. Consider the impact of unemployment, education, and family structures on crime rates. Your expertise will be valuable in identifying social interventions and community-based strategies that can help reduce violence."
+ },
+ {
+ "name": "Criminologist",
+ "thoughts": "The problem is directly related to crime and violence, making the expertise of a criminologist essential. A criminologist can provide insights into the patterns of criminal behavior and the effectiveness of law enforcement strategies.",
+ "details": "As a criminologist, you are knowledgeable about the causes and consequences of criminal behavior. You should focus on analyzing the data related to crime rates, parole violations, and juvenile inmates. Evaluate the effectiveness of current law enforcement and correctional strategies, and propose evidence-based interventions. Your understanding of criminal justice systems will be crucial in developing a comprehensive plan to curb violence in the city."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Data Analysis",
+ "description": "Evaluate the thoroughness and accuracy of the analysis of the provided data sets, including trends and correlations between violence and socio-economic factors."
+ },
+ {
+ "category": "Model Development",
+ "description": "Assess the mathematical model developed to predict or explain the relationship between the variables and violence, including the choice of modeling techniques and justification."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Identify and evaluate the assumptions made in the model, ensuring they are reasonable and clearly stated."
+ },
+ {
+ "category": "Strategic Recommendations",
+ "description": "Grade the effectiveness and feasibility of the proposed strategies to reduce violence based on the model's findings."
+ },
+ {
+ "category": "Integration of Data",
+ "description": "Assess how well the solution integrates different data sets (e.g., unemployment, high school, juvenile and parole data) to provide a comprehensive analysis."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Evaluate whether the solution includes a sensitivity analysis to understand the impact of changes in key variables on the model's outcomes."
+ },
+ {
+ "category": "Communication",
+ "description": "Grade the clarity and conciseness of the news release prepared for the mayor, ensuring it effectively communicates the key findings and recommendations."
+ }
+ ]
+ }
+ },
+ "2010_The_Sweet_Spot": {
+ "year": "2010",
+ "title": "The Sweet Spot",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2010/MCM-A/index.html",
+ "question": "Explain the \"sweet spot\" on a baseball bat. Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power is transferred to the ball when hit. Why isn\u2019t this spot at the end of the bat? A simple explanation based on torque might seem to identify the end of the bat as the sweet spot, but this is known to be empirically incorrect. Develop a model that helps explain this empirical finding. Some players believe that \"corking\" a bat (hollowing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhances the \"sweet spot\" effect. Augment your model to confirm or deny this effect. Does this explain why Major League Baseball prohibits \"corking\"? Does the material out of which the bat is constructed matter? That is, does this model predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major League Baseball prohibits metal bats?",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Develop a mathematical model that explains the location of the 'sweet spot' on a baseball bat, considering factors such as torque and energy transfer."
+ },
+ {
+ "category": "Empirical Explanation",
+ "description": "Provide a clear explanation of why the 'sweet spot' is not at the end of the bat, supported by empirical evidence and the developed model."
+ },
+ {
+ "category": "Corking Effect",
+ "description": "Augment the model to analyze the effect of 'corking' a bat on the 'sweet spot' and determine if it enhances the effect."
+ },
+ {
+ "category": "Regulatory Implications",
+ "description": "Use the model to explain why Major League Baseball prohibits 'corking' and whether the model supports this regulation."
+ },
+ {
+ "category": "Material Analysis",
+ "description": "Evaluate how the material of the bat (wood vs. metal) affects the 'sweet spot' and whether the model predicts different behaviors for these materials."
+ },
+ {
+ "category": "Regulatory Analysis for Materials",
+ "description": "Analyze why Major League Baseball prohibits metal bats based on the model's predictions and implications."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Identify and discuss any assumptions made in the model and their potential impact on the results and conclusions."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a deep understanding of physics and mathematical modeling to explain the dynamics of the \"sweet spot\" on a baseball bat, including concepts like torque, force distribution, and material properties.",
+ "details": "You are a mathematician with expertise in formulating and solving complex equations related to physical phenomena. You should focus on the mathematical principles that govern the interaction between the bat and the ball, such as torque and force distribution. Your role involves ensuring that the model accurately represents these principles and can predict the behavior of different materials and modifications like corking. Pay attention to the assumptions made in the model and verify their validity through mathematical reasoning."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing empirical data related to the performance of baseball bats, which requires data processing and statistical analysis to validate the model's predictions.",
+ "details": "You are a data scientist skilled in analyzing complex datasets to inform the model. Your role involves reviewing the empirical data on bat performance and ensuring that the model's predictions align with observed data. You should focus on statistical methods to test hypotheses about the \"sweet spot\" and the effects of corking. Pay attention to the data quality and the statistical significance of the findings, ensuring that the model is robust and reliable."
+ },
+ {
+ "name": "Physicist",
+ "thoughts": "The problem involves understanding the physical principles behind the \"sweet spot\" phenomenon, including the mechanics of impact and material properties.",
+ "details": "You are a physicist with expertise in the mechanics of materials and impact dynamics. Your role involves reviewing the model to ensure it accurately represents the physical interactions between the bat and the ball. You should focus on the material properties of wood and metal bats and how these affect the \"sweet spot.\" Pay attention to the physical assumptions made in the model and verify their accuracy based on your knowledge of physics. Evaluate the model's predictions about corking and material differences, considering the real-world implications."
+ },
+ {
+ "name": "Sports Engineer",
+ "thoughts": "The problem involves practical applications of engineering principles to sports equipment, requiring an understanding of design and performance optimization.",
+ "details": "You are a sports engineer with expertise in the design and optimization of sports equipment. Your role involves reviewing the model to ensure it considers the practical aspects of bat design and performance. You should focus on how modifications like corking affect the bat's structural integrity and performance. Pay attention to the engineering principles applied in the model and evaluate whether they align with real-world practices in sports equipment design. Consider the implications of the model's predictions for the rules and regulations in sports, such as the prohibition of corking and metal bats in Major League Baseball."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Develop a mathematical model that explains the location of the 'sweet spot' on a baseball bat, considering factors such as torque and energy transfer."
+ },
+ {
+ "category": "Empirical Explanation",
+ "description": "Provide a clear explanation of why the 'sweet spot' is not at the end of the bat, supported by empirical evidence and the developed model."
+ },
+ {
+ "category": "Corking Effect",
+ "description": "Augment the model to analyze the effect of 'corking' a bat on the 'sweet spot' and determine if it enhances the effect."
+ },
+ {
+ "category": "Regulatory Implications",
+ "description": "Use the model to explain why Major League Baseball prohibits 'corking' and whether the model supports this regulation."
+ },
+ {
+ "category": "Material Analysis",
+ "description": "Evaluate how the material of the bat (wood vs. metal) affects the 'sweet spot' and whether the model predicts different behaviors for these materials."
+ },
+ {
+ "category": "Regulatory Analysis for Materials",
+ "description": "Analyze why Major League Baseball prohibits metal bats based on the model's predictions and implications."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Identify and discuss any assumptions made in the model and their potential impact on the results and conclusions."
+ }
+ ]
+ }
+ },
+ "2011_How_environmentally_and": {
+ "year": "2011",
+ "title": "How environmentally and economically sound are electric vehicles? Is their widespread use feasible and practical?",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2011/ICM-C/index.html",
+ "question": "2011_ICM_Problem.pdf 2011_ICM_Problem.pdf How environmentally and economically sound are electric vehicles? Is their widespread use feasible and practical?\n\n### Text in the PDF File: 2011_ICM_Problem.pdf\n\n# 2011 The Interdisciplinary Contest in Modeling (ICM)\n\n## Key Issues to Consider for Electric Vehicles:\n\n1. **Fossil Fuel Savings**: Evaluate if electric vehicles (EVs) save fossil fuels or merely shift fossil fuel use from vehicles to electricity production. Identify conditions to maximize savings.\n\n2. **Alternative Energy Growth**: Assess the required increase in wind and solar energy to make EVs feasible and environmentally beneficial. Determine the likelihood and possibility of this growth.\n\n3. **Off-Peak Charging**: Analyze the benefits of charging EVs during off-peak times. Determine the necessary charging speed for efficiency and practicality. Evaluate how advancements in these areas affect environmental savings and practicality.\n\n4. **Transportation Efficiency**: Identify the most efficient transportation method and whether efficiency varies by region or nation.\n\n5. **Pollution Concerns**: Examine hidden pollutants associated with EVs. Compare the pollution from EVs to that from internal combustion engines, considering short and long-term climate and health effects.\n\n6. **Battery Disposal**: Investigate the environmental impact of disposing of large numbers of EV batteries compared to fossil fuel vehicles.\n\n7. **Economic and Human Factors**: Consider the convenience of EVs, battery recharge/replacement speed, and range limitations. Evaluate the role of EVs in short vs. long-range transportation. Discuss government subsidies for EV technology development.\n\n## Modeling Requirements:\n\n- Model the environmental, social, economic, and health impacts of widespread EV use. Identify key factors for government and manufacturer support.\n- Estimate global fossil fuel savings from widespread EV adoption.\n- Model the necessary electricity generation to support recommended EV use, maximizing benefits to the environment, society, business, and individuals.\n- Write a 20-page report detailing the model, analysis, and government roles in ensuring safe, efficient transportation. Discuss the value of widespread EV use in addressing global energy needs amid dwindling fossil fuel supplies.\n\n## References:\n\n- Global energy data: [BP Statistical Review of World Energy 2010](http://www.bp.com/liveassets/bp_internet/globalbp/globalbp_uk_english/reports_and_publications/statistical_energy_review_2008/STAGING/local_assets/2010_downloads/statistical_review_of_world_energy_full_report_2010.pdf)\n- US energy generation and usage summary: [EIA Energy Diagram](http://www.eia.doe.gov/aer/pecss_diagram.html)\n- Global data in spreadsheet form: [EIA International Energy Data](http://www.eia.doe.gov/iea/)",
+ "requirements": [
+ {
+ "category": "Fossil Fuel Savings",
+ "description": "Evaluate the extent to which electric vehicles save fossil fuels versus shifting fossil fuel use to electricity production. Identify conditions that maximize fossil fuel savings."
+ },
+ {
+ "category": "Alternative Energy Growth",
+ "description": "Assess the necessary increase in wind and solar energy to support electric vehicles and evaluate the feasibility of this growth."
+ },
+ {
+ "category": "Off-Peak Charging",
+ "description": "Analyze the benefits of off-peak charging for electric vehicles, including necessary charging speeds and their impact on environmental savings and practicality."
+ },
+ {
+ "category": "Transportation Efficiency",
+ "description": "Identify the most efficient transportation methods for electric vehicles and evaluate if efficiency varies by region or nation."
+ },
+ {
+ "category": "Pollution Concerns",
+ "description": "Examine hidden pollutants associated with electric vehicles and compare them to those from internal combustion engines, considering both short and long-term climate and health effects."
+ },
+ {
+ "category": "Battery Disposal",
+ "description": "Investigate the environmental impact of disposing of large numbers of electric vehicle batteries compared to fossil fuel vehicles."
+ },
+ {
+ "category": "Economic and Human Factors",
+ "description": "Evaluate the convenience of electric vehicles, including battery recharge/replacement speed, range limitations, and their role in short vs. long-range transportation. Discuss the impact of government subsidies on EV technology development."
+ },
+ {
+ "category": "Modeling Environmental, Social, Economic, and Health Impacts",
+ "description": "Develop a model that assesses the environmental, social, economic, and health impacts of widespread electric vehicle use, identifying key factors for government and manufacturer support."
+ },
+ {
+ "category": "Global Fossil Fuel Savings Estimation",
+ "description": "Estimate the global fossil fuel savings from widespread adoption of electric vehicles."
+ },
+ {
+ "category": "Electricity Generation Modeling",
+ "description": "Model the necessary electricity generation to support recommended electric vehicle use, maximizing benefits to the environment, society, business, and individuals."
+ },
+ {
+ "category": "Report Writing",
+ "description": "Write a detailed 20-page report that includes the model, analysis, and government roles in ensuring safe, efficient transportation, discussing the value of widespread electric vehicle use in addressing global energy needs amid dwindling fossil fuel supplies."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to evaluate the environmental and economic impacts of electric vehicles, including complex calculations related to energy savings, pollution, and transportation efficiency.",
+ "details": "As a mathematician, you are skilled in formulating and solving equations that model the various aspects of electric vehicle use. You should focus on creating models that accurately represent the relationships between fossil fuel savings, alternative energy growth, and pollution concerns. Pay attention to the assumptions made in the models and ensure they are mathematically sound and logically consistent."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets related to energy consumption, pollution levels, and economic factors to inform the model and provide insights into the feasibility of electric vehicles.",
+ "details": "As a data scientist, you are adept at processing and analyzing complex datasets to extract meaningful insights. You should focus on using statistical methods and machine learning techniques to analyze data from sources like the BP Statistical Review and EIA Energy Diagram. Ensure that the data used in the models is accurate, up-to-date, and relevant to the problem at hand."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem requires expertise in understanding the environmental impacts of electric vehicles, including pollution, fossil fuel savings, and battery disposal.",
+ "details": "As an environmental scientist, you are knowledgeable about the ecological effects of transportation methods. You should evaluate the environmental models for accuracy in representing pollution levels and the impact of battery disposal. Pay attention to the long-term climate and health effects of electric vehicle adoption and ensure that the models consider these factors comprehensively."
+ },
+ {
+ "name": "Economist",
+ "thoughts": "The problem involves assessing the economic feasibility and practicality of widespread electric vehicle use, including government subsidies, market dynamics, and human factors.",
+ "details": "As an economist, you are skilled in analyzing economic models and understanding market trends. You should focus on evaluating the economic aspects of the models, such as cost-benefit analyses, the role of government subsidies, and the impact on global energy markets. Ensure that the models accurately reflect the economic implications of electric vehicle adoption and consider factors like convenience, recharge speed, and range limitations."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Fossil Fuel Savings",
+ "description": "Evaluate the extent to which electric vehicles save fossil fuels versus shifting fossil fuel use to electricity production. Identify conditions that maximize fossil fuel savings."
+ },
+ {
+ "category": "Alternative Energy Growth",
+ "description": "Assess the necessary increase in wind and solar energy to support electric vehicles and evaluate the feasibility of this growth."
+ },
+ {
+ "category": "Off-Peak Charging",
+ "description": "Analyze the benefits of off-peak charging for electric vehicles, including necessary charging speeds and their impact on environmental savings and practicality."
+ },
+ {
+ "category": "Transportation Efficiency",
+ "description": "Identify the most efficient transportation methods for electric vehicles and evaluate if efficiency varies by region or nation."
+ },
+ {
+ "category": "Pollution Concerns",
+ "description": "Examine hidden pollutants associated with electric vehicles and compare them to those from internal combustion engines, considering both short and long-term climate and health effects."
+ },
+ {
+ "category": "Battery Disposal",
+ "description": "Investigate the environmental impact of disposing of large numbers of electric vehicle batteries compared to fossil fuel vehicles."
+ },
+ {
+ "category": "Economic and Human Factors",
+ "description": "Evaluate the convenience of electric vehicles, including battery recharge/replacement speed, range limitations, and their role in short vs. long-range transportation. Discuss the impact of government subsidies on EV technology development."
+ },
+ {
+ "category": "Modeling Environmental, Social, Economic, and Health Impacts",
+ "description": "Develop a model that assesses the environmental, social, economic, and health impacts of widespread electric vehicle use, identifying key factors for government and manufacturer support."
+ },
+ {
+ "category": "Global Fossil Fuel Savings Estimation",
+ "description": "Estimate the global fossil fuel savings from widespread adoption of electric vehicles."
+ },
+ {
+ "category": "Electricity Generation Modeling",
+ "description": "Model the necessary electricity generation to support recommended electric vehicle use, maximizing benefits to the environment, society, business, and individuals."
+ },
+ {
+ "category": "Report Writing",
+ "description": "Write a detailed 20-page report that includes the model, analysis, and government roles in ensuring safe, efficient transportation, discussing the value of widespread electric vehicle use in addressing global energy needs amid dwindling fossil fuel supplies."
+ }
+ ]
+ }
+ },
+ "2011_Repeater_Coordination": {
+ "year": "2011",
+ "title": "Repeater Coordination",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2011/MCM-B/index.html",
+ "question": "The VHF radio spectrum involves line-of-sight transmission and reception. This limitation can be overcome by \"repeaters,\" which pick up weak signals, amplify them, and retransmit them on a different frequency. Thus, using a repeater, low-power users (such as mobile stations) can communicate with one another in situations where direct user-to-user contact would not be possible. However, repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies. In addition to geographical separation, the \"continuous tone-coded squelch system\" (CTCSS), sometimes nicknamed \"private line\" (PL), technology can be used to mitigate interference problems. This system associates to each repeater a separate subaudible tone that is transmitted by all users who wish to communicate through that repeater. The repeater responds only to received signals with its specific PL tone. With this system, two nearby repeaters can share the same frequency pair (for receive and transmit); so more repeaters (and hence more users) can be accommodated in a particular area. For a circular flat area of radius 40 miles radius, determine the minimum number of repeaters necessary to accommodate 1,000 simultaneous users. Assume that the spectrum available is 145 to 148 MHz, the transmitter frequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency, and there are 54 different PL tones available. How does your solution change if there are 10,000 users? Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.",
+ "requirements": [
+ {
+ "category": "Objective Identification",
+ "description": "Clearly identify the main objective of determining the minimum number of repeaters needed for 1,000 and 10,000 users in a circular area of 40 miles radius."
+ },
+ {
+ "category": "Frequency Allocation",
+ "description": "Develop a strategy for allocating frequencies within the 145 to 148 MHz spectrum, considering the 600 kHz separation requirement between transmitter and receiver frequencies."
+ },
+ {
+ "category": "PL Tone Utilization",
+ "description": "Effectively utilize the 54 different PL tones to maximize repeater sharing and minimize interference, ensuring that repeaters can share frequencies when using different PL tones."
+ },
+ {
+ "category": "Geographical Considerations",
+ "description": "Address the impact of geographical features, such as mountainous areas, on line-of-sight propagation and propose solutions to mitigate these effects."
+ },
+ {
+ "category": "Scalability Analysis",
+ "description": "Analyze how the solution scales from accommodating 1,000 users to 10,000 users, including any changes in repeater requirements or configurations."
+ },
+ {
+ "category": "Mathematical Modeling",
+ "description": "Provide a detailed mathematical model that includes assumptions, calculations, and logical reasoning to support the proposed solution."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Identify and justify any assumptions made in the modeling process, and discuss the limitations of the proposed solution."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves complex calculations related to geometry, frequency allocation, and optimization, which are core areas of expertise for a mathematician.",
+ "details": "You are a mathematician with expertise in geometric modeling and optimization. Your role is to ensure that the mathematical models used to determine the placement and frequency allocation of repeaters are sound and efficient. You should pay attention to the assumptions made in the model, the accuracy of the calculations, and the feasibility of the proposed solutions. Your expertise in mathematical principles and problem-solving will be crucial in evaluating the effectiveness of the proposed solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing data related to user distribution, frequency usage, and potential interference, which are tasks well-suited for a data scientist.",
+ "details": "You are a data scientist skilled in data analysis and statistical modeling. Your role is to review the data-driven aspects of the solution, such as user distribution patterns and frequency usage statistics. You should ensure that the data used in the model is accurate and that the statistical methods applied are appropriate. Your expertise in machine learning and data processing will help in evaluating the robustness of the solution against varying user demands and environmental conditions."
+ },
+ {
+ "name": "Telecommunications Engineer",
+ "thoughts": "The problem is deeply rooted in telecommunications, involving radio frequency management, repeater technology, and signal propagation, which are areas of expertise for a telecommunications engineer.",
+ "details": "You are a telecommunications engineer with expertise in radio frequency management and signal propagation. Your role is to evaluate the technical feasibility of the proposed solutions, focusing on the practical aspects of repeater placement, frequency allocation, and interference mitigation. You should pay attention to the technical specifications of the equipment, the impact of environmental factors on signal propagation, and the overall system design. Your knowledge of telecommunications systems will be essential in ensuring that the solution is technically sound and implementable."
+ },
+ {
+ "name": "Geographic Information Systems (GIS) Specialist",
+ "thoughts": "The problem involves geographic considerations, such as the placement of repeaters in a circular area and the impact of terrain on signal propagation, which are areas where a GIS specialist can provide valuable insights.",
+ "details": "You are a GIS specialist with expertise in spatial analysis and geographic modeling. Your role is to assess the geographic aspects of the solution, such as the optimal placement of repeaters and the impact of terrain features on line-of-sight propagation. You should ensure that the geographic data used in the model is accurate and that the spatial analysis methods are appropriate. Your expertise in GIS technology will help in visualizing the solution and identifying potential geographic challenges that could affect the system's performance."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Objective Identification",
+ "description": "Clearly identify the main objective of determining the minimum number of repeaters needed for 1,000 and 10,000 users in a circular area of 40 miles radius."
+ },
+ {
+ "category": "Frequency Allocation",
+ "description": "Develop a strategy for allocating frequencies within the 145 to 148 MHz spectrum, considering the 600 kHz separation requirement between transmitter and receiver frequencies."
+ },
+ {
+ "category": "PL Tone Utilization",
+ "description": "Effectively utilize the 54 different PL tones to maximize repeater sharing and minimize interference, ensuring that repeaters can share frequencies when using different PL tones."
+ },
+ {
+ "category": "Geographical Considerations",
+ "description": "Address the impact of geographical features, such as mountainous areas, on line-of-sight propagation and propose solutions to mitigate these effects."
+ },
+ {
+ "category": "Scalability Analysis",
+ "description": "Analyze how the solution scales from accommodating 1,000 users to 10,000 users, including any changes in repeater requirements or configurations."
+ },
+ {
+ "category": "Mathematical Modeling",
+ "description": "Provide a detailed mathematical model that includes assumptions, calculations, and logical reasoning to support the proposed solution."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Identify and justify any assumptions made in the modeling process, and discuss the limitations of the proposed solution."
+ }
+ ]
+ }
+ },
+ "2011_Snowboard_Course": {
+ "year": "2011",
+ "title": "Snowboard Course",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2011/MCM-A/index.html",
+ "question": "Determine the shape of a snowboard course (currently known as a \"halfpipe\") to maximize the production of \"vertical air\" by a skilled snowboarder. \"Vertical air\" is the maximum vertical distance above the edge of the halfpipe. Tailor the shape to optimize other possible requirements, such as maximum twist in the air. What tradeoffs may be required to develop a \"practical\" course?",
+ "requirements": [
+ {
+ "category": "Objective Function",
+ "description": "Define and justify the objective function used to measure 'vertical air' and other performance metrics like twist."
+ },
+ {
+ "category": "Mathematical Modeling",
+ "description": "Develop a mathematical model of the halfpipe shape, including equations and constraints that represent the physical characteristics of the course."
+ },
+ {
+ "category": "Optimization Techniques",
+ "description": "Apply appropriate optimization techniques to find the shape that maximizes vertical air and other desired metrics, explaining the choice of method."
+ },
+ {
+ "category": "Tradeoff Analysis",
+ "description": "Identify and analyze tradeoffs between maximizing vertical air and other factors such as twist, safety, and practicality."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Clearly state and justify any assumptions made in the modeling process, such as snowboarder skill level or environmental conditions."
+ },
+ {
+ "category": "Validation",
+ "description": "Provide a method for validating the model and its predictions, possibly through simulation or comparison with real-world data."
+ },
+ {
+ "category": "Practical Considerations",
+ "description": "Discuss practical considerations for implementing the optimized halfpipe design, including construction feasibility and cost."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a deep understanding of geometric modeling and calculus to determine the optimal shape of the halfpipe for maximizing vertical air.",
+ "details": "You are a mathematician with expertise in geometric modeling and calculus. You should focus on the mathematical formulation of the halfpipe's shape, ensuring that the equations accurately represent the physical constraints and desired outcomes. Pay attention to the derivation of the equations and the assumptions made in the model. Your skills in optimization and differential equations will be crucial in evaluating the solutions for maximizing vertical air."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to snowboarder performance and environmental conditions to inform the model's parameters and validate its predictions.",
+ "details": "You are a data scientist with expertise in data analysis and machine learning. You should focus on the data-driven aspects of the model, such as the collection and analysis of performance data from snowboarders. Ensure that the data used is relevant and accurately reflects the conditions of the halfpipe. Your skills in statistical analysis and predictive modeling will be essential in evaluating the model's ability to predict vertical air and other performance metrics."
+ },
+ {
+ "name": "Sports Engineer",
+ "thoughts": "The problem requires an understanding of biomechanics and sports engineering to ensure the halfpipe design is practical and enhances snowboarder performance.",
+ "details": "You are a sports engineer with expertise in biomechanics and sports equipment design. You should focus on the practical aspects of the halfpipe design, ensuring that it is feasible and safe for snowboarders. Pay attention to the interaction between the snowboarder and the halfpipe, considering factors such as speed, angle, and material properties. Your skills in engineering design and human factors will be crucial in evaluating the tradeoffs between maximizing vertical air and ensuring safety and practicality."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem requires consideration of environmental factors that may affect the halfpipe's design and performance, such as weather conditions and sustainability.",
+ "details": "You are an environmental scientist with expertise in assessing environmental impacts and sustainability. You should focus on the environmental considerations of the halfpipe design, such as the impact of weather conditions on performance and the sustainability of materials used. Pay attention to how environmental factors may influence the model's predictions and the practicality of the design. Your skills in environmental assessment and sustainable design will be essential in evaluating the model's ability to balance performance with environmental responsibility."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Objective Function",
+ "description": "Define and justify the objective function used to measure 'vertical air' and other performance metrics like twist."
+ },
+ {
+ "category": "Mathematical Modeling",
+ "description": "Develop a mathematical model of the halfpipe shape, including equations and constraints that represent the physical characteristics of the course."
+ },
+ {
+ "category": "Optimization Techniques",
+ "description": "Apply appropriate optimization techniques to find the shape that maximizes vertical air and other desired metrics, explaining the choice of method."
+ },
+ {
+ "category": "Tradeoff Analysis",
+ "description": "Identify and analyze tradeoffs between maximizing vertical air and other factors such as twist, safety, and practicality."
+ },
+ {
+ "category": "Assumptions",
+ "description": "Clearly state and justify any assumptions made in the modeling process, such as snowboarder skill level or environmental conditions."
+ },
+ {
+ "category": "Validation",
+ "description": "Provide a method for validating the model and its predictions, possibly through simulation or comparison with real-world data."
+ },
+ {
+ "category": "Practical Considerations",
+ "description": "Discuss practical considerations for implementing the optimized halfpipe design, including construction feasibility and cost."
+ }
+ ]
+ }
+ },
+ "2011_Space_Shuttle_Problem:": {
+ "year": "2011",
+ "title": "Space Shuttle Problem: No More Space Shuttles",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2011/HIMCM-A/index.html",
+ "question": "On July 21, 2011, the 135th and final US Space Shuttle landed in Florida after its 13-day mission into orbit, complete with a docking at the International Space Station (ISS). NASA will now have to rely on other nations or commercial endeavors to travel into space until a replacement vehicle is developed and constructed. Develop a comprehensive ten-year plan complete with costs, payloads, and flight schedules to maintain the ISS.\n\nSome interesting facts possibly worthy of your consideration:\n\nThe ISS is at full capacity with 6 astronauts, but can surge during shuttle docks to as high as 13. The ISS is scheduled to remain in service until at least the year 2020. Historically, transport to the ISS using US Shuttles has cost between $5000-10,000 per pound. Shuttle missions have lasted approximately 10-14 days in orbit. Missions on board the ISS typically last around six months. Recently, progress has been made within private industry to launch unmanned rockets into space. Russia is willing to launch US astronauts into space at a cost of about $60 million each.",
+ "requirements": [
+ {
+ "category": "Feasibility and comprehensiveness",
+ "description": "Evaluate the overall feasibility of the proposed plan, including its ability to maintain the ISS with the given constraints and assumptions."
+ },
+ {
+ "category": "Cost analysis",
+ "description": "Assess the accuracy and thoroughness of the cost estimation for transportation, including comparisons between different options (e.g., Russian launches, private industry solutions)."
+ },
+ {
+ "category": "Payload management",
+ "description": "Examine the plan's approach to managing payloads, ensuring that the necessary supplies and equipment are delivered to the ISS efficiently and within budget."
+ },
+ {
+ "category": "Flight scheduling",
+ "description": "Analyze the proposed flight schedules for their ability to maintain the ISS's operational capacity, considering the duration of missions and the number of astronauts."
+ },
+ {
+ "category": "Use of private industry",
+ "description": "Evaluate the incorporation of private industry solutions in the plan, including the potential benefits and risks associated with these options."
+ },
+ {
+ "category": "Assumptions and constraints",
+ "description": "Identify and assess the assumptions made in the plan, such as the continued operation of the ISS until 2020 and the costs associated with different transportation methods."
+ },
+ {
+ "category": "Risk management",
+ "description": "Consider the plan's approach to managing risks, including contingencies for potential delays or failures in transportation and supply delivery."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to optimize flight schedules, payload capacities, and cost estimations over a ten-year period.",
+ "details": "You are a mathematician with expertise in formulating and solving complex equations related to space missions. You should focus on optimizing the mathematical models that predict costs, payload capacities, and flight schedules. Pay attention to the assumptions made in the models and ensure they are realistic and based on historical data. Your skills in calculus, linear algebra, and optimization techniques will be crucial in evaluating the solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing historical data and trends to inform the development of a ten-year plan for maintaining the ISS.",
+ "details": "You are a data scientist with expertise in data analysis and statistical modeling. Your role is to review the data-driven aspects of the modeling solutions, ensuring that the data used is accurate and relevant. You should evaluate the statistical methods used to forecast costs and payload requirements, and assess the reliability of the data sources. Your skills in machine learning and data visualization will help in interpreting complex datasets and providing insights into future trends."
+ },
+ {
+ "name": "Aerospace Engineer",
+ "thoughts": "The problem requires technical expertise in spacecraft design, payload management, and flight operations to develop a feasible plan for ISS maintenance.",
+ "details": "You are an aerospace engineer with expertise in spacecraft systems and operations. Your role is to review the technical feasibility of the proposed solutions, focusing on the design and capabilities of replacement vehicles and payload management strategies. You should assess the engineering aspects of flight schedules and ensure that they align with the operational requirements of the ISS. Your knowledge of propulsion systems, structural analysis, and mission planning will be essential in evaluating the practicality of the solutions."
+ },
+ {
+ "name": "Economist",
+ "thoughts": "The problem involves significant financial planning and cost analysis to ensure the sustainability of the ISS over the next decade.",
+ "details": "You are an economist with expertise in cost analysis and financial modeling. Your role is to review the economic aspects of the proposed solutions, focusing on cost estimations and budget allocations. You should evaluate the financial models used to predict expenses and revenues, ensuring they are based on sound economic principles. Your skills in market analysis and economic forecasting will be crucial in assessing the viability of commercial endeavors and international collaborations for space travel."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Feasibility and comprehensiveness",
+ "description": "Evaluate the overall feasibility of the proposed plan, including its ability to maintain the ISS with the given constraints and assumptions."
+ },
+ {
+ "category": "Cost analysis",
+ "description": "Assess the accuracy and thoroughness of the cost estimation for transportation, including comparisons between different options (e.g., Russian launches, private industry solutions)."
+ },
+ {
+ "category": "Payload management",
+ "description": "Examine the plan's approach to managing payloads, ensuring that the necessary supplies and equipment are delivered to the ISS efficiently and within budget."
+ },
+ {
+ "category": "Flight scheduling",
+ "description": "Analyze the proposed flight schedules for their ability to maintain the ISS's operational capacity, considering the duration of missions and the number of astronauts."
+ },
+ {
+ "category": "Use of private industry",
+ "description": "Evaluate the incorporation of private industry solutions in the plan, including the potential benefits and risks associated with these options."
+ },
+ {
+ "category": "Assumptions and constraints",
+ "description": "Identify and assess the assumptions made in the plan, such as the continued operation of the ISS until 2020 and the costs associated with different transportation methods."
+ },
+ {
+ "category": "Risk management",
+ "description": "Consider the plan's approach to managing risks, including contingencies for potential delays or failures in transportation and supply delivery."
+ }
+ ]
+ }
+ },
+ "2012_Camping_along_the": {
+ "year": "2012",
+ "title": "Camping along the Big Long River",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2012/MCM-B/index.html",
+ "question": "Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar-powered rubber rafts, which travel on average 4 mph, or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six-month period (the rest of the year it is too cold for river trips). There are Y campsites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long River\u2019s rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one-page summary sheet, prepare a one-page memo to the managers of the river describing your key findings.",
+ "requirements": [
+ {
+ "category": "Objective Identification",
+ "description": "Clearly identify the main objectives of the problem, including maximizing the number of trips and ensuring minimal contact between groups."
+ },
+ {
+ "category": "Trip Scheduling Model",
+ "description": "Develop a model to schedule trips of varying durations and propulsion types, ensuring efficient use of campsites and adherence to wilderness experience requirements."
+ },
+ {
+ "category": "Campsite Utilization",
+ "description": "Analyze and model the distribution and utilization of campsites along the river to prevent overlap and ensure no two groups occupy the same site simultaneously."
+ },
+ {
+ "category": "Carrying Capacity Determination",
+ "description": "Determine the carrying capacity of the river, considering factors such as campsite availability, trip duration, and propulsion type."
+ },
+ {
+ "category": "Assumptions and Constraints",
+ "description": "Identify and justify any assumptions made in the model, such as uniform distribution of campsites and average travel speeds of boats."
+ },
+ {
+ "category": "Optimization Techniques",
+ "description": "Apply appropriate optimization techniques to find the best mix of trips that maximizes the number of trips while meeting all constraints."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct sensitivity analysis to understand how changes in parameters (e.g., number of campsites, trip duration) affect the optimal schedule and carrying capacity."
+ },
+ {
+ "category": "Deliverable Requirements",
+ "description": "Prepare a one-page memo summarizing key findings and recommendations for river managers, ensuring clarity and conciseness."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves complex mathematical modeling to optimize the scheduling of river trips and determine the carrying capacity of the river. This requires formulating equations and constraints that account for the various factors such as trip duration, propulsion type, and campsite availability.",
+ "details": "You are a mathematician with expertise in optimization and mathematical modeling. Your role is to ensure that the mathematical formulations accurately represent the problem constraints and objectives. Pay attention to the assumptions made in the model and verify that the equations are correctly derived and solvable. Your skills in linear programming, combinatorial optimization, and constraint satisfaction will be crucial in evaluating the proposed solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing data related to trip durations, campsite usage, and river traffic to inform the model. A data-driven approach will help in understanding patterns and making predictions about the impact of increasing the number of trips.",
+ "details": "You are a data scientist with expertise in data analysis and statistical modeling. Your role is to review the data inputs used in the model, ensuring they are accurate and representative of real-world conditions. Focus on the data collection methods, data quality, and the statistical techniques used to analyze the data. Your knowledge of machine learning and predictive analytics will be valuable in assessing the model's ability to forecast the effects of different scheduling scenarios."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem involves ensuring that the increased number of trips does not negatively impact the river's ecosystem. An environmental scientist can provide insights into the ecological carrying capacity and the potential environmental impacts of increased river traffic.",
+ "details": "You are an environmental scientist with expertise in ecosystem management and environmental impact assessment. Your role is to evaluate the model's consideration of environmental factors, such as the impact of increased human activity on wildlife and natural resources. Pay attention to how the model incorporates ecological constraints and sustainability principles. Your understanding of environmental regulations and conservation practices will be essential in ensuring that the proposed solutions align with environmental protection goals."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem requires optimizing the scheduling and logistics of river trips, which is a classic operations research problem. An operations research analyst can provide expertise in developing efficient algorithms and decision-making processes.",
+ "details": "You are an operations research analyst with expertise in optimization and logistics. Your role is to assess the efficiency and feasibility of the proposed scheduling solutions. Focus on the algorithms used for trip scheduling and resource allocation, ensuring they are both effective and computationally efficient. Your skills in simulation, queuing theory, and decision analysis will be crucial in evaluating the model's ability to handle various scenarios and constraints."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Objective Identification",
+ "description": "Clearly identify the main objectives of the problem, including maximizing the number of trips and ensuring minimal contact between groups."
+ },
+ {
+ "category": "Trip Scheduling Model",
+ "description": "Develop a model to schedule trips of varying durations and propulsion types, ensuring efficient use of campsites and adherence to wilderness experience requirements."
+ },
+ {
+ "category": "Campsite Utilization",
+ "description": "Analyze and model the distribution and utilization of campsites along the river to prevent overlap and ensure no two groups occupy the same site simultaneously."
+ },
+ {
+ "category": "Carrying Capacity Determination",
+ "description": "Determine the carrying capacity of the river, considering factors such as campsite availability, trip duration, and propulsion type."
+ },
+ {
+ "category": "Assumptions and Constraints",
+ "description": "Identify and justify any assumptions made in the model, such as uniform distribution of campsites and average travel speeds of boats."
+ },
+ {
+ "category": "Optimization Techniques",
+ "description": "Apply appropriate optimization techniques to find the best mix of trips that maximizes the number of trips while meeting all constraints."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct sensitivity analysis to understand how changes in parameters (e.g., number of campsites, trip duration) affect the optimal schedule and carrying capacity."
+ },
+ {
+ "category": "Deliverable Requirements",
+ "description": "Prepare a one-page memo summarizing key findings and recommendations for river managers, ensuring clarity and conciseness."
+ }
+ ]
+ }
+ },
+ "2013_Bank_Service_Problem": {
+ "year": "2013",
+ "title": "Bank Service Problem",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2013/HIMCM-B/index.html",
+ "question": "The bank manager is trying to improve customer satisfaction by offering better service. Management wants the average customer to wait less than 2 minutes for service and the average length of the queue (length of the waiting line) to be 2 persons or fewer. The bank estimates it serves about 150 customers per day. The existing arrival and service times are given in the tables below.\n\nTime between arrival (min.) Probability \n0 0.10 \n1 0.15 \n2 0.10 \n3 0.35 \n4 0.25 \n5 0.05 \n\nTable 1: Arrival times\n\nService Time (min.) Probability \n1 0.25 \n2 0.20 \n3 0.40 \n4 0.15 \n\nTable 2: Service times\n\n(1) Build a mathematical model of the system.\n\n(2) Determine if the current customer service is satisfactory according to the manager guidelines. If not, determine, through modeling, the minimal changes for servers required to accomplish the manager's goal.\n\n(3) In addition to the contest's format, prepare a short 1-2 page non-technical letter to the bank's management with your final recommendations.",
+ "requirements": [
+ {
+ "category": "Model Construction",
+ "description": "Evaluate the mathematical model built to represent the bank's customer service system, including the use of arrival and service time distributions."
+ },
+ {
+ "category": "Analysis of Current System",
+ "description": "Assess the analysis of the current system's performance against the manager's guidelines, specifically the average wait time and queue length."
+ },
+ {
+ "category": "Solution Proposal",
+ "description": "Examine the proposed changes to the server system to meet the manager's goals, ensuring minimal changes are suggested and justified through modeling."
+ },
+ {
+ "category": "Assumptions and Justifications",
+ "description": "Check for any implicit assumptions made in the model and their justifications, such as customer arrival patterns and service time distributions."
+ },
+ {
+ "category": "Non-Technical Communication",
+ "description": "Evaluate the clarity and effectiveness of the non-technical letter to management, ensuring it accurately conveys the recommendations and their rationale."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires constructing a mathematical model to analyze the queuing system and determine the service efficiency. A mathematician is essential for formulating the equations that describe the arrival and service processes, and for applying queuing theory to assess the system's performance.",
+ "details": "You are a mathematician with expertise in queuing theory and mathematical modeling. Your role involves reviewing the mathematical formulation of the problem, ensuring that the model accurately represents the arrival and service processes. Pay attention to the assumptions made in the model and verify the calculations that predict waiting times and queue lengths. Your expertise will help ensure that the model is robust and provides reliable insights into the bank's service efficiency."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing probabilistic data related to customer arrivals and service times. A data scientist is crucial for processing this data, performing simulations, and using statistical methods to validate the model's predictions.",
+ "details": "You are a data scientist skilled in data analysis and statistical modeling. Your role is to review the data handling and simulation aspects of the solution. Ensure that the probabilistic data is correctly interpreted and that simulations are conducted to predict system performance under various scenarios. Your expertise in statistical methods will be vital in assessing the accuracy of the model's predictions and in recommending data-driven improvements to the service process."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem is centered around optimizing the bank's service operations to meet customer satisfaction goals. An operations research analyst is essential for applying optimization techniques to improve service efficiency and for recommending operational changes.",
+ "details": "You are an operations research analyst with expertise in optimization and efficiency improvement. Your role involves reviewing the solution for operational feasibility and effectiveness. Focus on the optimization techniques used to minimize waiting times and queue lengths, and evaluate the practicality of the proposed changes to the service process. Your insights will be crucial in ensuring that the recommendations are implementable and aligned with the bank's operational capabilities."
+ },
+ {
+ "name": "Customer Experience Specialist",
+ "thoughts": "The ultimate goal of the problem is to enhance customer satisfaction. A customer experience specialist is vital for ensuring that the proposed solutions align with customer expectations and improve their overall experience.",
+ "details": "You are a customer experience specialist with expertise in understanding customer needs and satisfaction metrics. Your role is to review the solution from the perspective of customer impact. Evaluate whether the proposed changes will genuinely enhance the customer experience and meet the satisfaction goals set by the bank manager. Your feedback will be important in ensuring that the recommendations are not only operationally sound but also customer-centric, leading to improved satisfaction and loyalty."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Construction",
+ "description": "Evaluate the mathematical model built to represent the bank's customer service system, including the use of arrival and service time distributions."
+ },
+ {
+ "category": "Analysis of Current System",
+ "description": "Assess the analysis of the current system's performance against the manager's guidelines, specifically the average wait time and queue length."
+ },
+ {
+ "category": "Solution Proposal",
+ "description": "Examine the proposed changes to the server system to meet the manager's goals, ensuring minimal changes are suggested and justified through modeling."
+ },
+ {
+ "category": "Assumptions and Justifications",
+ "description": "Check for any implicit assumptions made in the model and their justifications, such as customer arrival patterns and service time distributions."
+ },
+ {
+ "category": "Non-Technical Communication",
+ "description": "Evaluate the clarity and effectiveness of the non-technical letter to management, ensuring it accurately conveys the recommendations and their rationale."
+ }
+ ]
+ }
+ },
+ "2013_The_Ultimate_Brownie": {
+ "year": "2013",
+ "title": "The Ultimate Brownie Pan",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2013/MCM-A/index.html",
+ "question": "When baking in a rectangular pan, heat is concentrated in the 4 corners, and the product gets overcooked at the corners (and to a lesser extent at the edges). In a round pan, the heat is distributed evenly over the entire outer edge, and the product is not overcooked at the edges. However, since most ovens are rectangular in shape, using round pans is not efficient with respect to using the space in an oven. Develop a model to show the distribution of heat across the outer edge of a pan for pans of different shapes - rectangular to circular and other shapes in between.\n\nAssume 1. A width to length ratio of W/L for the oven, which is rectangular in shape. 2. Each pan must have an area of A. 3. Initially, two racks in the oven, evenly spaced.\n\nDevelop a model that can be used to select the best type of pan (shape) under the following conditions: 1. Maximize the number of pans that can fit in the oven (N) 2. Maximize even distribution of heat (H) for the pan 3. Optimize a combination of conditions (1) and (2) where weights p and (1-p) are assigned to illustrate how the results vary with different values of W/L and p.\n\nIn addition to your MCM formatted solution, prepare a one to two-page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results.",
+ "requirements": [
+ {
+ "category": "Heat Distribution Modeling",
+ "description": "Develop a mathematical model that accurately represents the heat distribution across the outer edge of pans of different shapes, including rectangular, circular, and intermediate shapes."
+ },
+ {
+ "category": "Pan Shape Optimization",
+ "description": "Create a model to determine the optimal pan shape that maximizes the number of pans fitting in the oven while ensuring even heat distribution."
+ },
+ {
+ "category": "Parameter Analysis",
+ "description": "Analyze how the results vary with different values of the width to length ratio (W/L) of the oven and the weight parameter (p) for optimizing pan selection."
+ },
+ {
+ "category": "Combination Optimization",
+ "description": "Develop a model that optimizes a combination of maximizing the number of pans (N) and maximizing even heat distribution (H), using weights p and (1-p)."
+ },
+ {
+ "category": "Assumptions and Constraints",
+ "description": "Clearly state and justify any assumptions made in the model, such as the fixed area of each pan and the initial setup of two racks in the oven."
+ },
+ {
+ "category": "Solution Validation",
+ "description": "Validate the model by comparing the theoretical results with expected real-world outcomes, ensuring the model's reliability and accuracy."
+ },
+ {
+ "category": "Advertising Sheet",
+ "description": "Prepare a concise and engaging one to two-page advertising sheet for the Brownie Gourmet Magazine that highlights the design and results of the model."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to understand the heat distribution across different pan shapes and optimize the space utilization in a rectangular oven.",
+ "details": "You are a mathematician with expertise in geometric modeling and optimization. Your role involves formulating equations that describe heat distribution patterns and solving these equations to find optimal pan shapes. Pay attention to the mathematical principles underlying heat transfer and spatial geometry. Ensure that the model accurately represents the physical constraints and objectives, such as maximizing pan count and even heat distribution."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to heat distribution and pan placement, requiring statistical methods to interpret results and optimize conditions.",
+ "details": "You are a data scientist skilled in data analysis and machine learning. Your role is to process and analyze data from simulations or experiments on heat distribution across different pan shapes. Focus on identifying patterns and correlations in the data that can inform the model's parameters. Use statistical tools to validate the model's predictions and ensure that the optimization criteria are met effectively."
+ },
+ {
+ "name": "Thermal Engineer",
+ "thoughts": "Understanding the principles of heat transfer and thermal dynamics is crucial to accurately model the heat distribution in different pan shapes.",
+ "details": "You are a thermal engineer with expertise in heat transfer and thermal dynamics. Your role is to provide insights into how heat interacts with different materials and shapes, ensuring the model reflects realistic thermal behavior. Pay attention to the material properties of the pans and the oven's heat source characteristics. Evaluate the model's assumptions about heat distribution and suggest improvements based on empirical thermal data."
+ },
+ {
+ "name": "Culinary Scientist",
+ "thoughts": "The problem involves practical considerations of baking, requiring knowledge of how different pan shapes affect cooking outcomes.",
+ "details": "You are a culinary scientist with expertise in food science and cooking techniques. Your role is to assess how the model's predictions align with real-world baking results. Consider the impact of pan shape on cooking quality, such as texture and doneness. Provide feedback on the model's applicability to actual baking scenarios and suggest adjustments to improve its relevance to culinary practices."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Heat Distribution Modeling",
+ "description": "Develop a mathematical model that accurately represents the heat distribution across the outer edge of pans of different shapes, including rectangular, circular, and intermediate shapes."
+ },
+ {
+ "category": "Pan Shape Optimization",
+ "description": "Create a model to determine the optimal pan shape that maximizes the number of pans fitting in the oven while ensuring even heat distribution."
+ },
+ {
+ "category": "Parameter Analysis",
+ "description": "Analyze how the results vary with different values of the width to length ratio (W/L) of the oven and the weight parameter (p) for optimizing pan selection."
+ },
+ {
+ "category": "Combination Optimization",
+ "description": "Develop a model that optimizes a combination of maximizing the number of pans (N) and maximizing even heat distribution (H), using weights p and (1-p)."
+ },
+ {
+ "category": "Assumptions and Constraints",
+ "description": "Clearly state and justify any assumptions made in the model, such as the fixed area of each pan and the initial setup of two racks in the oven."
+ },
+ {
+ "category": "Solution Validation",
+ "description": "Validate the model by comparing the theoretical results with expected real-world outcomes, ensuring the model's reliability and accuracy."
+ },
+ {
+ "category": "Advertising Sheet",
+ "description": "Prepare a concise and engaging one to two-page advertising sheet for the Brownie Gourmet Magazine that highlights the design and results of the model."
+ }
+ ]
+ }
+ },
+ "2014_The_Next_Plague?": {
+ "year": "2014",
+ "title": "The Next Plague?",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2014/HIMCM-B/index.html",
+ "question": "In 2014, the world saw the infectious Ebola virus spreading in western Africa. Throughout human history, epidemics have come and gone with some infecting and/or killing thousands and lasting for years and others taking less of a human toll. Some believe these events are just nature\u2019s way of controlling the growth of a species while others think they could be a conspiracy or deliberate act to cause harm. This problem will most likely come down to how to expend (or not expend) scarce resources (doctors, containment facilities, money, research, serums, etc...) to deal with a crisis.\n\nSituation: A routine humanitarian mission on an island in Indonesia reported a small village where almost half of its 300 inhabitants are showing similar symptoms. In the past week, 15 of the \"infected\" have died. This village is known to trade with nearby villages and other islands. Your modeling team works for a major center of disease control in the capital of your country (or if you prefer, for the International World Health Organization).\n\nRequirement 1: Develop a mathematical model(s) that performs the following functions as well as how/when to best allocate these scarce resources and... Determines and classifies the type and severity of the spread of the disease Determines if an epidemic is contained or not Triggers appropriate measures (when to treat, when to transport victims, when to restrict movement, when to let a disease run its course, etc...) to contain a disease Note: While you may want to start with the well-known \"SIR\" family of models for parts of this problem, consider others, modifications to the SIR, multiple models, or creating your own.\n\nRequirement 2: Based on the information given, your model, and the assumptions your team has made, what initial recommendations does your team have for your country\u2019s center for disease control? (Give 3-5 recommendations with justifications) Additional Situational Information: A multi-national research team just returned to your country\u2019s capital after spending 7 days gathering information in the infected village. Requirement 3: You can ask them up to 3 questions to improve your model. What would you ask and why? Additional Situational Information: The multi-national research team concluded that the disease: Appears to spread through contact with bodily fluids of an infected person The elderly and children are more likely to die if infected A nearby island is starting to show similar signs of infection One of the researchers that returned to your capital appears infected Requirement 4: How does the additional information above change/modify your model? Requirement 5: Write a one-page synopsis of your findings for your local non-technical news outlet.",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the mathematical model's ability to classify the type and severity of the disease spread, including the use of SIR models or other innovative approaches."
+ },
+ {
+ "category": "Resource Allocation",
+ "description": "Assess how the model determines the optimal allocation of scarce resources such as medical personnel, facilities, and funding to manage the outbreak."
+ },
+ {
+ "category": "Containment Strategy",
+ "description": "Grade the model's effectiveness in triggering appropriate measures for disease containment, including treatment, transportation, movement restrictions, and natural progression."
+ },
+ {
+ "category": "Initial Recommendations",
+ "description": "Evaluate the clarity, feasibility, and justification of the initial recommendations provided to the country's center for disease control based on the model and assumptions."
+ },
+ {
+ "category": "Question Formulation",
+ "description": "Assess the relevance and strategic importance of the three questions posed to the research team to improve the model."
+ },
+ {
+ "category": "Model Adaptation",
+ "description": "Evaluate how the model is modified or adapted in response to additional information about the disease's transmission, vulnerable populations, and new infection sites."
+ },
+ {
+ "category": "Communication",
+ "description": "Grade the effectiveness of the one-page synopsis in communicating findings to a non-technical audience, ensuring clarity and accessibility."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires the development of mathematical models to understand the spread and control of the disease, which is a fundamental task for a mathematician. They can apply their expertise in differential equations and modeling techniques to create and refine models like the SIR model or develop new ones tailored to the specific characteristics of the Ebola virus.",
+ "details": "You are a mathematician with expertise in epidemiological modeling. Your role is crucial in formulating mathematical models that can predict the spread of the disease and evaluate the effectiveness of different intervention strategies. You should focus on the accuracy of the model assumptions, the robustness of the equations used, and the applicability of the model to real-world scenarios. Your evaluation should ensure that the models are mathematically sound and capable of providing reliable predictions for resource allocation and containment measures."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing complex datasets related to the spread of the disease, patient demographics, and resource allocation. A data scientist can leverage statistical methods and machine learning techniques to extract insights from the data, which are essential for informing the mathematical models and making evidence-based recommendations.",
+ "details": "You are a data scientist with expertise in data analysis and machine learning. Your role is to process and analyze the data collected from the infected village and other sources to identify patterns and trends in the disease spread. You should pay attention to data quality, missing values, and potential biases in the data. Your evaluation should focus on the integration of data-driven insights into the mathematical models and the validation of model predictions against real-world data. You should also consider how data can inform the allocation of scarce resources effectively."
+ },
+ {
+ "name": "Epidemiologist",
+ "thoughts": "An epidemiologist is essential for understanding the biological and social factors influencing the spread of the disease. They can provide insights into transmission dynamics, risk factors, and the effectiveness of public health interventions, which are critical for developing accurate models and recommendations.",
+ "details": "You are an epidemiologist with expertise in infectious disease dynamics. Your role is to interpret the biological and social aspects of the disease spread, including transmission routes, population susceptibility, and intervention strategies. You should focus on the epidemiological validity of the model assumptions and the practical implications of the model outcomes. Your evaluation should ensure that the models consider the latest epidemiological research and are aligned with public health goals. You should also assess the feasibility and impact of the recommended interventions based on epidemiological evidence."
+ },
+ {
+ "name": "Public Health Expert",
+ "thoughts": "A public health expert is crucial for evaluating the practical implementation of the model recommendations and ensuring that they align with public health policies and resource constraints. They can provide insights into the logistics of resource allocation and the socio-economic impact of interventions.",
+ "details": "You are a public health expert with experience in managing health crises and resource allocation. Your role is to assess the practicality and effectiveness of the model recommendations in the context of public health policies and resource limitations. You should focus on the logistical aspects of implementing the interventions, including the availability of medical personnel, facilities, and funding. Your evaluation should ensure that the recommendations are feasible, cost-effective, and socially acceptable. You should also consider the broader socio-economic implications of the interventions and how they can be communicated effectively to the public."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the mathematical model's ability to classify the type and severity of the disease spread, including the use of SIR models or other innovative approaches."
+ },
+ {
+ "category": "Resource Allocation",
+ "description": "Assess how the model determines the optimal allocation of scarce resources such as medical personnel, facilities, and funding to manage the outbreak."
+ },
+ {
+ "category": "Containment Strategy",
+ "description": "Grade the model's effectiveness in triggering appropriate measures for disease containment, including treatment, transportation, movement restrictions, and natural progression."
+ },
+ {
+ "category": "Initial Recommendations",
+ "description": "Evaluate the clarity, feasibility, and justification of the initial recommendations provided to the country's center for disease control based on the model and assumptions."
+ },
+ {
+ "category": "Question Formulation",
+ "description": "Assess the relevance and strategic importance of the three questions posed to the research team to improve the model."
+ },
+ {
+ "category": "Model Adaptation",
+ "description": "Evaluate how the model is modified or adapted in response to additional information about the disease's transmission, vulnerable populations, and new infection sites."
+ },
+ {
+ "category": "Communication",
+ "description": "Grade the effectiveness of the one-page synopsis in communicating findings to a non-technical audience, ensuring clarity and accessibility."
+ }
+ ]
+ }
+ },
+ "2015_Is_it_sustainable?": {
+ "year": "2015",
+ "title": "Is it sustainable?",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2015/ICM-D/index.html",
+ "question": "2015_ICM_Problem_D.pdf 2015_ICM_Problem_D.pdf Is it sustainable?\n\n### Text in the PDF File: 2015_ICM_Problem_D.pdf\n\n**2015 ICM Problem D: Is it Sustainable?**\n\n**Background:**\nThe challenge is to manage increasing population and consumption with finite resources while increasing equity and eradicating poverty. Sustainable development, defined by the 1987 Brundtland Report, aims to meet present needs without compromising future generations. The UN predicts a population of 9 billion by 2050, increasing strain on resources. Sustainable development focuses on reducing poverty, promoting sustainable consumption, and protecting natural resources.\n\n**Problem Statement:**\nThe International Conglomerate of Money (ICM) seeks to use its resources to create a sustainable world, focusing on developing countries.\n\n**Tasks:**\n\n1. **Develop a Sustainability Model:**\n - Create a model to measure and distinguish sustainable countries and policies.\n - Factors may include human health, food security, clean water access, environmental quality, energy access, livelihoods, community vulnerability, and equitable development.\n - Define criteria for sustainability.\n\n2. **Select a Country:**\n - Choose a country from the UN's list of 48 Least Developed Countries (LDCs).\n - Develop a 20-year sustainable development plan for the selected country, considering demographic, natural resources, economic, social, and political conditions.\n\n3. **Evaluate the Plan:**\n - Assess the impact of the 20-year plan on the country's sustainability measure.\n - Predict changes over 20 years, considering factors like climate change, development aid, foreign investment, natural disasters, and government instability.\n - Identify the most effective strategies for sustainability.\n\n4. **Write a Report:**\n - Prepare a report detailing the model, sustainability measure, development plan, and its effects.\n - Discuss the model's strengths and weaknesses.\n - The report will guide ICM's investment in sustainability strategies for LDCs.\n\n**Resources:**\n- UN Sustainable Development Knowledge Platform\n- Ecological Footprint Network\n- World Bank Data\n- International Institute for Sustainable Development\n\n**References:**\n- WCED, \"Our Common Future,\" 1987.\n- UN, \"The Future We Want,\" 2012.\n- Bell & Morse, \"Sustainability Indicators,\" 2008.\n- Daly, \"Operational Principles of Sustainable Development,\" 1990.\n- Kates et al., \"What is Sustainable Development,\" 2005.",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the comprehensiveness and robustness of the sustainability model, including the selection and justification of factors such as human health, food security, and environmental quality."
+ },
+ {
+ "category": "Criteria Definition",
+ "description": "Assess the clarity and appropriateness of the criteria defined for measuring sustainability, ensuring they are specific, measurable, and relevant to the problem statement."
+ },
+ {
+ "category": "Country Selection",
+ "description": "Examine the rationale behind the choice of the country from the UN's list of Least Developed Countries, considering demographic, natural resources, economic, social, and political conditions."
+ },
+ {
+ "category": "Development Plan",
+ "description": "Grade the feasibility and comprehensiveness of the 20-year sustainable development plan, including strategies for addressing demographic, economic, social, and political challenges."
+ },
+ {
+ "category": "Impact Evaluation",
+ "description": "Evaluate the accuracy and depth of the assessment of the plan's impact on the country's sustainability measure, including predictions of changes over 20 years."
+ },
+ {
+ "category": "Strategy Identification",
+ "description": "Assess the identification and justification of the most effective strategies for achieving sustainability in the selected country."
+ },
+ {
+ "category": "Report Writing",
+ "description": "Grade the clarity, organization, and thoroughness of the report detailing the model, sustainability measure, development plan, and its effects, including discussion of strengths and weaknesses."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires the development of a sustainability model, which involves formulating and solving complex mathematical equations to measure and distinguish sustainable countries and policies.",
+ "details": "You are a mathematician with expertise in mathematical modeling and quantitative analysis. Your role is crucial in developing the sustainability model by applying mathematical principles to define criteria for sustainability. You should focus on ensuring the model is robust, accurate, and capable of handling various factors such as human health, food security, and environmental quality. Pay attention to the assumptions and limitations of the model, and ensure that it can be adapted to different countries and scenarios."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets related to sustainability factors, such as demographic, economic, and environmental data, to inform the model and evaluate the development plan.",
+ "details": "You are a data scientist skilled in data analysis, statistical methods, and machine learning. Your expertise is essential in processing and analyzing data from sources like the UN Sustainable Development Knowledge Platform and the World Bank. You should focus on extracting meaningful insights from the data to inform the sustainability model and development plan. Ensure that the data is clean, reliable, and relevant, and use advanced techniques to predict changes over 20 years, considering factors like climate change and government instability."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem involves assessing environmental factors such as clean water access, environmental quality, and natural resource management, which are critical for sustainable development.",
+ "details": "You are an environmental scientist with expertise in ecology, environmental policy, and resource management. Your role is to provide insights into the environmental aspects of the sustainability model and development plan. You should evaluate the impact of proposed strategies on natural resources and environmental quality, ensuring that they promote sustainable consumption and protect ecosystems. Pay attention to the potential effects of climate change and natural disasters, and recommend strategies to mitigate these risks."
+ },
+ {
+ "name": "Economist",
+ "thoughts": "The problem requires understanding economic factors such as livelihoods, equitable development, and foreign investment, which are vital for creating a sustainable development plan.",
+ "details": "You are an economist with expertise in development economics and policy analysis. Your role is to assess the economic viability of the sustainability model and development plan. You should analyze the economic conditions of the selected country, considering factors like poverty reduction, economic growth, and investment opportunities. Focus on identifying strategies that promote equitable development and improve livelihoods while ensuring long-term economic sustainability. Evaluate the potential impact of development aid and foreign investment on the country's economy."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the comprehensiveness and robustness of the sustainability model, including the selection and justification of factors such as human health, food security, and environmental quality."
+ },
+ {
+ "category": "Criteria Definition",
+ "description": "Assess the clarity and appropriateness of the criteria defined for measuring sustainability, ensuring they are specific, measurable, and relevant to the problem statement."
+ },
+ {
+ "category": "Country Selection",
+ "description": "Examine the rationale behind the choice of the country from the UN's list of Least Developed Countries, considering demographic, natural resources, economic, social, and political conditions."
+ },
+ {
+ "category": "Development Plan",
+ "description": "Grade the feasibility and comprehensiveness of the 20-year sustainable development plan, including strategies for addressing demographic, economic, social, and political challenges."
+ },
+ {
+ "category": "Impact Evaluation",
+ "description": "Evaluate the accuracy and depth of the assessment of the plan's impact on the country's sustainability measure, including predictions of changes over 20 years."
+ },
+ {
+ "category": "Strategy Identification",
+ "description": "Assess the identification and justification of the most effective strategies for achieving sustainability in the selected country."
+ },
+ {
+ "category": "Report Writing",
+ "description": "Grade the clarity, organization, and thoroughness of the report detailing the model, sustainability measure, development plan, and its effects, including discussion of strengths and weaknesses."
+ }
+ ]
+ }
+ },
+ "2016_Are_we_heading": {
+ "year": "2016",
+ "title": "Are we heading towards a thirsty planet?",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2016/ICM-E/index.html",
+ "question": "2016_ICM_Problem_E.pdf 2016_ICM_Problem_E.pdf Are we heading towards a thirsty planet?\n\n### Text in the PDF File: 2016_ICM_Problem_E.pdf\n\n**2016 ICM Problem E: Are we heading towards a thirsty planet?**\n\n**Overview:**\nThe United Nations reports that 1.6 billion people face water scarcity, with water use growing at twice the rate of population increase. Water scarcity arises from physical scarcity (inadequate water supply) and economic scarcity (poor management and infrastructure). Climate change and population growth may worsen this issue. The challenge is to determine if increasing personal or industrial consumption, or pollution, is contributing to scarcity.\n\n**Key Questions:**\n- Can clean water be provided to all?\n- How do environmental and social factors affect water availability?\n- What historical actions have impacted water scarcity?\n- What are the geological and ecological reasons for scarcity?\n- What potential exists for new water sources?\n- What demographic and health issues are linked to water scarcity?\n\n**Problem Statement:**\nThe International Clean Water Movement (ICM) seeks solutions to global water problems. Your task is to improve access to clean, fresh water.\n\n**Tasks:**\n\n1. **Model Development:**\n - Create a model to measure a region's ability to provide clean water, considering dynamic supply and demand factors.\n\n2. **Region Analysis:**\n - Select a country or region from the UN water scarcity map where water is heavily or moderately overloaded.\n - Explain the causes of water scarcity, addressing both social and environmental factors.\n\n3. **Future Projection:**\n - Use your model to predict the water situation in the chosen region in 15 years.\n - Assess the impact on citizens' lives, incorporating environmental drivers.\n\n4. **Intervention Plan:**\n - Design a plan addressing all drivers of water scarcity.\n - Discuss the plan's impact on the region and surrounding areas, highlighting strengths and weaknesses.\n\n5. **Future Water Availability:**\n - Project future water availability using your intervention plan and model.\n - Determine if the region can become less susceptible to scarcity and predict when scarcity might become critical.\n\n6. **Report Writing:**\n - Write a 20-page report detailing your model, the region's water scarcity without intervention, your intervention plan, and its effects.\n - Include strengths and weaknesses of your model.\n\n**Resources:**\n- An Overview of the State of the World\u2019s Fresh and Marine Waters (2008)\n- The World\u2019s Water: Information on the World\u2019s Freshwater Resources\n- AQUASTAT by the Food and Agriculture Organization of the United Nations\n- The State of the World's Land and Water Resources for food and agriculture (2011)\n- GrowingBlue: Water. Economics. Life.\n- World Resources Institute",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the comprehensiveness and accuracy of the model in measuring a region's ability to provide clean water, considering dynamic supply and demand factors."
+ },
+ {
+ "category": "Region Analysis",
+ "description": "Assess the selection of the region and the depth of analysis regarding the causes of water scarcity, including social and environmental factors."
+ },
+ {
+ "category": "Future Projection",
+ "description": "Grade the model's ability to predict the water situation in the chosen region in 15 years, including the impact on citizens' lives and environmental drivers."
+ },
+ {
+ "category": "Intervention Plan",
+ "description": "Evaluate the design and feasibility of the intervention plan addressing all drivers of water scarcity, and its potential impact on the region and surrounding areas."
+ },
+ {
+ "category": "Future Water Availability",
+ "description": "Assess the projection of future water availability using the intervention plan and model, including the region's susceptibility to scarcity and critical timelines."
+ },
+ {
+ "category": "Report Writing",
+ "description": "Evaluate the clarity, organization, and thoroughness of the 20-page report detailing the model, region analysis, intervention plan, and its effects, including strengths and weaknesses."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to quantify water scarcity, predict future scenarios, and evaluate intervention plans. Mathematical expertise is crucial for developing robust models that can handle dynamic supply and demand factors.",
+ "details": "You are a mathematician with expertise in creating and analyzing mathematical models related to water scarcity. You should focus on ensuring the model accurately represents the complex interactions between environmental, social, and economic factors. Pay attention to the assumptions made in the model and their implications on the predictions. Your skills in differential equations, optimization, and statistical analysis will be vital in evaluating the model's effectiveness and reliability."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves handling large datasets related to water usage, population growth, climate change, and other factors. Data scientists are essential for processing, analyzing, and extracting meaningful insights from these datasets to inform the model.",
+ "details": "You are a data scientist with expertise in data analysis and machine learning. Your role is to ensure that the data used in the model is accurate, relevant, and comprehensive. You should focus on data preprocessing, feature selection, and model validation. Your skills in statistical analysis, data visualization, and predictive modeling will be crucial in assessing the model's performance and making data-driven recommendations for intervention plans."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "Environmental scientists are crucial for understanding the ecological and geological factors contributing to water scarcity. Their expertise is needed to assess the environmental impact of water scarcity and the effectiveness of proposed interventions.",
+ "details": "You are an environmental scientist with expertise in ecological and geological factors affecting water availability. You should evaluate how environmental changes, such as climate change and land use, impact water resources. Your knowledge of hydrology, ecosystem dynamics, and environmental policy will be essential in reviewing the model's assumptions and predictions. Pay attention to the environmental sustainability of the intervention plans and their potential long-term effects on the region."
+ },
+ {
+ "name": "Public Policy Expert",
+ "thoughts": "Public policy experts are vital for addressing the social and economic factors of water scarcity. Their expertise is needed to design and evaluate intervention plans that consider governance, infrastructure, and community engagement.",
+ "details": "You are a public policy expert with expertise in governance and infrastructure related to water management. Your role is to assess the feasibility and effectiveness of intervention plans from a policy perspective. Focus on the social and economic drivers of water scarcity, such as governance structures, resource allocation, and community involvement. Your skills in policy analysis, stakeholder engagement, and strategic planning will be crucial in evaluating the strengths and weaknesses of the proposed solutions and their potential impact on the region and surrounding areas."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the comprehensiveness and accuracy of the model in measuring a region's ability to provide clean water, considering dynamic supply and demand factors."
+ },
+ {
+ "category": "Region Analysis",
+ "description": "Assess the selection of the region and the depth of analysis regarding the causes of water scarcity, including social and environmental factors."
+ },
+ {
+ "category": "Future Projection",
+ "description": "Grade the model's ability to predict the water situation in the chosen region in 15 years, including the impact on citizens' lives and environmental drivers."
+ },
+ {
+ "category": "Intervention Plan",
+ "description": "Evaluate the design and feasibility of the intervention plan addressing all drivers of water scarcity, and its potential impact on the region and surrounding areas."
+ },
+ {
+ "category": "Future Water Availability",
+ "description": "Assess the projection of future water availability using the intervention plan and model, including the region's susceptibility to scarcity and critical timelines."
+ },
+ {
+ "category": "Report Writing",
+ "description": "Evaluate the clarity, organization, and thoroughness of the 20-page report detailing the model, region analysis, intervention plan, and its effects, including strengths and weaknesses."
+ }
+ ]
+ }
+ },
+ "2016_Measuring_the_Evolution": {
+ "year": "2016",
+ "title": "Measuring the Evolution and Influence in Society's Information Networks",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2016/ICM-D/index.html",
+ "question": "2016_ICM_Problem_D.pdf 2016_ICM_Problem_D.pdf Measuring the Evolution and Influence in Society's Information Networks\n\n### Text in the PDF File: 2016_ICM_Problem_D.pdf\n\n**2016 ICM Problem D: Measuring the Evolution and Influence in Society\u2019s Information Networks**\n\n**Objective:** \nAnalyze the relationship between the speed/flow of information and its inherent value across different historical periods to understand the evolution of society's information networks.\n\n**Historical Periods for Analysis:** \n1. **1870s:** Newspapers delivered by trains, stories passed by telegraph.\n2. **1920s:** Radios became common household items.\n3. **1970s:** Televisions were in most homes.\n4. **1990s:** Households began connecting to the early internet.\n5. **2010s:** Mobile phones provided global connectivity.\n\n**Tasks:**\n\n(a) **Model Development:** \nCreate models to explore the flow of information and determine what qualifies as news.\n\n(b) **Model Validation:** \nUse historical data to validate the model's reliability and predict current information communication scenarios, comparing them with today's reality.\n\n(c) **Future Prediction:** \nUse the model to predict communication networks' relationships and capacities around 2050.\n\n(d) **Public Influence Modeling:** \nModel how public interest and opinion can be influenced through information networks in today's connected world.\n\n(e) **Information Spread Analysis:** \nDetermine how information value, initial opinions, message form, source, and network topology can be used to spread information and influence public opinion.\n\n**Data Sources:** \n- Circulation data and media availability reports.\n- Historical perspectives on news and media.\n- Consideration of significant world events and their hypothetical spread in different eras.\n\n**Useful Links for Data and Historical Context:**\n- Newspaper circulation trends: [Link](http://media-cmi.com/downloads/Sixty_Years_Daily_Newspaper_Circulation_Trends_050611.pdf)\n- Technology and media evolution: [Link](http://news.bbc.co.uk/2/hi/technology/8552410.stm)\n- Smartphone adoption: [Link](http://www.technologyreview.com/news/427787/are-smart-phones-spreading-faster-than-any-technology-in-human-history/)\n- Social media influence: [Link](http://newsroom.fb.com/content/default.aspx?NewsAreaId=22)\n- Media consumption habits: [Link](http://www.people-press.org/2012/09/27/section-1-watching-reading-and-listening-to-the-news-3/)\n- Spread of false information online: [Link](http://theconversation.com/hard-evidence-how-does-false-information-spread-online-25567)\n\n**References for Historical Context:**\n- \"Media & Culture: An Introduction to Mass Communication\" by Richard Campbell et al.\n- \"A History of Communications: Media and Society from the Evolution of Speech to the Internet\" by Marshall T. Poe.\n- \"Media/Impact: An Introduction to Mass Media\" by Shirley Biagi.",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the comprehensiveness and accuracy of models created to explore the flow of information and determine what qualifies as news across different historical periods."
+ },
+ {
+ "category": "Model Validation",
+ "description": "Assess the use of historical data to validate the model's reliability and its ability to predict current information communication scenarios, ensuring comparisons with today's reality are accurate."
+ },
+ {
+ "category": "Future Prediction",
+ "description": "Grade the model's capability to predict communication networks' relationships and capacities around 2050, including assumptions made and the robustness of predictions."
+ },
+ {
+ "category": "Public Influence Modeling",
+ "description": "Evaluate the model's effectiveness in simulating how public interest and opinion can be influenced through information networks in today's connected world."
+ },
+ {
+ "category": "Information Spread Analysis",
+ "description": "Assess the analysis of how information value, initial opinions, message form, source, and network topology can be used to spread information and influence public opinion."
+ },
+ {
+ "category": "Data Utilization",
+ "description": "Evaluate the use of provided data sources and historical context references to support model development and validation."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Assess the identification and justification of assumptions made in the models, as well as the acknowledgment of limitations."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to understand the flow and value of information across different historical periods. This involves creating equations and models that can capture the dynamics of information networks and their evolution.",
+ "details": "As a mathematician, you are skilled in developing and analyzing mathematical models that describe complex systems. You should focus on formulating equations that represent the flow of information and its value, considering factors such as speed, reach, and impact. Pay attention to the assumptions made in the models and ensure they are valid across different historical contexts. Your expertise in differential equations, network theory, and statistical analysis will be crucial in evaluating the robustness and accuracy of the proposed models."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing historical data to validate models and predict future scenarios. A data scientist's expertise in data analysis, machine learning, and statistical methods is essential for processing and interpreting complex datasets related to information networks.",
+ "details": "As a data scientist, you are adept at handling large datasets and extracting meaningful insights from them. You should focus on validating the models using historical data, ensuring that the predictions align with known trends and events. Your skills in data mining, pattern recognition, and predictive analytics will be vital in assessing the model's reliability and its ability to forecast future communication networks. Pay attention to the quality and relevance of the data sources used in the modeling process."
+ },
+ {
+ "name": "Historian",
+ "thoughts": "Understanding the historical context of information networks is crucial for accurately modeling their evolution and influence. A historian's expertise in analyzing historical events, media evolution, and societal changes is essential for providing context and validating assumptions in the models.",
+ "details": "As a historian, you are skilled in interpreting historical data and understanding the societal impact of media and communication technologies. You should focus on providing insights into how information networks have evolved over time and the factors that influenced their development. Your knowledge of historical events, media trends, and cultural shifts will be crucial in ensuring the models accurately reflect the historical context. Pay attention to the accuracy of historical data and the relevance of the chosen periods for analysis."
+ },
+ {
+ "name": "Sociologist",
+ "thoughts": "The problem involves modeling public influence and opinion through information networks, which requires an understanding of social behavior and communication dynamics. A sociologist's expertise in social theory, communication studies, and public opinion analysis is essential for evaluating the impact of information networks on society.",
+ "details": "As a sociologist, you are skilled in analyzing social behavior and communication patterns. You should focus on modeling how public interest and opinion are influenced by information networks, considering factors such as message form, source credibility, and network topology. Your expertise in social dynamics, media influence, and public opinion will be vital in assessing the models' ability to capture the societal impact of information networks. Pay attention to the assumptions made about social behavior and the validity of the models in different cultural contexts."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the comprehensiveness and accuracy of models created to explore the flow of information and determine what qualifies as news across different historical periods."
+ },
+ {
+ "category": "Model Validation",
+ "description": "Assess the use of historical data to validate the model's reliability and its ability to predict current information communication scenarios, ensuring comparisons with today's reality are accurate."
+ },
+ {
+ "category": "Future Prediction",
+ "description": "Grade the model's capability to predict communication networks' relationships and capacities around 2050, including assumptions made and the robustness of predictions."
+ },
+ {
+ "category": "Public Influence Modeling",
+ "description": "Evaluate the model's effectiveness in simulating how public interest and opinion can be influenced through information networks in today's connected world."
+ },
+ {
+ "category": "Information Spread Analysis",
+ "description": "Assess the analysis of how information value, initial opinions, message form, source, and network topology can be used to spread information and influence public opinion."
+ },
+ {
+ "category": "Data Utilization",
+ "description": "Evaluate the use of provided data sources and historical context references to support model development and validation."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Assess the identification and justification of assumptions made in the models, as well as the acknowledgment of limitations."
+ }
+ ]
+ }
+ },
+ "2016_Modeling_Refugee_Immigration": {
+ "year": "2016",
+ "title": "Modeling Refugee Immigration Policies",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2016/ICM-F/index.html",
+ "question": "2016_ICM_Problem_F.pdf 2016_ICM_Problem_F.pdf Modeling Refugee Immigration Policies\n\n### Text in the PDF File: 2016_ICM_Problem_F.pdf\n\n**2016 ICM Problem F: Modeling Refugee Immigration Policies**\n\n**Context:**\nThe refugee crisis in Europe, driven by political unrest and warfare in the Middle East, has led to a significant influx of refugees seeking asylum. By October 2015, over 715,000 asylum applications were filed in Europe, with Hungary receiving the highest number per capita. A quota system has been established, with France and Germany bearing the majority of the resettlement burden. Refugees travel through various routes, each with different safety and accessibility levels.\n\n**Tasks:**\n\n1. **Metrics of Refugee Crises:**\n - Identify factors that enable or inhibit refugee movement, including individual attributes, routes, transportation types, and countries' capacities.\n - Develop measures and parameters for analysis.\n\n2. **Flow of Refugees:**\n - Model optimal refugee movement across six travel routes, considering transportation, safety, and resource capacities.\n - Justify new elements and explain model sensitivities.\n\n3. **Dynamics of the Crisis:**\n - Identify changing environmental factors and incorporate capacity into the model.\n - Determine resource allocation priorities and the role of NGOs.\n - Assess model applicability to other regions like Canada, China, and the US.\n\n4. **Policy to Support Refugee Model:**\n - Propose policies ensuring optimal migration patterns, prioritizing health and safety.\n - Consider laws, cultural constraints, and NGO roles.\n\n5. **Exogenous Events:**\n - Analyze model shifts due to major events, like terrorist attacks.\n - Assess cascading effects on refugee movement and design resilient policies.\n\n6. **Scalability:**\n - Expand the model to a larger scale by a factor of 10.\n - Identify non-scalable features and new parameters.\n - Address prolonged integration issues, such as disease control and education.\n\n**Helpful References:**\n- [BBC News on Refugee Routes](http://www.bbc.com/news/world-europe-34131911)\n- [International Organization for Migration](http://www.iom.int/)\n- [UNHCR](http://www.unhcr.org/pages/49c3646c4d6.html)\n- [New York Times on Migrants and Refugees](http://www.nytimes.com/2015/08/28/world/migrants-refugees-europe-syria.html?_r=0)\n- [World Health Organization on Migration and Health](http://www.who.int/features/qa/88/en/)",
+ "requirements": [
+ {
+ "category": "Metrics of Refugee Crises",
+ "description": "Evaluate the identification and justification of factors that enable or inhibit refugee movement, including individual attributes, routes, transportation types, and countries' capacities."
+ },
+ {
+ "category": "Metrics of Refugee Crises",
+ "description": "Assess the development of measures and parameters for analyzing refugee movement and crisis metrics."
+ },
+ {
+ "category": "Flow of Refugees",
+ "description": "Grade the modeling of optimal refugee movement across six travel routes, considering transportation, safety, and resource capacities."
+ },
+ {
+ "category": "Flow of Refugees",
+ "description": "Evaluate the justification of new elements introduced in the model and the explanation of model sensitivities."
+ },
+ {
+ "category": "Dynamics of the Crisis",
+ "description": "Assess the identification and incorporation of changing environmental factors and capacity into the model."
+ },
+ {
+ "category": "Dynamics of the Crisis",
+ "description": "Evaluate the determination of resource allocation priorities and the role of NGOs in the model."
+ },
+ {
+ "category": "Dynamics of the Crisis",
+ "description": "Grade the assessment of model applicability to other regions like Canada, China, and the US."
+ },
+ {
+ "category": "Policy to Support Refugee Model",
+ "description": "Evaluate the proposed policies ensuring optimal migration patterns, prioritizing health and safety."
+ },
+ {
+ "category": "Policy to Support Refugee Model",
+ "description": "Assess the consideration of laws, cultural constraints, and NGO roles in policy proposals."
+ },
+ {
+ "category": "Exogenous Events",
+ "description": "Grade the analysis of model shifts due to major events, such as terrorist attacks, and the assessment of cascading effects on refugee movement."
+ },
+ {
+ "category": "Exogenous Events",
+ "description": "Evaluate the design of resilient policies in response to exogenous events."
+ },
+ {
+ "category": "Scalability",
+ "description": "Assess the expansion of the model to a larger scale by a factor of 10, identifying non-scalable features and new parameters."
+ },
+ {
+ "category": "Scalability",
+ "description": "Evaluate the addressing of prolonged integration issues, such as disease control and education, in the scalability context."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to analyze complex systems involving refugee movements, resource allocation, and policy impacts. A mathematician can develop and refine models to simulate these dynamics accurately.",
+ "details": "You are a mathematician with expertise in creating and analyzing mathematical models related to refugee immigration policies. You should focus on formulating equations that capture the dynamics of refugee flows, resource distribution, and policy impacts. Pay attention to the assumptions made in the models and ensure they are mathematically sound and applicable to real-world scenarios. Your skills in optimization and sensitivity analysis will be crucial in evaluating the robustness of the proposed solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves handling large datasets related to refugee movements, demographics, and resource capacities. A data scientist can analyze these datasets to extract meaningful insights and inform the modeling process.",
+ "details": "You are a data scientist with expertise in processing and analyzing complex datasets related to refugee immigration. You should focus on identifying key data points that influence refugee movements and resource allocation. Utilize statistical methods and machine learning techniques to uncover patterns and trends in the data. Your ability to handle big data and perform predictive analytics will be essential in assessing the model's accuracy and scalability."
+ },
+ {
+ "name": "Political Scientist",
+ "thoughts": "The problem is deeply rooted in political contexts, requiring an understanding of international relations, policy-making, and the socio-political factors influencing refugee movements. A political scientist can provide insights into the policy implications and geopolitical dynamics.",
+ "details": "You are a political scientist with expertise in analyzing the political aspects of refugee immigration policies. You should focus on understanding the impact of international laws, cultural constraints, and geopolitical factors on refugee movements. Evaluate the proposed policies for their feasibility and alignment with international standards. Your knowledge of political systems and diplomacy will be crucial in assessing the model's applicability to different regions and ensuring that the solutions are politically viable."
+ },
+ {
+ "name": "Humanitarian Aid Expert",
+ "thoughts": "The problem involves the role of NGOs and resource allocation priorities, requiring expertise in humanitarian aid and crisis management. A humanitarian aid expert can provide insights into effective resource distribution and support mechanisms for refugees.",
+ "details": "You are a humanitarian aid expert with experience in managing refugee crises and resource allocation. You should focus on evaluating the model's approach to resource distribution and the role of NGOs in supporting refugees. Assess the proposed solutions for their effectiveness in ensuring health, safety, and integration of refugees. Your expertise in crisis management and humanitarian logistics will be essential in reviewing the model's capacity to address prolonged integration issues and respond to exogenous events."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Metrics of Refugee Crises",
+ "description": "Evaluate the identification and justification of factors that enable or inhibit refugee movement, including individual attributes, routes, transportation types, and countries' capacities."
+ },
+ {
+ "category": "Metrics of Refugee Crises",
+ "description": "Assess the development of measures and parameters for analyzing refugee movement and crisis metrics."
+ },
+ {
+ "category": "Flow of Refugees",
+ "description": "Grade the modeling of optimal refugee movement across six travel routes, considering transportation, safety, and resource capacities."
+ },
+ {
+ "category": "Flow of Refugees",
+ "description": "Evaluate the justification of new elements introduced in the model and the explanation of model sensitivities."
+ },
+ {
+ "category": "Dynamics of the Crisis",
+ "description": "Assess the identification and incorporation of changing environmental factors and capacity into the model."
+ },
+ {
+ "category": "Dynamics of the Crisis",
+ "description": "Evaluate the determination of resource allocation priorities and the role of NGOs in the model."
+ },
+ {
+ "category": "Dynamics of the Crisis",
+ "description": "Grade the assessment of model applicability to other regions like Canada, China, and the US."
+ },
+ {
+ "category": "Policy to Support Refugee Model",
+ "description": "Evaluate the proposed policies ensuring optimal migration patterns, prioritizing health and safety."
+ },
+ {
+ "category": "Policy to Support Refugee Model",
+ "description": "Assess the consideration of laws, cultural constraints, and NGO roles in policy proposals."
+ },
+ {
+ "category": "Exogenous Events",
+ "description": "Grade the analysis of model shifts due to major events, such as terrorist attacks, and the assessment of cascading effects on refugee movement."
+ },
+ {
+ "category": "Exogenous Events",
+ "description": "Evaluate the design of resilient policies in response to exogenous events."
+ },
+ {
+ "category": "Scalability",
+ "description": "Assess the expansion of the model to a larger scale by a factor of 10, identifying non-scalable features and new parameters."
+ },
+ {
+ "category": "Scalability",
+ "description": "Evaluate the addressing of prolonged integration issues, such as disease control and education, in the scalability context."
+ }
+ ]
+ }
+ },
+ "2016_Record_Insurance": {
+ "year": "2016",
+ "title": "Record Insurance",
+ "level": "High School",
+ "source": "IM2C",
+ "link": "Problems/2016/IM2C/index.html",
+ "question": "2016_IMMC_Problem.pdf 2016_IMMC_Problem.pdf Record Insurance\n\n### Text in the PDF File: 2016_IMMC_Problem.pdf\n\n**2016 IM2C Problem: Record Insurance**\n\n**Context:**\nIn athletics, a 15,000-meter (15k) run is a common event, with world records set for such distances. Organizing committees often offer significant bonuses for setting new world records to attract top runners. For instance, a 15k race in the Netherlands offered a 25,000 euro bonus for breaking the world record. However, the committee faced financial risks as they did not purchase insurance.\n\n**Problem Overview:**\n1. **Average Cost of Bonus:**\n - Calculate the average cost of the bonus for a 15k run with a 25,000 euro bonus. This is defined as the bonus amount divided by the expected number of races before the record is broken. For example, if the record is expected to be broken every 25 races, the average cost is 1,000 euros per race.\n\n2. **Insurance Company Criteria:**\n - Determine the criteria for an insurance company to decide the additional amount to add to the average cost. Consider factors like operating costs, time value of money, and profit margins. For instance, an insurer might add 20% to cover these aspects.\n\n3. **Organizing Committee Decision:**\n - (a) Criteria for deciding whether to purchase insurance, considering long-term sponsorship plans and potential savings from self-insuring.\n - (b) Evaluate the risk of not purchasing insurance.\n\n4. **Multiple Event Insurance Decision:**\n - For a major track meet with 40 events (20 men's and 20 women's), decide which events to insure. Consider factors like the likelihood of records being broken and financial implications.\n\n5. **General Decision Scheme:**\n - Develop a decision-making framework for organizing committees to determine whether to purchase insurance or self-insure for each event. This should be clear and implementable.\n\n**Zevenheuvelenloop Race Overview:**\n- The Zevenheuvelenloop is an annual 15k road race in Nijmegen, Netherlands, first organized in 1984. It is one of the largest road races in the country, attracting over 30,000 runners in 2008. The race is known for its fast course, with world records set by Felix Limo in 2001 and Tirunesh Dibaba in 2009. Leonard Komon improved the men's world record in 2010.\n\n**Race Statistics:**\n- Notable winners include Haile Gebrselassie and Tegla Loroupe, each with multiple victories.\n- The race has been a test event for the ChampionChip timing system.\n\n**Winners by Country:**\n- Ethiopia: 10 men's and 10 women's wins\n- Netherlands: 7 men's and 6 women's wins\n- Kenya: 7 men's and 6 women's wins\n\nThis problem requires a strategic approach to managing financial risks associated with athletic events, particularly in offering bonuses for world records. The solution should consider both the financial implications and the attractiveness of the event to top athletes.",
+ "requirements": [
+ {
+ "category": "Average Cost Calculation",
+ "description": "Calculate the average cost of the bonus per race, considering the expected number of races before a record is broken."
+ },
+ {
+ "category": "Insurance Company Criteria",
+ "description": "Determine the criteria for an insurance company to decide the additional amount to add to the average cost, including factors like operating costs, time value of money, and profit margins."
+ },
+ {
+ "category": "Organizing Committee Decision - Insurance Purchase",
+ "description": "Develop criteria for the organizing committee to decide whether to purchase insurance, considering long-term sponsorship plans and potential savings from self-insuring."
+ },
+ {
+ "category": "Organizing Committee Decision - Risk Evaluation",
+ "description": "Evaluate the risk of not purchasing insurance, including potential financial implications and impact on event attractiveness."
+ },
+ {
+ "category": "Multiple Event Insurance Decision",
+ "description": "Decide which events to insure in a major track meet with multiple events, considering the likelihood of records being broken and financial implications."
+ },
+ {
+ "category": "General Decision Scheme",
+ "description": "Develop a clear and implementable decision-making framework for organizing committees to determine whether to purchase insurance or self-insure for each event."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves calculating probabilities and expected values, which are fundamental concepts in mathematics. A mathematician can help develop models to predict the likelihood of records being broken and calculate the average cost of bonuses.",
+ "details": "You are a mathematician with expertise in probability theory and statistical modeling. You should focus on ensuring that the mathematical models used to predict the frequency of record-breaking events are robust and accurate. Pay attention to the assumptions made in the models and verify that they are reasonable given the historical data and context of the races."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing historical race data to inform the models and decisions. A data scientist can process and interpret large datasets to provide insights into trends and probabilities.",
+ "details": "You are a data scientist skilled in data analysis and machine learning. Your role is to extract meaningful patterns from the race data, such as trends in record-breaking performances and factors influencing these outcomes. Ensure that the data is clean and that the models are trained on relevant features. Evaluate the predictive accuracy of the models and suggest improvements where necessary."
+ },
+ {
+ "name": "Actuary",
+ "thoughts": "The problem involves assessing financial risks and determining insurance premiums, which are core responsibilities of an actuary. An actuary can evaluate the financial implications of offering bonuses and the cost-effectiveness of purchasing insurance.",
+ "details": "You are an actuary with expertise in risk assessment and insurance modeling. Your focus should be on calculating the expected costs and benefits of insuring against record-breaking performances. Consider factors such as the probability of records being broken, the financial stability of the organizing committee, and the potential savings from self-insuring. Ensure that the insurance models account for all relevant financial variables and provide a clear rationale for the recommended insurance premiums."
+ },
+ {
+ "name": "Sports Economist",
+ "thoughts": "The problem involves understanding the economic impact of athletic events and the incentives for top athletes. A sports economist can analyze the broader economic implications of offering bonuses and purchasing insurance.",
+ "details": "You are a sports economist with expertise in the economic analysis of sports events. Your role is to evaluate the attractiveness of the event to top athletes and the potential economic benefits of offering bonuses. Consider the long-term sponsorship plans and the impact of record-breaking performances on the event's reputation and financial success. Provide insights into how the organizing committee can balance financial risks with the goal of attracting elite competitors."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Average Cost Calculation",
+ "description": "Calculate the average cost of the bonus per race, considering the expected number of races before a record is broken."
+ },
+ {
+ "category": "Insurance Company Criteria",
+ "description": "Determine the criteria for an insurance company to decide the additional amount to add to the average cost, including factors like operating costs, time value of money, and profit margins."
+ },
+ {
+ "category": "Organizing Committee Decision - Insurance Purchase",
+ "description": "Develop criteria for the organizing committee to decide whether to purchase insurance, considering long-term sponsorship plans and potential savings from self-insuring."
+ },
+ {
+ "category": "Organizing Committee Decision - Risk Evaluation",
+ "description": "Evaluate the risk of not purchasing insurance, including potential financial implications and impact on event attractiveness."
+ },
+ {
+ "category": "Multiple Event Insurance Decision",
+ "description": "Decide which events to insure in a major track meet with multiple events, considering the likelihood of records being broken and financial implications."
+ },
+ {
+ "category": "General Decision Scheme",
+ "description": "Develop a clear and implementable decision-making framework for organizing committees to determine whether to purchase insurance or self-insure for each event."
+ }
+ ]
+ }
+ },
+ "2017_Jet_Lag": {
+ "year": "2017",
+ "title": "Jet Lag",
+ "level": "High School",
+ "source": "IM2C",
+ "link": "Problems/2017/IM2C/index.html",
+ "question": "Organizing international meetings is not easy in many ways, including the problem that some of the participants may experience the effects of jet lag after recent travel from their home country to the meeting location which may be in a different time-zone, or in a different climate and time of year, and so on. All these things may dramatically affect the productivity of the meeting.\n\nThe International Meeting Management Corporation (IMMC) has asked your expert group (your team) to help solve the problem by creating an algorithm that suggests the best place(s) to hold a meeting given the number of participants, their home cities, approximate dates of the meeting and other information that the meeting management company may request from its clients.\n\nThe participants are usually from all corners of the Earth, and the business or scientific meeting implies doing hard intellectual team work for three intensive days, with the participants contributing approximately equally to the end result. Assume that there are no visa problems or political limitations, and so any country or city can be a potential meeting location.\n\nThe output of the algorithm should be a list of recommended places (regions, zones, or specific cities) that maximize the overall productivity of the meeting. The questions of costs are not of primary importance, but the IMMC, just as any other company, has a limited budget. So the costs may be considered as a secondary criterion. And the IMMC definitely cannot afford bringing the participants in a week before the meeting to acclimatize or give them the time to rest after a long exhausting journey.\n\nTest your algorithm at least on the two following datasets:\n\nScenario 1) \u201cSmall Meeting\u201d:\n\nTime: mid-June Participants: 6 individuals from: Monterey CA, USA Zutphen, Netherlands Melbourne, Australia Shanghai, China Hong Kong (SAR), China Moscow, Russia\n\nScenario 2) \u201cBig meeting\u201d:\n\nTime: January Participants: 11 individuals from: Boston MA, USA (2 people) Singapore Beijing, China Hong Kong (SAR), China (2 people) Moscow, Russia Utrecht, Netherlands Warsaw, Poland Copenhagen, Denmark Melbourne, Australia",
+ "requirements": [
+ {
+ "category": "Algorithm Design",
+ "description": "Evaluate the algorithm's ability to incorporate factors such as time zones, climate differences, and jet lag into the decision-making process for selecting meeting locations."
+ },
+ {
+ "category": "Productivity Optimization",
+ "description": "Assess how well the algorithm maximizes overall productivity of the meeting by balancing participant contributions and minimizing negative effects like jet lag."
+ },
+ {
+ "category": "Cost Consideration",
+ "description": "Analyze how the algorithm incorporates cost as a secondary criterion, ensuring that the recommended locations are within a reasonable budget."
+ },
+ {
+ "category": "Scenario Testing",
+ "description": "Check the algorithm's performance and adaptability by testing it on the provided datasets for 'Small Meeting' and 'Big Meeting' scenarios."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Evaluate the clarity and validity of any assumptions made, such as ignoring visa and political limitations, and how these affect the algorithm's recommendations."
+ },
+ {
+ "category": "Output Quality",
+ "description": "Examine the quality and relevance of the list of recommended places, ensuring they are practical and align with the problem's objectives."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to optimize the selection of meeting locations based on various factors such as time zones, climate, and participant distribution.",
+ "details": "As a mathematician, you will focus on developing and reviewing the mathematical models that underpin the algorithm. You should pay attention to the formulation of equations that represent the constraints and objectives of the problem, such as minimizing jet lag and maximizing productivity. Your expertise in optimization techniques and mathematical analysis will be crucial in ensuring the model is robust and effective."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves processing and analyzing data related to participant locations, time zones, and climate conditions to inform the algorithm's recommendations.",
+ "details": "As a data scientist, you will be responsible for handling the datasets that include participant information and potential meeting locations. You should focus on data preprocessing, feature extraction, and applying machine learning techniques to predict the impact of various factors on meeting productivity. Your skills in data visualization and statistical analysis will help in interpreting the results and refining the algorithm."
+ },
+ {
+ "name": "Climatologist",
+ "thoughts": "The problem requires understanding the climate conditions of potential meeting locations, which can affect participant comfort and productivity.",
+ "details": "As a climatologist, you will evaluate the climate data for each potential meeting location. You should consider factors such as temperature, humidity, and seasonal variations that could impact the participants' ability to perform at their best. Your expertise in climate modeling and analysis will be essential in assessing how different climates might affect the meeting's success and in providing recommendations for optimal locations."
+ },
+ {
+ "name": "Travel Logistics Expert",
+ "thoughts": "The problem involves logistical considerations related to travel, such as flight durations, time zone differences, and accessibility of meeting locations.",
+ "details": "As a travel logistics expert, you will assess the travel routes and schedules for participants from various locations. You should focus on minimizing travel time and jet lag by selecting meeting locations that are easily accessible and have favorable time zone alignments. Your knowledge of international travel logistics and experience in coordinating complex itineraries will be vital in ensuring the algorithm accounts for practical travel considerations and enhances overall meeting productivity."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Algorithm Design",
+ "description": "Evaluate the algorithm's ability to incorporate factors such as time zones, climate differences, and jet lag into the decision-making process for selecting meeting locations."
+ },
+ {
+ "category": "Productivity Optimization",
+ "description": "Assess how well the algorithm maximizes overall productivity of the meeting by balancing participant contributions and minimizing negative effects like jet lag."
+ },
+ {
+ "category": "Cost Consideration",
+ "description": "Analyze how the algorithm incorporates cost as a secondary criterion, ensuring that the recommended locations are within a reasonable budget."
+ },
+ {
+ "category": "Scenario Testing",
+ "description": "Check the algorithm's performance and adaptability by testing it on the provided datasets for 'Small Meeting' and 'Big Meeting' scenarios."
+ },
+ {
+ "category": "Assumptions and Limitations",
+ "description": "Evaluate the clarity and validity of any assumptions made, such as ignoring visa and political limitations, and how these affect the algorithm's recommendations."
+ },
+ {
+ "category": "Output Quality",
+ "description": "Examine the quality and relevance of the list of recommended places, ensuring they are practical and align with the problem's objectives."
+ }
+ ]
+ }
+ },
+ "2017_Sustainable_Cities_Needed!": {
+ "year": "2017",
+ "title": "Sustainable Cities Needed!",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2017/ICM-E/index.html",
+ "question": "2017_ICM_Problem_E.pdf 2017_ICM_Problem_E.pdf Sustainable Cities Needed!\n\n### Text in the PDF File: 2017_ICM_Problem_E.pdf\n\n**2017 ICM Problem E: Sustainable Cities Needed!**\n\n**Background:**\nCommunities are adopting smart growth initiatives to achieve long-term, sustainable urban planning. Smart growth aims to make cities economically prosperous, socially equitable, and environmentally sustainable. With rapid urbanization, it's projected that by 2050, 66% of the global population will live in urban areas, adding 2.5 billion people to urban populations. Urban planning is crucial to provide equitable and sustainable living conditions.\n\nSmart growth, originating in the 1990s, addresses urban sprawl and farmland loss. Its ten principles are:\n1. Mix land uses\n2. Utilize compact building design\n3. Offer diverse housing options\n4. Create walkable neighborhoods\n5. Foster distinctive communities with a strong sense of place\n6. Preserve open spaces and critical environmental areas\n7. Direct development towards existing communities\n8. Provide diverse transportation options\n9. Ensure predictable, fair, and cost-effective development decisions\n10. Encourage community and stakeholder collaboration\n\nThese principles must be adapted to each community's unique needs, considering demographics, growth needs, and geographical conditions.\n\n**Tasks:**\nThe International City Management Group (ICM) seeks assistance in applying smart growth theories to city design globally. Select two mid-sized cities (population 100,000-500,000) on different continents.\n\n1. Define a metric to measure smart growth success, considering the three E\u2019s of sustainability and/or the 10 smart growth principles.\n2. Research and evaluate the current growth plans of the selected cities against smart growth principles using your metric.\n3. Develop a smart growth plan for both cities for the coming decades, justifying your choices based on geography, growth rates, and economic opportunities. Evaluate the success of your plans using your metric.\n4. Rank the initiatives within your smart growth plan from most to least potential using your metric. Compare and contrast the initiatives and their rankings between the two cities.\n5. Explain how your plan supports a 50% population increase by 2050.\n\n**References:**\n1. Smart Growth America: https://smartgrowthamerica.org/\n2. EPA Smart Growth Publication: https://www.epa.gov/smartgrowth/smart-growth-publication\n3. UN World Urbanization Prospects: https://esa.un.org/unpd/wup/Publications/Files/WUP2014-Highlights.pdf\n4. EPA Smart Growth Guide: http://www.sustainablecitiesinstitute.org/Documents/SCI/Report_Guide/Guide_EPA_SmartGrowthGHGReduction_2011.pdf\n5. The Smart Growth Manual by Duany, Speck, and Lydon.",
+ "requirements": [
+ {
+ "category": "Metric Definition",
+ "description": "Define a comprehensive metric to measure smart growth success, incorporating the three E\u2019s of sustainability and/or the 10 smart growth principles."
+ },
+ {
+ "category": "Current Plan Evaluation",
+ "description": "Research and evaluate the current growth plans of the selected cities against smart growth principles using the defined metric."
+ },
+ {
+ "category": "Smart Growth Plan Development",
+ "description": "Develop a detailed smart growth plan for both cities for the coming decades, justifying choices based on geography, growth rates, and economic opportunities."
+ },
+ {
+ "category": "Plan Evaluation",
+ "description": "Evaluate the success of the developed smart growth plans using the defined metric."
+ },
+ {
+ "category": "Initiative Ranking",
+ "description": "Rank the initiatives within the smart growth plan from most to least potential using the metric, and compare and contrast the initiatives and their rankings between the two cities."
+ },
+ {
+ "category": "Population Growth Accommodation",
+ "description": "Explain how the smart growth plan supports a 50% population increase by 2050, ensuring sustainable urban development."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires the development of a metric to measure smart growth success, which involves mathematical modeling and quantitative analysis. A mathematician's expertise is crucial in formulating and solving the equations and models that will underpin this metric.",
+ "details": "You are a mathematician with expertise in creating and analyzing mathematical models. Your role involves developing a robust metric that can accurately measure the success of smart growth initiatives. You should focus on ensuring that the metric is comprehensive, taking into account the three E\u2019s of sustainability (economic, social equity, and environmental) and the ten smart growth principles. Your attention to detail and ability to work with complex mathematical concepts will be essential in evaluating the effectiveness of the proposed smart growth plans."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves researching and evaluating current growth plans, which requires analyzing large datasets and extracting meaningful insights. A data scientist's skills in data analysis, statistical methods, and machine learning are vital for this task.",
+ "details": "You are a data scientist with expertise in handling and analyzing complex datasets. Your role is to gather data on the selected cities, evaluate their current growth plans, and compare them against the smart growth principles using the developed metric. You should focus on using statistical methods and machine learning techniques to identify patterns and trends in the data. Your ability to interpret data and provide actionable insights will be crucial in developing and justifying the smart growth plans for the cities."
+ },
+ {
+ "name": "Urban Planner",
+ "thoughts": "The problem centers around urban planning and the application of smart growth principles, which are directly within the domain of urban planners. Their expertise in city design and development is essential for creating effective and sustainable growth plans.",
+ "details": "You are an urban planner with a deep understanding of smart growth principles and urban design. Your role is to develop comprehensive smart growth plans for the selected cities, considering their unique geographical, demographic, and economic contexts. You should focus on creating plans that are not only sustainable but also adaptable to future growth and changes. Your expertise in stakeholder collaboration and community engagement will be vital in ensuring that the plans are well-received and effectively implemented."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem involves ensuring environmental sustainability, which is a key component of smart growth. An environmental scientist's expertise in assessing environmental impacts and promoting sustainable practices is crucial for this task.",
+ "details": "You are an environmental scientist with expertise in evaluating and mitigating environmental impacts. Your role is to ensure that the smart growth plans prioritize environmental sustainability, preserving open spaces, and protecting critical environmental areas. You should focus on assessing the environmental implications of the proposed initiatives and providing recommendations to minimize negative impacts. Your knowledge of sustainable practices and environmental regulations will be essential in creating plans that support long-term ecological health and resilience."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Metric Definition",
+ "description": "Define a comprehensive metric to measure smart growth success, incorporating the three E\u2019s of sustainability and/or the 10 smart growth principles."
+ },
+ {
+ "category": "Current Plan Evaluation",
+ "description": "Research and evaluate the current growth plans of the selected cities against smart growth principles using the defined metric."
+ },
+ {
+ "category": "Smart Growth Plan Development",
+ "description": "Develop a detailed smart growth plan for both cities for the coming decades, justifying choices based on geography, growth rates, and economic opportunities."
+ },
+ {
+ "category": "Plan Evaluation",
+ "description": "Evaluate the success of the developed smart growth plans using the defined metric."
+ },
+ {
+ "category": "Initiative Ranking",
+ "description": "Rank the initiatives within the smart growth plan from most to least potential using the metric, and compare and contrast the initiatives and their rankings between the two cities."
+ },
+ {
+ "category": "Population Growth Accommodation",
+ "description": "Explain how the smart growth plan supports a 50% population increase by 2050, ensuring sustainable urban development."
+ }
+ ]
+ }
+ },
+ "2019_Bottle_Battles": {
+ "year": "2019",
+ "title": "Bottle Battles",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2019/HIMCM-B/index.html",
+ "question": "A number of communities (campuses, towns, cities, etc.) around the world have proposed and enacted plastic water bottle bans in some form. \n\n2019_HiMCM_Problem_B_FAQ.pdf 2019_HiMCM_Problem_B_FAQ.pdf\n\nIn 2013, the small town of Concord, Massachusetts (population approximately 19,000) became the first town or city in the United States to ban the sale of single-serving Polyethylene terephthalate (PET) bottles less than or equal to 1 liter (34 ounces) containing water which is non-sparkling and non-flavored (in other words, plain water)[1]. The sale of water in bottles of any size made of other types of plastic or other materials, as well as PET bottles of flavored or sparkling water, soda, tea, juices, and other non-plain water beverages, regardless of size, is allowed[2]. See attached FAQ document. Concord citizens supporting this action stated various reasons including: concerns of plastic garbage and litter, use of fossil fuels in the production of plastic, product transportation emissions, damage to water-providing aquifers, and beliefs that businesses shouldn\u2019t profit on the sale of a free resource. Since enactment of Concord's ban, a handful of other communities in the United States have enacted single-serving water bottle bans, the largest being the city of San Francisco (population approximately 885,000) who banned the sale of single-serving water bottles on city property in 2014[3]. Just recently, the San Francisco Airport decided to comply with its city\u2019s law and banned the sale of single-serving water bottles, making it the first airport to do so[4]. Not everyone is in favor of these bans, nor does everyone think that these bans will have any impact on the issues they are trying to address. Opponents include the International Bottled Water Association (IBWA) who, after the San Francisco ban, stated that there are unintended consequences to these bans as they may lead to \"more packaging, more additives (e.g., sugar, caffeine), and greater environmental impacts than bottled water[5].\" Additionally, as we have seen in recent world news, in some areas (e.g. unavailability/inaccessibility of fresh water) and under some circumstances (e.g. natural disasters, compromises in water delivery) bottled water is a necessary and critical resource.\n\n1. Model the impacts of a ban on the sale of single-serving water bottles in a town or city. Use your model to discuss the impacts of the bans in the Town of Concord and the City of San Francisco.\n\n a. Identify the possible impacts (positive and negative) of a ban on the sale of single-serving water bottles within a town or city.\n\n b. What information and data do you need to model and measure these impacts? How would you collect this information and these data? (Note: You do not need to actually collect information and data, but need to identify what you need and how you might obtain it.)\n\n c. Develop a model or set of models to measure water bottle ban impacts.\n\n d. Discuss the application of your model to Concord and San Francisco.\n\n2. Address the impacts of a ban on the sale of single-serving water bottles within an airport. How are the impacts similar to and different from a ban in a town or city? How would your initial model for a town or city change, if at all, to model bottle ban impacts within an airport?\n\n3. Discuss and recommend possible changes to Concord\u2019s water bottle ban, or other related community measures, that would enhance beneficial impacts and reduce adverse impacts. Use your suggested changes to adjust your impact model. Address whether or not your new model is generalizable to larger communities (e.g. large cities, regions, states, countries).\n\n4. Write a one-page article for your local newspaper reporting your findings and recommendations.\n\n2019_HiMCM_Problem_B_FAQ.pdf 2019_HiMCM_Problem_B_FAQ.pdf\n\nNote: Reference List and any appendices do not count toward the page limit and should appear after your completed solution.\n\nAttachment: Town of Concord, Massachusetts. Town Bylaws. (Updated January 9, 2013). Frequently asked questions about interpretation and enforcement of the drinking water in single-serve PET bottles bylaw.\n\nReferences:\n\n[1] NBC News, US News. (2012, September 7). Concord, Mass., the first US city to ban sale of plastic water bottles.\n\n[2] Town of Concord, Massachusetts. Town Bylaws. Sale of drinking water in single-serve PET bottles bylaw.\n\n[3] Levin, Sam T. The Guardian, US Edition. (2017, June 28). How San Francisco is leading the way out of bottled water culture.\n\n[4] CBS News, CBS This Morning. (2019, August 20). San Francisco International Airport rolls out ban on water bottles.\n\n[5] International Bottled Water Association. (2013, December 18). Proposed bottled water ban not in the best interest of San Franciscans.\n\nGlossary:\n\n- Aquifers: geological formations containing or conducting ground water.\n- Flavored (water): having been given a taste by an additive (e.g. sweetener, fruit juice, etc.).\n- Sparkling (water): effervescent beverage consisting of water charged with carbon dioxide (also known as seltzer water, fizzy water, water with gas).\n- Polyethylene terephthalate (PET) bottles: bottles made from PET, a plastic form of polyester and a type of thermoplastic polymer resin.\n\n### Text in the PDF File: 2019_HiMCM_Problem_B_FAQ.pdf\n\n**Frequently Asked Questions about the Drinking Water in Single-Serve PET Bottles Bylaw**\n\n**Effective Date:**\n- The bylaw became effective on January 1, 2013.\n\n**Identifying PET Bottles:**\n- Most clear plastic beverage bottles are made of polyethylene terephthalate (PET or PETE). These bottles have the number 1 and/or PETE with the recycling symbol.\n\n**Prohibited Bottles:**\n- The bylaw prohibits the sale of non-sparkling, unflavored drinking water in PET bottles of 1 liter (34 ounces) or less.\n- Bottles made from other plastics are allowed.\n- The sale of juice beverages, flavored waters, and sparkling water in any size is permitted.\n\n**Electrolyte or Mineral-Added Water:**\n- Unflavored, non-sparkling water with added electrolytes or minerals in bottles of 34 ounces or less cannot be sold.\n- Flavored versions of such water can be sold regardless of size.\n\n**Cases of Bottled Water:**\n- Selling cases of small bottles (1 liter or less) of non-sparkling, unflavored water is prohibited.\n\n**Vending Machines and Civic Events:**\n- Bottled water in PET bottles of 1 liter or less cannot be sold in vending machines or at civic events if it is plain, non-sparkling, and unflavored.\n\n**Free Water:**\n- Bottled or cup water can be offered for free.\n\n**Voluntary Donations:**\n- Businesses cannot solicit donations for bottled water, as it is considered a sale.\n\n**Enforcement:**\n- The Health Division is responsible for ensuring compliance. Inspections began in January 2013.\n- First-time violators receive a written warning. A $25 fine is issued upon a second violation, and a $50 fine for subsequent violations.\n\n**Appeal Process:**\n- To contest a Non-Criminal Citation, a written request for a hearing must be filed at District Court within 21 days of receiving the citation.",
+ "requirements": [
+ {
+ "category": "Impact Identification",
+ "description": "Identify and categorize the possible positive and negative impacts of a ban on single-serving water bottles within a town or city."
+ },
+ {
+ "category": "Data Requirements",
+ "description": "Specify the information and data needed to model and measure the impacts of the water bottle ban, and propose methods for collecting this data."
+ },
+ {
+ "category": "Model Development",
+ "description": "Develop a mathematical model or set of models to measure the impacts of the water bottle ban, ensuring the model is robust and can handle various scenarios."
+ },
+ {
+ "category": "Application to Specific Cases",
+ "description": "Apply the developed model to analyze the impacts of the water bottle ban in Concord and San Francisco, and discuss the findings."
+ },
+ {
+ "category": "Airport Impact Analysis",
+ "description": "Analyze the impacts of a water bottle ban within an airport, comparing and contrasting these impacts with those in a town or city, and adjust the model accordingly."
+ },
+ {
+ "category": "Policy Recommendations",
+ "description": "Discuss and recommend possible changes to Concord\u2019s water bottle ban or related measures to enhance beneficial impacts and reduce adverse impacts, and adjust the model based on these recommendations."
+ },
+ {
+ "category": "Generalizability",
+ "description": "Evaluate whether the adjusted model is generalizable to larger communities, such as large cities, regions, states, or countries."
+ },
+ {
+ "category": "Communication",
+ "description": "Write a concise one-page article for a local newspaper reporting the findings and recommendations, ensuring clarity and accessibility for a general audience."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to quantify the impacts of the water bottle ban, including environmental, economic, and social factors. A mathematician can develop equations and models to simulate these impacts and predict outcomes.",
+ "details": "As a mathematician, you are skilled in creating and analyzing mathematical models that can simulate complex systems. You should focus on formulating equations that represent the various impacts of the water bottle ban, such as reductions in plastic waste, changes in consumer behavior, and economic effects on local businesses. Your expertise in differential equations, optimization, and statistical analysis will be crucial in ensuring the models are robust and accurate."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves collecting and analyzing data to measure the impacts of the water bottle ban. A data scientist can identify relevant datasets, perform statistical analyses, and interpret the results to inform the model.",
+ "details": "As a data scientist, you are adept at handling large datasets and extracting meaningful insights from them. You should focus on identifying the types of data needed, such as sales figures, environmental impact metrics, and public opinion surveys. Your skills in data cleaning, machine learning, and visualization will be essential in processing the data and presenting the findings in a clear and actionable manner."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem has significant environmental implications, such as the reduction of plastic waste and the impact on local ecosystems. An environmental scientist can provide insights into these aspects and help assess the ecological benefits and drawbacks of the ban.",
+ "details": "As an environmental scientist, you are knowledgeable about the interactions between human activities and natural systems. You should focus on evaluating the environmental impacts of the water bottle ban, such as changes in plastic pollution levels and effects on local wildlife. Your expertise in environmental assessment, sustainability practices, and ecological modeling will be vital in ensuring the model accurately reflects the environmental consequences of the ban."
+ },
+ {
+ "name": "Economist",
+ "thoughts": "The problem involves economic considerations, such as the impact on local businesses and consumer spending. An economist can analyze these factors and help assess the economic viability and consequences of the ban.",
+ "details": "As an economist, you are skilled in analyzing market dynamics and economic policies. You should focus on evaluating the economic impacts of the water bottle ban, such as changes in sales revenue for local businesses and shifts in consumer spending patterns. Your expertise in economic modeling, cost-benefit analysis, and policy evaluation will be crucial in ensuring the model accurately reflects the economic implications of the ban."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Impact Identification",
+ "description": "Identify and categorize the possible positive and negative impacts of a ban on single-serving water bottles within a town or city."
+ },
+ {
+ "category": "Data Requirements",
+ "description": "Specify the information and data needed to model and measure the impacts of the water bottle ban, and propose methods for collecting this data."
+ },
+ {
+ "category": "Model Development",
+ "description": "Develop a mathematical model or set of models to measure the impacts of the water bottle ban, ensuring the model is robust and can handle various scenarios."
+ },
+ {
+ "category": "Application to Specific Cases",
+ "description": "Apply the developed model to analyze the impacts of the water bottle ban in Concord and San Francisco, and discuss the findings."
+ },
+ {
+ "category": "Airport Impact Analysis",
+ "description": "Analyze the impacts of a water bottle ban within an airport, comparing and contrasting these impacts with those in a town or city, and adjust the model accordingly."
+ },
+ {
+ "category": "Policy Recommendations",
+ "description": "Discuss and recommend possible changes to Concord\u2019s water bottle ban or related measures to enhance beneficial impacts and reduce adverse impacts, and adjust the model based on these recommendations."
+ },
+ {
+ "category": "Generalizability",
+ "description": "Evaluate whether the adjusted model is generalizable to larger communities, such as large cities, regions, states, or countries."
+ },
+ {
+ "category": "Communication",
+ "description": "Write a concise one-page article for a local newspaper reporting the findings and recommendations, ensuring clarity and accessibility for a general audience."
+ }
+ ]
+ }
+ },
+ "2019_Charge!": {
+ "year": "2019",
+ "title": "Charge!",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2019/HIMCM-A/index.html",
+ "question": "In our school and social lives we exist in a mobile electronic world. Each day we \"plug in\" and charge our electronic devices and equipment. These electronics may range from small items (cell phones) to large items (electric vehicles). While in our own home, our family is most likely responsible for purchasing the charging equipment, and then paying an electric company/provider for the electricity we use.\n\nPublic places are continually expanding the availability of electrical outlets, charging stations, and even electric vehicle charging parking spots. For example, many airports have recently refurbished their parking lots, terminals, and aircraft to allow for electrical charging of everything from portable devices to vehicles. In some locations, these charging ports require a fee, but many public places worldwide offer charging for \"free.\" But, what is the impact of \"plugging in\" our electronics at these \"free\" charging sites in public places such as airports, railway terminals, schools, libraries, shopping malls, coffee shops, and offices? And, who pays for it?\n\n1. Discuss how this type of energy consumption has changed over recent years and how it will continue to change. Identify impacts on, and requirements of, public places with these increasing energy (electricity) and charging demands.\n\n2. Use your identified impacts and requirements to develop a model for the resulting costs of the increased demands and energy usage on public places. Discuss the extent of these costs and how they are paid.\n\n3. Discuss how your model changes, if at all, for different types of public places (e.g. a school vs. a cafe/coffee shop vs. an airport vs. a shopping mall, etc.)?\n\n4. What initiatives should be explored to reduce the cost of this increased energy usage in public places? How would implementation of these initiatives adjust your cost model?\n\n5. Write a one-page article for your school newspaper describing your findings and recommendations.",
+ "requirements": [
+ {
+ "category": "Energy Consumption Trends",
+ "description": "Evaluate the analysis of how energy consumption for charging devices in public places has changed over recent years and predictions for future changes."
+ },
+ {
+ "category": "Impact Identification",
+ "description": "Assess the identification of impacts and requirements on public places due to increased energy and charging demands."
+ },
+ {
+ "category": "Cost Modeling",
+ "description": "Grade the development of a mathematical model that calculates the costs associated with increased energy usage in public places."
+ },
+ {
+ "category": "Cost Analysis",
+ "description": "Evaluate the discussion on the extent of these costs and the mechanisms by which they are paid."
+ },
+ {
+ "category": "Model Adaptation",
+ "description": "Assess how the cost model is adapted for different types of public places, such as schools, cafes, airports, and shopping malls."
+ },
+ {
+ "category": "Initiatives for Cost Reduction",
+ "description": "Evaluate the exploration of initiatives to reduce energy usage costs and how these initiatives would affect the cost model."
+ },
+ {
+ "category": "Communication of Findings",
+ "description": "Grade the clarity and effectiveness of the one-page article written for the school newspaper, summarizing findings and recommendations."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves developing a mathematical model to quantify the costs and impacts of increased energy usage in public places. This requires expertise in formulating equations and understanding the relationships between various factors such as energy consumption, costs, and public infrastructure.",
+ "details": "As a mathematician, you are skilled in creating and analyzing mathematical models that can predict and explain complex phenomena. In reviewing the modeling solutions to this problem, you should focus on the accuracy and validity of the equations used, ensuring they appropriately represent the real-world scenarios described. Pay attention to the assumptions made in the model and evaluate whether they are reasonable and justified. Your expertise in mathematical principles will be crucial in assessing the robustness and reliability of the proposed solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing data related to energy consumption patterns, costs, and usage trends in public places. A data scientist can provide insights into how these factors have changed over time and predict future trends, which are essential for developing an accurate cost model.",
+ "details": "As a data scientist, you are adept at handling large datasets and extracting meaningful insights through statistical analysis and machine learning techniques. When reviewing the modeling solutions, focus on the data sources used, the methods of data collection, and the analytical techniques applied. Ensure that the data is representative and that the conclusions drawn are supported by empirical evidence. Your ability to interpret data trends and patterns will be vital in evaluating the effectiveness of the proposed models and their applicability to different public places."
+ },
+ {
+ "name": "Electrical Engineer",
+ "thoughts": "The problem involves understanding the technical aspects of energy consumption and charging infrastructure in public places. An electrical engineer can provide insights into the design, efficiency, and requirements of charging systems, which are crucial for assessing the impacts and costs associated with increased energy usage.",
+ "details": "As an electrical engineer, you have expertise in the design and operation of electrical systems, including charging stations and energy distribution networks. In reviewing the modeling solutions, focus on the technical feasibility and efficiency of the proposed charging infrastructure. Evaluate whether the models consider the capacity, scalability, and maintenance requirements of these systems. Your knowledge of electrical engineering principles will be essential in assessing the practicality and sustainability of the solutions, ensuring they align with current technological standards and innovations."
+ },
+ {
+ "name": "Economist",
+ "thoughts": "The problem involves analyzing the economic implications of increased energy usage in public places, including cost distribution and payment mechanisms. An economist can provide insights into the financial impacts and explore initiatives to reduce costs, which are crucial for developing a comprehensive cost model.",
+ "details": "As an economist, you are skilled in evaluating economic systems and understanding the financial dynamics of energy consumption. When reviewing the modeling solutions, focus on the cost analysis and economic assumptions made. Assess the proposed payment mechanisms and initiatives for cost reduction, ensuring they are economically viable and sustainable. Your expertise in economic theory and policy will be vital in evaluating the broader economic impacts of the solutions and their potential to influence public policy and infrastructure investment."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Energy Consumption Trends",
+ "description": "Evaluate the analysis of how energy consumption for charging devices in public places has changed over recent years and predictions for future changes."
+ },
+ {
+ "category": "Impact Identification",
+ "description": "Assess the identification of impacts and requirements on public places due to increased energy and charging demands."
+ },
+ {
+ "category": "Cost Modeling",
+ "description": "Grade the development of a mathematical model that calculates the costs associated with increased energy usage in public places."
+ },
+ {
+ "category": "Cost Analysis",
+ "description": "Evaluate the discussion on the extent of these costs and the mechanisms by which they are paid."
+ },
+ {
+ "category": "Model Adaptation",
+ "description": "Assess how the cost model is adapted for different types of public places, such as schools, cafes, airports, and shopping malls."
+ },
+ {
+ "category": "Initiatives for Cost Reduction",
+ "description": "Evaluate the exploration of initiatives to reduce energy usage costs and how these initiatives would affect the cost model."
+ },
+ {
+ "category": "Communication of Findings",
+ "description": "Grade the clarity and effectiveness of the one-page article written for the school newspaper, summarizing findings and recommendations."
+ }
+ ]
+ }
+ },
+ "2020_Drowning_in_Plastic": {
+ "year": "2020",
+ "title": "Drowning in Plastic",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2020/ICM-E/index.html",
+ "question": "Since the 1950s, the manufacturing of plastics has grown exponentially because of its variety of uses, such as food packaging, consumer products, medical devices, and construction. While there are significant benefits, the negative implications associated with increased production of plastics are concerning. Plastic products do not readily break down, are difficult to dispose of, and only about 9% of plastics are recycled[1]. Effects can be seen by the approximately 4-12 million tons of plastic waste that enter the oceans each year[1,2]. Plastic waste has severe environmental consequences and it is predicted that if our current trends continue, the oceans will be filled with more plastic than fish by 2050[2]. The effect on marine life has been studied[3], but the effects on human health are not yet completely understood[4]. The rise of single-use and disposable plastic products results in entire industries dedicated to creating plastic waste. It also suggests that the amount of time the product is useful is significantly shorter than the time it takes to properly mitigate the plastic waste. Consequently, to solve the plastic waste problem, we need to slow down the flow of plastic production and improve how we manage plastic waste.\n\nYour team has been hired by the International Council of Plastic Waste Management (ICM) to address this escalating environmental crisis. You must develop a plan to significantly reduce, if not eliminate, single-use and disposable plastic product waste.\n\nDevelop a model to estimate the maximum levels of single-use or disposable plastic product waste that can safely be mitigated without further environmental damage. You may need to consider, among many factors, the source of this waste, the extent of the current waste problem, and the availability of resources to process the waste.\n\nDiscuss to what extent plastic waste can be reduced to reach an environmentally safe level. This may involve considering factors impacting the levels of plastic waste to include, but not limited to, sources and uses of single-use or disposable plastics, the availability of alternatives to plastics, the impact on the lives of citizens, or policies of cities, regions, countries, and continents to decrease single-use or disposable plastic and the effectiveness of such policies. These can vary between regions, so considering regional-specific constraints may make some policies more effective than others.\n\nUsing your model and discussion, set a target for the minimal achievable level of global waste of single-use or disposable plastic products and discuss the impacts for achieving such levels. You may consider ways in which human life is altered, the environmental impacts, or the effects on the multi-trillion-dollar plastic industry.\n\nWhile this is a global problem, the causes and effects are not equally distributed across nations or regions. Discuss the equity issues that arise from the global crisis and your intended solutions. How do you suggest ICM address these issues?\n\nWrite a two-page memo to the ICM describing a realistic global target minimum achievable level of global single-use or disposable plastic product waste, a timeline to reach this level, and any circumstances that may accelerate or hinder the achievement of your target and timeline.\n\nYour submission should consist of:\n\nOne-page Summary Sheet, Two-page Memo. Your solution of no more than 20 pages.\n\nGlossary\n\nDisposable Plastic Products: plastic materials or products that are not recyclable and become trash. Mitigate: To make less severe, to moderate, to alleviate. Plastic Waste: plastic objects that have not been recycled properly or cannot be recycled; debris made of plastic. Single-Use Plastic Products: products made of plastic intended for one time use before being discarded.",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the mathematical model's ability to estimate maximum levels of single-use or disposable plastic waste that can be safely mitigated without further environmental damage."
+ },
+ {
+ "category": "Factor Consideration",
+ "description": "Assess the extent to which the model considers various factors such as sources of waste, current waste levels, and resource availability for waste processing."
+ },
+ {
+ "category": "Waste Reduction Discussion",
+ "description": "Examine the discussion on reducing plastic waste to environmentally safe levels, including the consideration of alternatives to plastics and the impact on citizens' lives."
+ },
+ {
+ "category": "Policy Analysis",
+ "description": "Analyze the evaluation of policies aimed at reducing single-use plastics, including regional-specific constraints and effectiveness."
+ },
+ {
+ "category": "Target Setting",
+ "description": "Evaluate the setting of a realistic global target for minimal achievable levels of plastic waste and the discussion of impacts on human life, the environment, and the plastic industry."
+ },
+ {
+ "category": "Equity Issues",
+ "description": "Assess the discussion on equity issues arising from the global plastic waste crisis and the proposed solutions to address these issues."
+ },
+ {
+ "category": "Timeline and Circumstances",
+ "description": "Evaluate the proposed timeline to reach the target waste levels and the identification of circumstances that may accelerate or hinder achieving the target."
+ },
+ {
+ "category": "Memo and Summary",
+ "description": "Review the clarity and conciseness of the two-page memo and one-page summary sheet in communicating the model, findings, and recommendations to the ICM."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to estimate the maximum levels of plastic waste that can be safely mitigated. This involves formulating equations and models that can predict waste levels and their environmental impact.",
+ "details": "As a mathematician, you are adept at creating and analyzing mathematical models that can simulate complex systems. In this context, your expertise is crucial for developing models that estimate the safe levels of plastic waste mitigation. You should focus on ensuring that the models are robust, accurate, and take into account various factors such as waste sources, recycling rates, and environmental impact. Your attention to detail and ability to work with abstract concepts will be essential in reviewing the modeling solutions to ensure they are mathematically sound and applicable to real-world scenarios."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets related to plastic production, waste, and recycling. A data scientist can process and interpret this data to inform the model and provide insights into trends and patterns.",
+ "details": "As a data scientist, your role is to handle and analyze complex datasets that pertain to plastic waste and its management. You are skilled in using statistical methods and machine learning techniques to extract meaningful insights from data. When reviewing the modeling solutions, you should ensure that the data used is accurate, relevant, and comprehensive. Your expertise in data visualization and interpretation will be crucial in understanding the current state of plastic waste and predicting future trends. You should also evaluate the effectiveness of proposed solutions based on data-driven evidence."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem is deeply rooted in environmental science, as it involves understanding the ecological impact of plastic waste and developing sustainable waste management strategies.",
+ "details": "As an environmental scientist, you bring a deep understanding of the ecological consequences of plastic waste. Your expertise is vital in assessing the environmental impact of different levels of plastic waste and the effectiveness of mitigation strategies. You should focus on evaluating the proposed models for their environmental sustainability and feasibility. Your knowledge of ecosystems, pollution, and conservation will help ensure that the solutions are environmentally sound and contribute to long-term ecological health. You should also consider the regional variations in environmental impact and the equity issues related to waste management."
+ },
+ {
+ "name": "Policy Analyst",
+ "thoughts": "The problem involves policy-making to reduce plastic waste, requiring an understanding of existing regulations, potential policy interventions, and their socio-economic impacts.",
+ "details": "As a policy analyst, your role is to evaluate the effectiveness of current policies and propose new regulations to manage plastic waste. You are skilled in analyzing the socio-economic implications of policy changes and understanding the political landscape. When reviewing the modeling solutions, you should assess the feasibility and potential impact of proposed policies on reducing plastic waste. Your expertise in policy analysis will help ensure that the solutions are not only effective but also equitable and considerate of different regional constraints. You should also consider how policies can be tailored to address the specific needs and challenges of various communities and industries."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the mathematical model's ability to estimate maximum levels of single-use or disposable plastic waste that can be safely mitigated without further environmental damage."
+ },
+ {
+ "category": "Factor Consideration",
+ "description": "Assess the extent to which the model considers various factors such as sources of waste, current waste levels, and resource availability for waste processing."
+ },
+ {
+ "category": "Waste Reduction Discussion",
+ "description": "Examine the discussion on reducing plastic waste to environmentally safe levels, including the consideration of alternatives to plastics and the impact on citizens' lives."
+ },
+ {
+ "category": "Policy Analysis",
+ "description": "Analyze the evaluation of policies aimed at reducing single-use plastics, including regional-specific constraints and effectiveness."
+ },
+ {
+ "category": "Target Setting",
+ "description": "Evaluate the setting of a realistic global target for minimal achievable levels of plastic waste and the discussion of impacts on human life, the environment, and the plastic industry."
+ },
+ {
+ "category": "Equity Issues",
+ "description": "Assess the discussion on equity issues arising from the global plastic waste crisis and the proposed solutions to address these issues."
+ },
+ {
+ "category": "Timeline and Circumstances",
+ "description": "Evaluate the proposed timeline to reach the target waste levels and the identification of circumstances that may accelerate or hinder achieving the target."
+ },
+ {
+ "category": "Memo and Summary",
+ "description": "Review the clarity and conciseness of the two-page memo and one-page summary sheet in communicating the model, findings, and recommendations to the ICM."
+ }
+ ]
+ }
+ },
+ "2020_Moving_North": {
+ "year": "2020",
+ "title": "Moving North",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2020/MCM-A/index.html",
+ "question": "Global ocean temperatures affect the quality of habitats for certain ocean-dwelling species. When temperature changes are too great for their continued thriving, these species move to seek other habitats better suited to their present and future living and reproductive success. One example of this is seen in the lobster population of Maine, USA, that is slowly migrating north to Canada where the lower ocean temperatures provide a more suitable habitat. This geographic population shift can significantly disrupt the livelihood of companies who depend on the stability of ocean-dwelling species.\n\nYour team has been hired as consultants by a Scottish North Atlantic fishery management consortium. The consortium wants to gain a better understanding of issues related to the potential migration of Scottish herring and mackerel from their current habitats near Scotland if and when global ocean temperatures increase. These two fish species represent a significant economic contribution to the Scottish fishing industry. Changes in population locations of herring and mackerel could make it economically impractical for smaller Scotland-based fishing companies, who use fishing vessels without on-board refrigeration, to harvest and deliver fresh fish to markets in Scotland fishing ports.\n\nRequirements\n\n1. Build a mathematical model to identify the most likely locations for these two fish species over the next 50 years, assuming that water temperatures are going to change enough to cause the populations to move.\n\n2. Based upon how rapidly the ocean water temperature change occurs, use your model to predict best case, worst case, and most likely elapsed time(s) until these populations will be too far away for small fishing companies to harvest if the small fishing companies continue to operate out of their current locations.\n\n3. In light of your predictive analysis, should these small fishing companies make changes to their operations?\n\n a. If yes, use your model to identify and assess practical and economically attractive strategies for small fishing companies. Your strategies should consider, but not be limited to, realistic options that include:\n - Relocating some or all of a fishing company\u2019s assets from a current location in a Scottish port to closer to where both fish populations are moving;\n - Using some proportion of small fishing vessels capable of operating without land-based support for a period of time while still ensuring the freshness and high quality of the catch.\n - Other options that your team may identify and model.\n\n b. If your team rejects the need for any changes, justify reasons for your rejection based on your modeling results as they relate to the assumptions your team has made.\n\n4. Use your model to address how your proposal is affected if some proportion of the fishery moves into the territorial waters (sea) of another country.\n\n5. In addition to your technical report, prepare a one- to two-page article for Hook Line and Sinker magazine to help fishermen understand the seriousness of the problem and how your proposed solution(s) will improve their future business prospects.\n\nYour submission should consist of:\n\n- One-page Summary Sheet\n- One- to Two-page Article\n- Your solution of no more than 20 pages, for a maximum of 24 pages with your summary and article.\n\nGlossary\n\nFishery: The collection of fish of a given species and the area that they inhabit.\n\nHabitat: The type of environment in which an organism or group normally lives or occurs.\n\nSmall Fishing Company: A company engaged in commercial fishing with limited or very limited financial resources to invest in new equipment/vessels.\n\nTerritorial Waters (sea): \"as defined by the 1982 United Nations Convention on the Law of the Sea, is a belt of coastal waters extending at most 12 nautical miles (22.2 km; 13.8 mi) from the baseline (usually the mean low-water mark) of a coastal state. The territorial sea is regarded as the sovereign territory of the state, although foreign ships (military and civilian) are allowed innocent passage through it, or transit passage for straits; this sovereignty also extends to the airspace over and seabed below.\"",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the mathematical model's ability to predict the most likely future locations of herring and mackerel over the next 50 years based on projected ocean temperature changes."
+ },
+ {
+ "category": "Temperature Change Scenarios",
+ "description": "Assess the model's capability to handle different rates of ocean temperature change and predict best case, worst case, and most likely scenarios for the time until fish populations move beyond the reach of small fishing companies."
+ },
+ {
+ "category": "Operational Strategy Recommendations",
+ "description": "Evaluate the practicality and economic attractiveness of the proposed strategies for small fishing companies, including asset relocation, vessel upgrades, and other innovative solutions."
+ },
+ {
+ "category": "Justification of No Change",
+ "description": "If no operational changes are recommended, assess the justification provided based on the model's results and assumptions."
+ },
+ {
+ "category": "International Waters Consideration",
+ "description": "Examine how the model addresses the impact of fish populations moving into the territorial waters of another country and the implications for the fishing companies."
+ },
+ {
+ "category": "Communication and Outreach",
+ "description": "Evaluate the clarity and effectiveness of the one- to two-page article intended for fishermen, ensuring it communicates the seriousness of the problem and the proposed solutions."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires the development of a mathematical model to predict the migration patterns of fish species based on changing ocean temperatures. This involves complex calculations and the formulation of equations that can accurately represent environmental and biological factors.",
+ "details": "As a mathematician, you are crucial in constructing the mathematical framework needed to predict fish migration patterns. You should focus on ensuring the model accurately represents the relationship between temperature changes and fish habitat preferences. Pay attention to the assumptions made in the model and verify the mathematical integrity of the equations used. Your expertise in differential equations, statistical modeling, and optimization will be essential in evaluating the robustness and reliability of the proposed solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets related to ocean temperatures, fish populations, and economic factors. A data scientist is needed to process this data, identify trends, and validate the model predictions.",
+ "details": "As a data scientist, your role is to handle the data-driven aspects of the problem. You should ensure that the data used in the model is accurate, comprehensive, and up-to-date. Your skills in data analysis, machine learning, and statistical methods will be vital in interpreting the results and providing insights into the migration patterns. You should also focus on the visualization of data to make the findings accessible and understandable to stakeholders."
+ },
+ {
+ "name": "Marine Biologist",
+ "thoughts": "Understanding the biological and ecological aspects of fish migration is crucial. A marine biologist can provide insights into the behavior and habitat preferences of herring and mackerel, which are essential for accurate modeling.",
+ "details": "As a marine biologist, your expertise in fish ecology and behavior is critical. You should review the model to ensure it accurately reflects the biological factors influencing fish migration. Consider the impact of temperature changes on fish physiology and reproduction, and how these factors might drive migration. Your knowledge of marine ecosystems will help assess the feasibility of proposed strategies for fishing companies and ensure they align with ecological realities."
+ },
+ {
+ "name": "Environmental Economist",
+ "thoughts": "The economic implications of fish migration are significant for the Scottish fishing industry. An environmental economist can evaluate the economic impact and propose viable strategies for small fishing companies.",
+ "details": "As an environmental economist, your role is to assess the economic consequences of fish migration and the proposed solutions. You should focus on the cost-benefit analysis of different strategies, considering both short-term and long-term impacts on the fishing industry. Your expertise in economic modeling and resource management will be essential in evaluating the practicality and attractiveness of relocation or investment in new technologies. Ensure that the economic assumptions in the model are realistic and consider external factors such as international trade and policy changes."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the mathematical model's ability to predict the most likely future locations of herring and mackerel over the next 50 years based on projected ocean temperature changes."
+ },
+ {
+ "category": "Temperature Change Scenarios",
+ "description": "Assess the model's capability to handle different rates of ocean temperature change and predict best case, worst case, and most likely scenarios for the time until fish populations move beyond the reach of small fishing companies."
+ },
+ {
+ "category": "Operational Strategy Recommendations",
+ "description": "Evaluate the practicality and economic attractiveness of the proposed strategies for small fishing companies, including asset relocation, vessel upgrades, and other innovative solutions."
+ },
+ {
+ "category": "Justification of No Change",
+ "description": "If no operational changes are recommended, assess the justification provided based on the model's results and assumptions."
+ },
+ {
+ "category": "International Waters Consideration",
+ "description": "Examine how the model addresses the impact of fish populations moving into the territorial waters of another country and the implications for the fishing companies."
+ },
+ {
+ "category": "Communication and Outreach",
+ "description": "Evaluate the clarity and effectiveness of the one- to two-page article intended for fishermen, ensuring it communicates the seriousness of the problem and the proposed solutions."
+ }
+ ]
+ }
+ },
+ "2020_The_Best_Summer": {
+ "year": "2020",
+ "title": "The Best Summer Job",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2020/HIMCM-A/index.html",
+ "question": "Although it's only November, you need to start planning for your 2021 summer job. You have a variety of choices this year and want to determine your \"best\" choice. You pose this problem for your team of math friends: We have many opportunities for a summer job. Some allow us to work from home virtually/electronically, some are a walk or bike ride away, and others require us to drive or take a train. Each job offers differing numbers of hours each week and the hourly rates also vary. Some involve physical activity, or at least not sitting at a desk (e.g. cashier at a store, lifeguarding, or wait staff at a restaurant), while others are mostly sedentary and perhaps use analytical and organizational skills (e.g. data analysis, office administration, or research). Let's develop a model that will evaluate the choices we have for our summer jobs and help us all find the \"best\" job. While we certainly want to earn and save some money, we also want to have time for recreation activities (e.g. exercise, outings, and social time with friends). Let's make our model one that will be helpful for all high school students to think about and analyze their summer job options.\n\n1. What factors should high school students who are looking for a summer job consider? List and describe the various factors your team identifies. Note that factors may be quantitative or qualitative, constant or variable, and deterministic or probabilistic. Be sure to include units as appropriate.\n\n2. Use your factors to develop a model or algorithm (or set of models/algorithms) for a high school student to use to evaluate their summer job options based on their own situation and preferences as inputs to your model.\n\n3. Test your model with at least ten fictional persons that you create with reasonable data. Explain your development of these fictional persons and the data you chose. Analyze the results of the application of your model on these persons.\n\nYour PDF solution of no more than 25 total pages should include:\n\n- One-page Summary Sheet.\n- Your complete solution.\n\nGlossary:\n\n- Deterministic: processes that have only one (predetermined) outcome.\n- Fictional: not real or true; made up.\n- Probabilistic: processes based on the theory of probability or that randomness plays a role in predicting future events.\n- Sedentary: characterized by much sitting and little physical activity.",
+ "requirements": [
+ {
+ "category": "Factor Identification",
+ "description": "Identify and describe relevant factors for evaluating summer job options, including both quantitative (e.g., hourly rate, distance) and qualitative (e.g., job satisfaction, physical activity) aspects. Ensure factors are clearly defined with appropriate units and classifications (constant, variable, deterministic, probabilistic)."
+ },
+ {
+ "category": "Model Development",
+ "description": "Develop a comprehensive model or algorithm that incorporates the identified factors. The model should allow for input of individual preferences and situations, and be applicable to a wide range of high school students. The model should be logically structured and mathematically sound."
+ },
+ {
+ "category": "Model Testing",
+ "description": "Create at least ten fictional personas with reasonable and diverse data to test the model. Clearly explain the rationale behind the creation of these personas and the selection of their data. Ensure the personas cover a range of scenarios and preferences."
+ },
+ {
+ "category": "Result Analysis",
+ "description": "Analyze the results obtained from applying the model to the fictional personas. Discuss the effectiveness of the model in evaluating job options and its ability to accommodate different preferences. Highlight any patterns or insights gained from the analysis."
+ },
+ {
+ "category": "Model Applicability",
+ "description": "Evaluate the model's applicability and usefulness for high school students in general. Discuss any limitations or assumptions made in the model and suggest potential improvements or extensions."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves creating a mathematical model to evaluate various job options based on multiple factors. A mathematician's expertise is crucial in formulating the equations and algorithms that will underpin the model, ensuring it accurately reflects the relationships between different variables.",
+ "details": "You are a mathematician with expertise in developing and analyzing mathematical models. Your role is to ensure that the model accurately represents the problem's constraints and objectives. You should focus on the logical structure of the model, the assumptions made, and the mathematical techniques used to solve it. Pay attention to how the model incorporates both quantitative and qualitative factors and ensure that it can handle the variability and uncertainty inherent in the problem."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing various datasets related to job options, such as hourly rates, work hours, and job locations. A data scientist's skills in data analysis and machine learning are essential for processing this data and extracting meaningful insights that will inform the model.",
+ "details": "You are a data scientist with expertise in data analysis and machine learning. Your role is to review how data is collected, processed, and integrated into the model. You should evaluate the methods used for data cleaning, feature selection, and the application of statistical techniques. Ensure that the model can adapt to different datasets and that it provides accurate and actionable insights for high school students evaluating their job options."
+ },
+ {
+ "name": "Career Counselor",
+ "thoughts": "The problem involves evaluating job options based on personal preferences and career goals. A career counselor's expertise is valuable in understanding the qualitative aspects of job selection, such as personal interests, skill development, and long-term career impact.",
+ "details": "You are a career counselor with expertise in guiding individuals through career decisions. Your role is to assess how well the model incorporates personal preferences and career aspirations. Pay attention to how the model balances financial considerations with personal growth and satisfaction. Ensure that the model provides a holistic view of job options, helping students make informed decisions that align with their long-term goals."
+ },
+ {
+ "name": "Human Resources Specialist",
+ "thoughts": "The problem involves understanding the nature of different job roles and their requirements. A human resources specialist's knowledge of job descriptions, work environments, and employment conditions is crucial for accurately evaluating job options.",
+ "details": "You are a human resources specialist with expertise in job analysis and employment conditions. Your role is to review how the model accounts for the various aspects of job roles, such as physical demands, work environment, and skill requirements. Ensure that the model accurately reflects the realities of different job types and provides realistic assessments of job suitability for high school students. Pay attention to how the model addresses work-life balance and the potential for skill development in each job option."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Factor Identification",
+ "description": "Identify and describe relevant factors for evaluating summer job options, including both quantitative (e.g., hourly rate, distance) and qualitative (e.g., job satisfaction, physical activity) aspects. Ensure factors are clearly defined with appropriate units and classifications (constant, variable, deterministic, probabilistic)."
+ },
+ {
+ "category": "Model Development",
+ "description": "Develop a comprehensive model or algorithm that incorporates the identified factors. The model should allow for input of individual preferences and situations, and be applicable to a wide range of high school students. The model should be logically structured and mathematically sound."
+ },
+ {
+ "category": "Model Testing",
+ "description": "Create at least ten fictional personas with reasonable and diverse data to test the model. Clearly explain the rationale behind the creation of these personas and the selection of their data. Ensure the personas cover a range of scenarios and preferences."
+ },
+ {
+ "category": "Result Analysis",
+ "description": "Analyze the results obtained from applying the model to the fictional personas. Discuss the effectiveness of the model in evaluating job options and its ability to accommodate different preferences. Highlight any patterns or insights gained from the analysis."
+ },
+ {
+ "category": "Model Applicability",
+ "description": "Evaluate the model's applicability and usefulness for high school students in general. Discuss any limitations or assumptions made in the model and suggest potential improvements or extensions."
+ }
+ ]
+ }
+ },
+ "2021_Hot_Dog_Concession": {
+ "year": "2021",
+ "title": "Hot Dog Concession Stand",
+ "level": "Middle School",
+ "source": "MidMCM",
+ "link": "Problems/2021/MidMCMsample/index.html",
+ "question": "2021_MidMCM_HotDogs.pdf Hot Dog Concession Stand\n\n### Text in the PDF File: 2021_MidMCM_HotDogs.pdf\n\n**Hot Dog Concession Stand Problem Overview**\n\n**Objective:** \nManage a concession stand to maximize funds raised for student activities by selling hot dogs at 10 monthly school events. The challenge is to balance purchasing enough hot dogs to meet demand without overbuying, as unsold hot dogs must be discarded.\n\n**Data Provided:**\n- Historical sales data for hot dogs over the past 5 years (Table 1).\n- Hot dog package purchasing options (Table 2).\n\n**Table 1: Hot Dogs Sold Over the Past 5 Years**\n\n| Event # | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |\n|---------|--------|--------|--------|--------|--------|\n| 1 | 149 | 167 | 161 | 176 | 208 |\n| 2 | 183 | 193 | 166 | 174 | 164 |\n| 3 | 220 | 163 | 186 | 171 | 152 |\n| 4 | 172 | 146 | 156 | 152 | 186 |\n| 5 | 188 | 166 | 180 | 147 | 148 |\n| 6 | 164 | 198 | 155 | 189 | 177 |\n| 7 | 181 | 188 | 139 | 190 | 202 |\n| 8 | 181 | 218 | 213 | 201 | 202 |\n| 9 | 162 | 167 | 181 | 153 | 174 |\n| 10 | 160 | 142 | 198 | 175 | 178 |\n\n**Table 2: Cost of Hot Dog Packages**\n\n| Hot Dogs in a Package | Cost (US Dollars) |\n|-----------------------|-------------------|\n| 8 | $5.00 |\n| 16 | $8.00 |\n| 24 | $10.00 |\n\n**Initial Fund:** $75 for the first event.\n\n**Tasks:**\n\n1. **Planning for Hot Dog Purchases:**\n - Analyze past sales data to predict future demand.\n - Develop a purchasing plan to maximize profits while minimizing waste.\n - Consider factors such as changing demand and budget constraints.\n\n2. **Financial Management:**\n - Track expected fund deposits and withdrawals.\n - Ensure sufficient funds are available for each event.\n - Estimate total funds raised by year-end and identify factors affecting this estimate.\n\n3. **Increasing Sales:**\n - Propose strategies to boost sales, such as price adjustments or promotions.\n - Use mathematical models to support your strategy.\n\n**Submission Requirements:**\n- A document with a one-page summary, and complete solution.\n- The document should not exceed 25 pages.\n\n**Additional Considerations:**\n- Explore the potential for selling other items or managing overhead costs.\n- Consider alternative uses for unsold hot dogs to reduce waste.",
+ "requirements": [
+ {
+ "category": "Demand Prediction",
+ "description": "Analyze historical sales data to accurately predict future demand for each event, considering trends and variability in past data."
+ },
+ {
+ "category": "Purchasing Strategy",
+ "description": "Develop a purchasing plan that balances the need to meet demand with minimizing waste, taking into account package sizes and costs."
+ },
+ {
+ "category": "Budget Management",
+ "description": "Ensure that the initial fund and subsequent revenues are managed effectively to cover costs for each event, with a clear plan for fund deposits and withdrawals."
+ },
+ {
+ "category": "Profit Maximization",
+ "description": "Estimate the total funds raised by the end of the year, identifying key factors that influence this estimate and strategies to maximize profits."
+ },
+ {
+ "category": "Sales Strategy",
+ "description": "Propose and justify strategies to increase sales, such as pricing adjustments or promotions, supported by mathematical models."
+ },
+ {
+ "category": "Waste Reduction",
+ "description": "Consider alternative uses for unsold hot dogs to reduce waste and explore the potential for selling other items or managing overhead costs."
+ },
+ {
+ "category": "Model Justification",
+ "description": "Provide a clear rationale for the chosen mathematical models and strategies, including assumptions and limitations."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct a sensitivity analysis to understand how changes in key parameters affect the outcomes of the model."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to predict future demand based on historical sales data and to optimize purchasing strategies to maximize profits while minimizing waste.",
+ "details": "As a mathematician, you are adept at creating and analyzing mathematical models that can predict future sales based on historical data. You should focus on ensuring that the models used are robust and account for variability in demand. Pay attention to the assumptions made in the models and verify that they are reasonable given the context of the problem. Your expertise in optimization techniques will be crucial in developing a purchasing plan that balances cost and demand effectively."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing historical sales data to identify patterns and trends that can inform future purchasing decisions and sales strategies.",
+ "details": "As a data scientist, you are skilled in data analysis and statistical methods. You should focus on extracting meaningful insights from the historical sales data, identifying trends, and using these insights to inform predictive models. Your expertise in machine learning and data visualization will be valuable in developing accurate demand forecasts and in presenting data-driven recommendations for purchasing and sales strategies. Ensure that the data is clean and that any anomalies are addressed before analysis."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem involves optimizing the purchasing and inventory management process to maximize profits and minimize waste, which is a classic operations research problem.",
+ "details": "As an operations research analyst, you specialize in using mathematical and analytical methods to help make better decisions. You should focus on developing optimization models that can determine the best purchasing strategy given the constraints of budget and demand variability. Your expertise in linear programming and inventory management will be crucial in ensuring that the purchasing plan is both cost-effective and efficient. Pay attention to the constraints and objectives outlined in the problem and ensure that the proposed solutions are feasible and practical."
+ },
+ {
+ "name": "Marketing Strategist",
+ "thoughts": "The problem includes increasing sales through strategies such as price adjustments or promotions, which requires expertise in marketing and consumer behavior.",
+ "details": "As a marketing strategist, you are skilled in developing and implementing strategies to boost sales and engage customers. You should focus on identifying opportunities to increase sales through targeted promotions, pricing strategies, and customer engagement initiatives. Your understanding of consumer behavior and market trends will be valuable in proposing strategies that are both innovative and effective. Ensure that the proposed strategies are supported by data and align with the overall objectives of maximizing funds raised for student activities."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Demand Prediction",
+ "description": "Analyze historical sales data to accurately predict future demand for each event, considering trends and variability in past data."
+ },
+ {
+ "category": "Purchasing Strategy",
+ "description": "Develop a purchasing plan that balances the need to meet demand with minimizing waste, taking into account package sizes and costs."
+ },
+ {
+ "category": "Budget Management",
+ "description": "Ensure that the initial fund and subsequent revenues are managed effectively to cover costs for each event, with a clear plan for fund deposits and withdrawals."
+ },
+ {
+ "category": "Profit Maximization",
+ "description": "Estimate the total funds raised by the end of the year, identifying key factors that influence this estimate and strategies to maximize profits."
+ },
+ {
+ "category": "Sales Strategy",
+ "description": "Propose and justify strategies to increase sales, such as pricing adjustments or promotions, supported by mathematical models."
+ },
+ {
+ "category": "Waste Reduction",
+ "description": "Consider alternative uses for unsold hot dogs to reduce waste and explore the potential for selling other items or managing overhead costs."
+ },
+ {
+ "category": "Model Justification",
+ "description": "Provide a clear rationale for the chosen mathematical models and strategies, including assumptions and limitations."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct a sensitivity analysis to understand how changes in key parameters affect the outcomes of the model."
+ }
+ ]
+ }
+ },
+ "2021_Re-Optimizing_Food_Systems": {
+ "year": "2021",
+ "title": "Re-Optimizing Food Systems",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2021/ICM-E/index.html",
+ "question": "2021_ICM_Problem_E.pdf Re-Optimizing Food Systems\n\n### Text in the PDF File: 2021_ICM_Problem_E.pdf\n\n**2021 ICM Problem E: Re-Optimizing Food Systems**\n\n**Overview:**\nThe global food system, while efficient and profitable, is unstable and contributes significantly to environmental issues. Despite sufficient food production, 821 million people suffer from hunger worldwide. The system is responsible for 29% of greenhouse gas emissions, 80% of biodiversity loss, 80% of deforestation, and 70% of freshwater use. As the global population grows, it is crucial to produce more food sustainably.\n\n**Challenge:**\nThe International Comestibles Management (ICM) Committee invites teams to develop a model to re-imagine and reprioritize food systems. The model should be adaptable to optimize for efficiency, profitability, sustainability, and equity.\n\n**Key Considerations:**\n- Impact of optimizing food systems for equity and sustainability.\n- Differences between the proposed system and the current one.\n- Timeframe for implementing a new system.\n- Benefits and costs of changing food system priorities, and their timing.\n- Differences in impact between developed and developing countries.\n- Scalability and adaptability of the model to various regions.\n\n**Task:**\nDevelop a food system model and apply it to at least one developed and one developing country. Discuss the model's scalability and adaptability.\n\n**Submission Requirements:**\n- A solution of no more than 25 pages, including:\n - One-page Summary Sheet\n - Complete solution\n\n**Glossary:**\n- **Food Insecure:** Lack of reliable access to sufficient affordable and nutritious food.\n- **Food Scarcity:** Insufficient quantities of food and nutrients to sustain the local population, due to production shortfalls or uneven resource distribution.\n\n**References:**\n1. World Hunger and Poverty Facts: [World Hunger News](https://www.worldhunger.org/world-hunger-and-poverty-facts-and-statistics/)",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "The model should effectively integrate efficiency, profitability, sustainability, and equity in food systems."
+ },
+ {
+ "category": "Impact Analysis",
+ "description": "Evaluate the impact of the proposed model on equity and sustainability compared to the current system."
+ },
+ {
+ "category": "Implementation Timeframe",
+ "description": "Provide a realistic and detailed timeframe for implementing the new food system model."
+ },
+ {
+ "category": "Cost-Benefit Analysis",
+ "description": "Analyze the benefits and costs of changing food system priorities, including the timing of these changes."
+ },
+ {
+ "category": "Geographical Application",
+ "description": "Apply the model to at least one developed and one developing country, highlighting differences in impact."
+ },
+ {
+ "category": "Scalability and Adaptability",
+ "description": "Discuss the model's scalability and adaptability to various regions and contexts."
+ },
+ {
+ "category": "Comparison with Current System",
+ "description": "Identify and explain the differences between the proposed system and the current food system."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem of re-optimizing food systems involves complex mathematical modeling to balance efficiency, profitability, sustainability, and equity. A mathematician's expertise is crucial in formulating and solving the equations that represent these multifaceted relationships.",
+ "details": "As a mathematician, you are adept at developing and analyzing mathematical models that can simulate the dynamics of food systems. Your role involves ensuring that the models are mathematically sound and capable of accurately representing the various factors involved, such as resource allocation, environmental impact, and economic viability. You should pay close attention to the assumptions made in the models and verify that they are reasonable and justifiable. Your expertise in optimization techniques will be essential in finding the best solutions that meet the problem's objectives."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem requires analyzing large datasets related to food production, environmental impact, and socio-economic factors. A data scientist's skills in data processing, statistical analysis, and machine learning are vital for extracting insights and informing the model.",
+ "details": "As a data scientist, you are skilled in handling and analyzing complex datasets that are crucial for understanding the current state of global food systems. Your role involves cleaning and processing data, identifying patterns and trends, and using statistical methods to inform the model's parameters. You should focus on ensuring data accuracy and relevance, and apply machine learning techniques to predict outcomes and optimize the model. Your ability to visualize data effectively will also help communicate findings to stakeholders."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem emphasizes sustainability and environmental impact, making the expertise of an environmental scientist essential. They can provide insights into the ecological consequences of different food system models and suggest sustainable practices.",
+ "details": "As an environmental scientist, you bring a deep understanding of the environmental challenges associated with food systems, such as greenhouse gas emissions, biodiversity loss, and deforestation. Your role is to evaluate the ecological impact of proposed models and ensure that they align with sustainability goals. You should assess the potential environmental benefits and costs of different strategies and provide recommendations for minimizing negative impacts. Your knowledge of sustainable practices and technologies will be invaluable in guiding the development of environmentally friendly food systems."
+ },
+ {
+ "name": "Agricultural Economist",
+ "thoughts": "The problem involves economic considerations such as profitability and equity, which are central to the role of an agricultural economist. They can analyze the economic implications of different food system models and ensure that they are financially viable and equitable.",
+ "details": "As an agricultural economist, you specialize in the economic aspects of food systems, including market dynamics, resource allocation, and policy implications. Your role is to assess the economic feasibility of proposed models and ensure that they promote equity and profitability. You should analyze the costs and benefits of different strategies, considering both short-term and long-term economic impacts. Your expertise in economic modeling and policy analysis will help ensure that the solutions are not only effective but also equitable and sustainable across different regions and populations."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "The model should effectively integrate efficiency, profitability, sustainability, and equity in food systems."
+ },
+ {
+ "category": "Impact Analysis",
+ "description": "Evaluate the impact of the proposed model on equity and sustainability compared to the current system."
+ },
+ {
+ "category": "Implementation Timeframe",
+ "description": "Provide a realistic and detailed timeframe for implementing the new food system model."
+ },
+ {
+ "category": "Cost-Benefit Analysis",
+ "description": "Analyze the benefits and costs of changing food system priorities, including the timing of these changes."
+ },
+ {
+ "category": "Geographical Application",
+ "description": "Apply the model to at least one developed and one developing country, highlighting differences in impact."
+ },
+ {
+ "category": "Scalability and Adaptability",
+ "description": "Discuss the model's scalability and adaptability to various regions and contexts."
+ },
+ {
+ "category": "Comparison with Current System",
+ "description": "Identify and explain the differences between the proposed system and the current food system."
+ }
+ ]
+ }
+ },
+ "2021_Storing_the_Sun": {
+ "year": "2021",
+ "title": "Storing the Sun",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2021/HIMCM-A/index.html",
+ "question": "2021_HiMCM_Problem_A.pdf Storing the Sun\n\n### Text in the PDF File: 2021_HiMCM_Problem_A.pdf\n\n**Problem A: Storing the Sun**\n\n**Objective:** Plan the use of solar power to provide electricity to a 1600 square-foot home in a remote area, focusing on energy storage to support the home at night and on cloudy days.\n\n**Background:**\n- Energy storage systems capture electricity, store it, and make it available when needed.\n- Most solar-powered homes use battery storage, either a single large battery or a bank of batteries.\n- Key battery specifications include continuous power rating, instantaneous power rating, usable capacity, and round-trip efficiency.\n\n**Battery Types:**\n- **Lead-acid batteries:** Known for low prices and reliability.\n- **Lithium-ion batteries:** More expensive, require no maintenance. Lithium iron phosphate (LFP) batteries offer long lifetimes and high safety ratings.\n\n**Requirements:**\n\n1. **Energy Needs Analysis:**\n - Determine energy requirements by asking questions such as:\n - How many people will use energy in the home?\n - What appliances will need energy and how much?\n - When will energy be used?\n\n2. **Model Development:**\n - Create a mathematical model or algorithm to choose the best battery storage system based on the analysis and criteria.\n\n3. **Battery Selection:**\n - Use the model to select the best battery option from available choices, considering factors like cost, power ratings, efficiency, and capacity.\n\n4. **Model Generalization:**\n - Adapt the model for different homes and preferences, evaluating its flexibility and effectiveness.\n\n5. **Cement Batteries:**\n - Explore the potential of using cement as a battery for energy storage.\n - Identify advantages and disadvantages, and discuss how cement batteries could be integrated into home energy systems.\n\n6. **Information for Cement Battery Comparison:**\n - Determine additional data needed to compare cement batteries with current options.\n\n7. **News Article:**\n - Write a non-technical article describing the decision model and future possibilities of cement batteries.\n\n**Battery Options:**\n\n| Battery | Cost (USD) | Type | Weight (lbs.) | Dimensions (L\u00d7W\u00d7D in inches) | Continuous Power (kW) | Instantaneous Power (kW) | Efficiency (%) | Capacity (kWh) |\n|---------|------------|------|---------------|-------------------------------|-----------------------|--------------------------|----------------|----------------|\n| Deka Solar 8GCC2 6V 198 | $368 | Sealed Gel Lead Acid | 68 | 10.25 \u00d7 7.1 \u00d7 10.9 | 0.049 (20 hrs) - 0.017 (100 hrs) | N/A | 80-85 | 1.18 |\n| Trojan L-16 -SPRE 6V 415 | $492 | Flooded Lead Acid | 118 | 11.7 \u00d7 6.9 \u00d7 17.6 | 0.19 (10 hrs) - 0.023 (100 hrs) | N/A | 80-85 | 2.5 |\n| Discover AES 7.4 kWh | $6,478 | Lithium Iron Phosphate | 192 | 18.5 \u00d7 13.3 \u00d7 14.7 | 6.65 | 14.4 (3 sec) | >95 | 7.4 |\n| Electriq PowerPod 2 | $13,000 | Lithium Iron Phosphate | 346 | 27.5 \u00d7 50 \u00d7 9 | 7.6 | 9 (60 sec) | 96.60 | 10 |\n| Tesla Powerwall+ | $8,500 | Lithium Nickel Manganese Cobalt Oxide | 343.9 | 62.8 \u00d7 29.7 \u00d7 6.3 | 7 | 10 (10 sec) | 90.00 | 13.5 |",
+ "requirements": [
+ {
+ "category": "Energy Needs Analysis",
+ "description": "Evaluate the thoroughness and accuracy of the energy requirements analysis, including the consideration of household size, appliance energy consumption, and usage patterns."
+ },
+ {
+ "category": "Model Development",
+ "description": "Assess the mathematical model or algorithm developed to choose the best battery storage system, focusing on its ability to incorporate various criteria such as cost, power ratings, efficiency, and capacity."
+ },
+ {
+ "category": "Battery Selection",
+ "description": "Grade the application of the model in selecting the best battery option, ensuring that the choice is justified based on the analysis and criteria provided."
+ },
+ {
+ "category": "Model Generalization",
+ "description": "Evaluate the model's adaptability and effectiveness when applied to different homes and user preferences, including its flexibility to accommodate varying energy needs."
+ },
+ {
+ "category": "Cement Batteries Exploration",
+ "description": "Assess the exploration of cement batteries, including the identification of their advantages and disadvantages, and the discussion on their integration into home energy systems."
+ },
+ {
+ "category": "Information for Cement Battery Comparison",
+ "description": "Evaluate the identification of additional data needed to effectively compare cement batteries with current battery options."
+ },
+ {
+ "category": "News Article",
+ "description": "Grade the clarity and accessibility of the non-technical article describing the decision model and the potential future of cement batteries, ensuring it is understandable to a general audience."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires developing a mathematical model to analyze energy needs and select the optimal battery storage system. This involves formulating equations and algorithms to handle various parameters such as power ratings, efficiency, and capacity.",
+ "details": "As a mathematician, you are skilled in creating and analyzing mathematical models. You should focus on ensuring the model accurately represents the energy requirements and battery specifications. Pay attention to the assumptions made in the model and verify the mathematical rigor and validity of the solutions proposed. Your expertise in optimization and problem-solving will be crucial in evaluating the effectiveness of the model."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to energy consumption patterns, battery specifications, and costs. A data scientist can leverage statistical methods and machine learning algorithms to process this data and inform the model development.",
+ "details": "As a data scientist, you are adept at handling large datasets and extracting meaningful insights. You should focus on the data analysis aspect of the problem, ensuring that the data used in the model is accurate and comprehensive. Your skills in predictive modeling and data visualization will be essential in evaluating how well the model can adapt to different scenarios and preferences."
+ },
+ {
+ "name": "Electrical Engineer",
+ "thoughts": "The problem involves technical aspects of battery storage systems, including power ratings, efficiency, and capacity. An electrical engineer can provide insights into the practical implementation and integration of these systems into home energy setups.",
+ "details": "As an electrical engineer, you have expertise in the design and operation of electrical systems. You should evaluate the technical feasibility of the proposed battery solutions, considering factors like installation requirements and safety standards. Your knowledge of electrical circuits and energy systems will be vital in assessing the practicality and reliability of the model's recommendations."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem involves the use of solar power and energy storage, which have environmental implications. An environmental scientist can assess the sustainability and ecological impact of different battery options and energy solutions.",
+ "details": "As an environmental scientist, you are skilled in evaluating the environmental impact of energy systems. You should focus on the sustainability aspect of the problem, considering the lifecycle and ecological footprint of the battery options. Your expertise in renewable energy and environmental policy will be crucial in assessing the long-term viability and environmental benefits of the proposed solutions."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Energy Needs Analysis",
+ "description": "Evaluate the thoroughness and accuracy of the energy requirements analysis, including the consideration of household size, appliance energy consumption, and usage patterns."
+ },
+ {
+ "category": "Model Development",
+ "description": "Assess the mathematical model or algorithm developed to choose the best battery storage system, focusing on its ability to incorporate various criteria such as cost, power ratings, efficiency, and capacity."
+ },
+ {
+ "category": "Battery Selection",
+ "description": "Grade the application of the model in selecting the best battery option, ensuring that the choice is justified based on the analysis and criteria provided."
+ },
+ {
+ "category": "Model Generalization",
+ "description": "Evaluate the model's adaptability and effectiveness when applied to different homes and user preferences, including its flexibility to accommodate varying energy needs."
+ },
+ {
+ "category": "Cement Batteries Exploration",
+ "description": "Assess the exploration of cement batteries, including the identification of their advantages and disadvantages, and the discussion on their integration into home energy systems."
+ },
+ {
+ "category": "Information for Cement Battery Comparison",
+ "description": "Evaluate the identification of additional data needed to effectively compare cement batteries with current battery options."
+ },
+ {
+ "category": "News Article",
+ "description": "Grade the clarity and accessibility of the non-technical article describing the decision model and the potential future of cement batteries, ensuring it is understandable to a general audience."
+ }
+ ]
+ }
+ },
+ "2022_Forestry_for_Carbon": {
+ "year": "2022",
+ "title": "Forestry for Carbon Sequestration",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2022/ICM-E/index.html",
+ "question": "2022_ICM_Problem_E.pdf Forestry for Carbon Sequestration\n\n### Text in the PDF File: 2022_ICM_Problem_E.pdf\n\n**2022 ICM Problem E: Forestry for Carbon Sequestration**\n\n**Background**\n\nClimate change is a significant threat, necessitating actions to reduce atmospheric greenhouse gases. Carbon sequestration, the process of capturing and storing carbon dioxide, is crucial. Forests play a vital role in this process by sequestering carbon in living plants and forest products like furniture and paper. Effective forest management, including appropriate harvesting, can enhance carbon sequestration. However, overharvesting can reduce these benefits. Forest managers must balance the value of forest products with the benefits of allowing forests to grow and sequester carbon.\n\n**Requirements**\n\nThe International Carbon Management (ICM) Collaboration aims to guide forest managers worldwide. A universal approach is not feasible due to diverse forest characteristics and values. The task involves:\n\n- Developing a carbon sequestration model to estimate how much carbon dioxide a forest and its products can sequester over time. The model should identify the most effective forest management plan for carbon sequestration.\n- Creating a decision model to balance carbon sequestration with other forest values, such as conservation, recreation, and cultural considerations.\n\n**Key Questions for Model Development:**\n\n- What management plans might your decision model suggest?\n- Under what conditions should a forest remain uncut?\n- Are there universal transition points between management plans?\n- How do specific forest characteristics and location influence these transition points?\n\n**Application of Models:**\n\n- Apply models to various forests and identify one where harvesting should be included in the management plan.\n - Estimate carbon sequestration over 100 years.\n - Recommend a forest management plan and justify it.\n - If the best plan extends the time between harvests by 10 years, propose a transition strategy that considers the needs of forest managers and users.\n\n**Public Communication:**\n\n- Write a one- to two-page newspaper article explaining why harvesting is included in the management plan for a specific forest, addressing community concerns.\n\n**Submission Requirements:**\n\n- A solution of no more than 25 pages, including:\n - One-page Summary Sheet\n - Complete solution\n - Newspaper article\n\n**Glossary**\n\n- **Biosphere:** Parts of Earth where life exists.\n- **Carbon Sequestration:** Capturing and storing atmospheric carbon dioxide.\n- **Forest Manager:** Entity managing a forest, making decisions on its use.\n- **Forest Products:** Items made from harvested wood, like furniture and paper.\n- **Greenhouse Gases:** Gases that trap heat in the atmosphere, e.g., carbon dioxide.\n- **Harvesting (trees):** Cutting down trees for forest products.\n- **Forest Management:** Managing a forest, including decisions on tree harvesting and regeneration.",
+ "requirements": [
+ {
+ "category": "Carbon Sequestration Model",
+ "description": "Evaluate the accuracy and reliability of the carbon sequestration model in estimating carbon dioxide sequestration over time for different forest types."
+ },
+ {
+ "category": "Decision Model",
+ "description": "Assess the decision model's ability to balance carbon sequestration with other forest values such as conservation, recreation, and cultural considerations."
+ },
+ {
+ "category": "Management Plan Suggestions",
+ "description": "Examine the range and feasibility of management plans suggested by the decision model, including conditions under which a forest should remain uncut."
+ },
+ {
+ "category": "Transition Points",
+ "description": "Determine the clarity and universality of transition points between management plans, and how they are influenced by specific forest characteristics and location."
+ },
+ {
+ "category": "Application to Various Forests",
+ "description": "Evaluate the application of models to different forests, including the justification for including harvesting in the management plan for a specific forest."
+ },
+ {
+ "category": "Carbon Sequestration Estimation",
+ "description": "Assess the accuracy of the estimated carbon sequestration over a 100-year period for a forest where harvesting is included."
+ },
+ {
+ "category": "Management Plan Recommendation",
+ "description": "Evaluate the rationale and justification provided for the recommended forest management plan, including any proposed transition strategies."
+ },
+ {
+ "category": "Public Communication",
+ "description": "Assess the effectiveness of the newspaper article in explaining the inclusion of harvesting in the management plan and addressing community concerns."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires developing mathematical models to estimate carbon sequestration and balance various forest values, which involves complex equations and optimization techniques.",
+ "details": "You are a mathematician with expertise in formulating and solving mathematical models related to carbon sequestration. You should focus on ensuring the models accurately represent the dynamics of carbon capture and storage in forests. Pay attention to the assumptions made in the models and verify the mathematical consistency and validity of the solutions. Your skills in differential equations, optimization, and statistical analysis are crucial for evaluating the effectiveness of the proposed models."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing diverse datasets related to forest characteristics, carbon sequestration rates, and management plans, requiring data processing and statistical analysis.",
+ "details": "You are a data scientist with expertise in handling and analyzing complex datasets. You should focus on the data-driven aspects of the models, ensuring that the data used is accurate, relevant, and properly integrated into the modeling process. Your skills in data mining, machine learning, and statistical analysis are essential for evaluating the robustness and predictive power of the models. Pay attention to the data sources, preprocessing techniques, and validation methods used in the modeling solutions."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem involves understanding the ecological impact of forest management on carbon sequestration, requiring expertise in environmental science and ecology.",
+ "details": "You are an environmental scientist with expertise in the ecological aspects of carbon sequestration. You should focus on evaluating how the proposed models account for ecological factors such as biodiversity, soil health, and ecosystem services. Your knowledge of forest ecology, conservation biology, and environmental impact assessment is crucial for assessing the sustainability and environmental implications of the management plans. Pay attention to how the models incorporate ecological data and the potential trade-offs between carbon sequestration and other forest values."
+ },
+ {
+ "name": "Forestry Expert",
+ "thoughts": "The problem involves practical forest management strategies for carbon sequestration, requiring expertise in forestry practices and management.",
+ "details": "You are a forestry expert with practical knowledge of forest management techniques. You should focus on evaluating the feasibility and effectiveness of the proposed management plans in real-world scenarios. Your expertise in silviculture, forest economics, and sustainable forestry practices is essential for assessing the practicality and economic viability of the solutions. Pay attention to the management strategies suggested by the models and how they align with current forestry practices and policies."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Carbon Sequestration Model",
+ "description": "Evaluate the accuracy and reliability of the carbon sequestration model in estimating carbon dioxide sequestration over time for different forest types."
+ },
+ {
+ "category": "Decision Model",
+ "description": "Assess the decision model's ability to balance carbon sequestration with other forest values such as conservation, recreation, and cultural considerations."
+ },
+ {
+ "category": "Management Plan Suggestions",
+ "description": "Examine the range and feasibility of management plans suggested by the decision model, including conditions under which a forest should remain uncut."
+ },
+ {
+ "category": "Transition Points",
+ "description": "Determine the clarity and universality of transition points between management plans, and how they are influenced by specific forest characteristics and location."
+ },
+ {
+ "category": "Application to Various Forests",
+ "description": "Evaluate the application of models to different forests, including the justification for including harvesting in the management plan for a specific forest."
+ },
+ {
+ "category": "Carbon Sequestration Estimation",
+ "description": "Assess the accuracy of the estimated carbon sequestration over a 100-year period for a forest where harvesting is included."
+ },
+ {
+ "category": "Management Plan Recommendation",
+ "description": "Evaluate the rationale and justification provided for the recommended forest management plan, including any proposed transition strategies."
+ },
+ {
+ "category": "Public Communication",
+ "description": "Assess the effectiveness of the newspaper article in explaining the inclusion of harvesting in the management plan and addressing community concerns."
+ }
+ ]
+ }
+ },
+ "2022_Power_Profile_of": {
+ "year": "2022",
+ "title": "Power Profile of a Cyclist",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2022/MCM-A/index.html",
+ "question": "2022_MCM_Problem_A.pdf 2022_MCM_Problem_A.pdf Power Profile of a Cyclist\n\n### Text in the PDF File: 2022_MCM_Problem_A.pdf\n\n**2022 MCM Problem A: Power Profile of a Cyclist**\n\n**Background**\nIn bicycle road races, such as individual time trials, cyclists aim to complete a course in the shortest time. A rider's power curve shows the maximum power they can sustain over different durations. More power typically means less time before needing recovery. Riders must manage their power to minimize race time, considering fatigue and energy limits.\n\n**Objective**\nDevelop a model to determine the relationship between a cyclist's position on a course and the power they apply, considering energy limits and past exertion.\n\n**Model Requirements**\n1. Define power profiles for two rider types: a time trial specialist and another type (consider gender differences).\n2. Apply the model to:\n - 2021 Olympic Time Trial course in Tokyo, Japan\n - A custom-designed course with at least four sharp turns and a nontrivial road grade, ending near its start.\n3. Assess the impact of weather conditions, such as wind direction and strength.\n4. Evaluate sensitivity to deviations from target power distribution.\n5. Extend the model for a team time trial with six riders, focusing on the fourth rider's finish time.\n\n**Deliverables**\n- A two-page race guidance for a Directeur Sportif, focusing on one rider and one course, with an overview and model summary.\n- A complete solution of no more than 25 pages, including:\n - One-page Summary Sheet\n - Complete solution\n - Two-page rider\u2019s race guidance\n\n**Glossary**\n- **Criterium**: A race on a closed course, defined by laps or time.\n- **Directeur Sportif**: Team director managing riders and race strategy.\n- **Individual Time Trial**: Riders race alone on a set course; fastest time wins.\n- **Power Curve**: Graph of maximum power a rider can sustain over time.\n\n**Rider Types**\n- **Climber**: Excels in long climbs.\n- **Puncheur**: Specializes in short, steep climbs and accelerations.\n- **Rouleur**: Versatile across various terrains.\n- **Sprinter**: High power for short bursts, focuses on race finishes.\n- **Time Trial Specialist**: Excels in individual time trials.",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "The model should accurately determine the relationship between a cyclist's position on a course and the power they apply, considering energy limits and past exertion."
+ },
+ {
+ "category": "Rider Type Profiles",
+ "description": "Define and differentiate power profiles for at least two rider types, including a time trial specialist and another type, considering potential gender differences."
+ },
+ {
+ "category": "Course Application",
+ "description": "Apply the model to the 2021 Olympic Time Trial course in Tokyo and a custom-designed course with specific features like sharp turns and road grades."
+ },
+ {
+ "category": "Weather Conditions",
+ "description": "Assess the impact of weather conditions, such as wind direction and strength, on the cyclist's power application and race time."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Evaluate the model's sensitivity to deviations from the target power distribution and how these deviations affect race outcomes."
+ },
+ {
+ "category": "Team Time Trial Extension",
+ "description": "Extend the model to a team time trial scenario with six riders, focusing on the finish time of the fourth rider."
+ },
+ {
+ "category": "Race Guidance Deliverable",
+ "description": "Provide a two-page race guidance document for a Directeur Sportif, focusing on one rider and one course, summarizing the model and offering strategic insights."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a strong foundation in mathematical modeling to accurately represent the relationship between a cyclist's power output and their position on a course. This involves formulating equations that account for variables such as energy limits, fatigue, and course characteristics.",
+ "details": "As a mathematician, you are adept at developing and analyzing mathematical models. Your expertise in differential equations, optimization, and calculus will be crucial in formulating the power profiles and understanding the dynamics of power application over time. When reviewing the modeling solutions, pay attention to the mathematical rigor and the assumptions made in the model. Ensure that the equations accurately capture the complexities of the cyclist's power dynamics and that the solutions are both mathematically sound and practically applicable."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing complex datasets related to cyclist performance, course characteristics, and environmental conditions. A data scientist's skills in data analysis and machine learning are essential for processing this data and informing the model.",
+ "details": "As a data scientist, you bring expertise in handling large datasets, statistical analysis, and predictive modeling. Your role involves extracting meaningful insights from data on cyclist performance, weather conditions, and course profiles. When reviewing the modeling solutions, focus on the data-driven aspects of the model. Evaluate the quality and relevance of the data used, the statistical methods applied, and the robustness of any machine learning models. Ensure that the data analysis supports the model's conclusions and that any predictions are based on sound statistical principles."
+ },
+ {
+ "name": "Exercise Physiologist",
+ "thoughts": "Understanding the physiological aspects of a cyclist's performance is crucial for modeling power output and fatigue. An exercise physiologist can provide insights into how different rider types manage energy and recover during a race.",
+ "details": "As an exercise physiologist, you specialize in the study of human performance and endurance. Your knowledge of how the body responds to prolonged exertion, energy expenditure, and recovery processes is vital for accurately modeling a cyclist's power profile. When reviewing the modeling solutions, assess how well the model incorporates physiological principles, such as energy systems, fatigue thresholds, and recovery rates. Ensure that the model realistically represents the physical capabilities and limitations of the cyclists, and that it accounts for variations between different rider types and genders."
+ },
+ {
+ "name": "Sports Engineer",
+ "thoughts": "The design and characteristics of the course, as well as the impact of environmental factors like wind, require expertise in sports engineering. A sports engineer can evaluate how these elements affect a cyclist's performance and power application.",
+ "details": "As a sports engineer, you have expertise in the technical aspects of sports performance, including biomechanics, aerodynamics, and equipment design. Your role involves analyzing how course design, road grade, and environmental conditions influence a cyclist's power output and speed. When reviewing the modeling solutions, focus on the integration of engineering principles. Evaluate how well the model accounts for factors such as wind resistance, road surface, and course layout. Ensure that the model accurately reflects the physical challenges posed by the course and that it provides realistic guidance for optimizing performance under varying conditions."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "The model should accurately determine the relationship between a cyclist's position on a course and the power they apply, considering energy limits and past exertion."
+ },
+ {
+ "category": "Rider Type Profiles",
+ "description": "Define and differentiate power profiles for at least two rider types, including a time trial specialist and another type, considering potential gender differences."
+ },
+ {
+ "category": "Course Application",
+ "description": "Apply the model to the 2021 Olympic Time Trial course in Tokyo and a custom-designed course with specific features like sharp turns and road grades."
+ },
+ {
+ "category": "Weather Conditions",
+ "description": "Assess the impact of weather conditions, such as wind direction and strength, on the cyclist's power application and race time."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Evaluate the model's sensitivity to deviations from the target power distribution and how these deviations affect race outcomes."
+ },
+ {
+ "category": "Team Time Trial Extension",
+ "description": "Extend the model to a team time trial scenario with six riders, focusing on the finish time of the fourth rider."
+ },
+ {
+ "category": "Race Guidance Deliverable",
+ "description": "Provide a two-page race guidance document for a Directeur Sportif, focusing on one rider and one course, summarizing the model and offering strategic insights."
+ }
+ ]
+ }
+ },
+ "2022_The_Need_for": {
+ "year": "2022",
+ "title": "The Need for Bees (and not just for honey)",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2022/HIMCM-A/index.html",
+ "question": "2022_HiMCM_Problem_A.pdf 2022_HiMCM_Problem_A.pdf The Need for Bees (and not just for honey)\n\n### Text in the PDF File: 2022_HiMCM_Problem_A.pdf\n\n# Problem A: The Need for Bees (and not just for honey)\n\nHoneybees are essential for human survival due to their role in pollination and honey production. The decline in honeybee populations, known as Colony Collapse Disorder (CCD), is attributed to factors like viruses, pesticides, predators, habitat destruction, and environmental conditions.\n\n### Key Information:\n- **Travel Range**: Honeybees can travel up to 20 km, typically staying within 6 km of their hive.\n- **Hive Population**: A typical hive contains 20,000 to 80,000 honeybees.\n- **Flower Visits**: A single honeybee can visit approximately 2,000 flowers or more in a day.\n- **Lifespan**: Honeybees have a shorter lifespan in summer due to high workload, but may live 4-6 months in autumn and winter.\n- **Factors Affecting Lifespan**: Activity level, pollen consumption, and protein abundance.\n\n### Tasks:\n1. **Model Development**: Create a model to determine the population of a honeybee colony over time.\n2. **Sensitivity Analysis**: Identify which factors (e.g., lifespans, egg laying rates) most impact colony size.\n3. **Pollination Prediction**: Estimate the number of hives needed to support pollination of a 20-acre (81,000 square meters) land with crops.\n4. **Communication**: Develop a non-technical, one-page blog or infographic summarizing your findings.\n\n### Submission Requirements:\n- A solution of no more than 25 pages, including:\n - One-page Summary Sheet\n - Complete Solution\n - One-page Blog or Infographic",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the mathematical model's ability to accurately simulate the population dynamics of a honeybee colony over time, considering factors like lifespan, egg laying rates, and environmental conditions."
+ },
+ {
+ "category": "Model Assumptions",
+ "description": "Assess the clarity and justification of assumptions made in the model, such as the impact of environmental factors and the typical behavior of honeybees."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Analyze the thoroughness of the sensitivity analysis in identifying which factors most significantly impact the colony size and how these factors are quantified."
+ },
+ {
+ "category": "Pollination Prediction",
+ "description": "Evaluate the accuracy and practicality of the estimation of the number of hives needed to support pollination of a 20-acre land area, considering the travel range and flower visit capacity of honeybees."
+ },
+ {
+ "category": "Communication",
+ "description": "Assess the effectiveness of the non-technical blog or infographic in summarizing the findings in a clear and engaging manner for a general audience."
+ },
+ {
+ "category": "Integration and Coherence",
+ "description": "Evaluate how well the different components of the solution (model development, sensitivity analysis, and pollination prediction) are integrated into a coherent and logical overall solution."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires the development of a mathematical model to predict the population dynamics of a honeybee colony over time. This involves understanding and applying mathematical principles to create equations that can simulate real-world scenarios.",
+ "details": "As a mathematician, you are adept at formulating and solving complex equations that describe the behavior of honeybee populations. You should focus on ensuring the mathematical rigor of the model, checking for logical consistency, and verifying that the assumptions made are reasonable and well-justified. Your expertise in differential equations, probability, and statistics will be crucial in evaluating the accuracy and reliability of the proposed model."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing various datasets related to honeybee populations, environmental factors, and pollination needs. A data scientist's role is crucial in processing and interpreting these datasets to inform the model and perform sensitivity analysis.",
+ "details": "As a data scientist, you are skilled in data analysis, statistical methods, and machine learning techniques. You should pay attention to the quality and relevance of the data used in the model, ensuring that it is comprehensive and accurately represents the factors affecting honeybee populations. Your ability to perform sensitivity analysis will help identify the most critical factors impacting colony size, which is essential for refining the model and making accurate predictions."
+ },
+ {
+ "name": "Ecologist",
+ "thoughts": "The problem involves understanding the ecological factors affecting honeybee populations, such as habitat destruction and environmental conditions. An ecologist's expertise is vital in assessing these factors and their impact on honeybee behavior and survival.",
+ "details": "As an ecologist, you have a deep understanding of the interactions between honeybees and their environment. You should evaluate how well the model incorporates ecological principles and whether it accurately reflects the impact of environmental changes on honeybee populations. Your insights into habitat requirements, predator-prey dynamics, and ecosystem services will be invaluable in ensuring the model's ecological validity."
+ },
+ {
+ "name": "Agricultural Scientist",
+ "thoughts": "The problem includes estimating the number of hives needed for effective pollination of crops, which requires knowledge of agricultural practices and crop pollination requirements. An agricultural scientist's expertise is crucial in aligning the model with real-world agricultural needs.",
+ "details": "As an agricultural scientist, you are knowledgeable about crop pollination, agricultural ecosystems, and the role of honeybees in enhancing crop yields. You should assess whether the model accurately estimates the pollination needs of a 20-acre land and if it considers factors such as crop type, flowering periods, and pollination efficiency. Your expertise will help ensure that the model's predictions are practical and applicable to agricultural settings."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the mathematical model's ability to accurately simulate the population dynamics of a honeybee colony over time, considering factors like lifespan, egg laying rates, and environmental conditions."
+ },
+ {
+ "category": "Model Assumptions",
+ "description": "Assess the clarity and justification of assumptions made in the model, such as the impact of environmental factors and the typical behavior of honeybees."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Analyze the thoroughness of the sensitivity analysis in identifying which factors most significantly impact the colony size and how these factors are quantified."
+ },
+ {
+ "category": "Pollination Prediction",
+ "description": "Evaluate the accuracy and practicality of the estimation of the number of hives needed to support pollination of a 20-acre land area, considering the travel range and flower visit capacity of honeybees."
+ },
+ {
+ "category": "Communication",
+ "description": "Assess the effectiveness of the non-technical blog or infographic in summarizing the findings in a clear and engaging manner for a general audience."
+ },
+ {
+ "category": "Integration and Coherence",
+ "description": "Evaluate how well the different components of the solution (model development, sensitivity analysis, and pollination prediction) are integrated into a coherent and logical overall solution."
+ }
+ ]
+ }
+ },
+ "2022_Water_and_Hydroelectric": {
+ "year": "2022",
+ "title": "Water and Hydroelectric Power Sharing",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2022/MCM-B/index.html",
+ "question": "2022_MCM_Problem_B.pdf 2022_MCM_Problem_B.pdf Water and Hydroelectric Power Sharing\n\n### Text in the PDF File: 2022_MCM_Problem_B.pdf\n\n**2022 MCM Problem B: Water and Hydroelectric Power Sharing**\n\n**Background**\n\nDams have been used for centuries to manage water supplies, create reservoirs, and generate hydroelectric power. However, climate change is reducing water volumes, impacting both water supply and electricity generation. In the U.S., states like Arizona, California, Wyoming, New Mexico, and Colorado are negotiating water and electricity management at the Glen Canyon and Hoover dams. Current agreements allocate more water than is available, and continued drought could lead to shortages.\n\n**Task**\n\nDevelop a water allocation plan for the five states, considering:\n\n- Coordination between Glen Canyon (Lake Powell) and Hoover (Lake Mead) dams.\n- Allocation of water and electricity to agriculture, industry, and residences.\n- Mexico's rights to residual water.\n- Potential water flow into the Gulf of California.\n\n**Model Requirements**\n\n1. Create a mathematical model to manage fixed water supply and demand conditions.\n2. Determine water draw from Lake Mead and Lake Powell to meet demands.\n3. Assess how long demands can be met without additional water supply.\n4. Recommend solutions for competing interests between water usage and electricity production.\n5. Address scenarios where water is insufficient to meet all demands.\n\n**Considerations**\n\n- Changes in water and electricity demands due to population and industrial growth or decline.\n- Increased use of renewable energy technologies.\n- Implementation of water and electricity conservation measures.\n\n**Submission Requirements**\n\n- A mathematical solution for water allocation, independent of historical agreements or political influences.\n- A one- to two-page article for \"Drought and Thirst\" magazine.\n- A complete solution within 25 pages, including a summary and main solution content.",
+ "requirements": [
+ {
+ "category": "Mathematical Model Development",
+ "description": "Evaluate the creation of a mathematical model that effectively manages fixed water supply and demand conditions, ensuring it is robust and adaptable to changes in variables."
+ },
+ {
+ "category": "Water Allocation Strategy",
+ "description": "Assess the strategy for determining water draw from Lake Mead and Lake Powell, ensuring it meets the demands of agriculture, industry, and residences while considering Mexico's rights."
+ },
+ {
+ "category": "Sustainability Assessment",
+ "description": "Analyze the model's ability to assess how long current demands can be met without additional water supply, including the impact of prolonged drought conditions."
+ },
+ {
+ "category": "Conflict Resolution",
+ "description": "Evaluate the proposed solutions for competing interests between water usage and electricity production, ensuring they are practical and equitable."
+ },
+ {
+ "category": "Insufficient Water Scenarios",
+ "description": "Examine how the model addresses scenarios where water is insufficient to meet all demands, including prioritization and mitigation strategies."
+ },
+ {
+ "category": "Demand Variation Consideration",
+ "description": "Check the model's consideration of changes in water and electricity demands due to population and industrial growth or decline."
+ },
+ {
+ "category": "Renewable Energy Integration",
+ "description": "Evaluate the incorporation of increased use of renewable energy technologies in the model to reduce dependency on hydroelectric power."
+ },
+ {
+ "category": "Conservation Measures",
+ "description": "Assess the implementation of water and electricity conservation measures within the model to enhance sustainability."
+ },
+ {
+ "category": "Independence from Historical Agreements",
+ "description": "Ensure the solution is independent of historical agreements or political influences, focusing solely on mathematical and practical considerations."
+ },
+ {
+ "category": "Communication and Presentation",
+ "description": "Evaluate the clarity and effectiveness of the one- to two-page article for 'Drought and Thirst' magazine, ensuring it communicates the solution succinctly and effectively."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a robust mathematical model to allocate water resources effectively while considering various constraints and demands. A mathematician's expertise is crucial in formulating equations and optimizing solutions to balance water and electricity needs.",
+ "details": "You are a mathematician with expertise in creating and analyzing mathematical models. Your role involves developing equations that represent the water allocation problem, considering constraints such as fixed water supply, demand conditions, and competing interests. You should focus on ensuring the model's accuracy and feasibility, using techniques like optimization and systems of equations to find the best solutions. Pay attention to the assumptions made in the model and validate them against real-world scenarios."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets related to water levels, electricity generation, and consumption patterns. A data scientist's skills are essential for processing this data to inform the model and make data-driven decisions.",
+ "details": "You are a data scientist skilled in data analysis, statistical methods, and machine learning. Your role is to gather and analyze data on water levels, electricity usage, and demand trends. You should focus on identifying patterns and insights that can inform the mathematical model, such as changes in demand due to population growth or industrial shifts. Ensure that the data used is accurate and up-to-date, and consider using predictive analytics to forecast future scenarios."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem involves understanding the environmental impact of water allocation and electricity generation. An environmental scientist's expertise is crucial in assessing the ecological consequences and ensuring sustainable practices.",
+ "details": "You are an environmental scientist with expertise in water resource management and ecological impact assessment. Your role is to evaluate the environmental implications of different water allocation strategies, considering factors like ecosystem health, biodiversity, and water quality. You should focus on ensuring that the proposed solutions are sustainable and minimize negative environmental impacts. Pay attention to the potential effects on the Gulf of California and Mexico's water rights, and recommend conservation measures to mitigate adverse outcomes."
+ },
+ {
+ "name": "Policy Analyst",
+ "thoughts": "The problem requires understanding the legal and policy frameworks governing water and electricity allocation. A policy analyst's expertise is essential in navigating these frameworks and proposing feasible solutions.",
+ "details": "You are a policy analyst with expertise in water and energy policy. Your role is to review the legal and regulatory aspects of water allocation and electricity generation, ensuring that the proposed solutions comply with existing agreements and laws. You should focus on identifying potential policy barriers and opportunities for negotiation between states and stakeholders. Pay attention to the implications of the model on interstate agreements and international treaties, and recommend policy changes that could facilitate better resource management."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Mathematical Model Development",
+ "description": "Evaluate the creation of a mathematical model that effectively manages fixed water supply and demand conditions, ensuring it is robust and adaptable to changes in variables."
+ },
+ {
+ "category": "Water Allocation Strategy",
+ "description": "Assess the strategy for determining water draw from Lake Mead and Lake Powell, ensuring it meets the demands of agriculture, industry, and residences while considering Mexico's rights."
+ },
+ {
+ "category": "Sustainability Assessment",
+ "description": "Analyze the model's ability to assess how long current demands can be met without additional water supply, including the impact of prolonged drought conditions."
+ },
+ {
+ "category": "Conflict Resolution",
+ "description": "Evaluate the proposed solutions for competing interests between water usage and electricity production, ensuring they are practical and equitable."
+ },
+ {
+ "category": "Insufficient Water Scenarios",
+ "description": "Examine how the model addresses scenarios where water is insufficient to meet all demands, including prioritization and mitigation strategies."
+ },
+ {
+ "category": "Demand Variation Consideration",
+ "description": "Check the model's consideration of changes in water and electricity demands due to population and industrial growth or decline."
+ },
+ {
+ "category": "Renewable Energy Integration",
+ "description": "Evaluate the incorporation of increased use of renewable energy technologies in the model to reduce dependency on hydroelectric power."
+ },
+ {
+ "category": "Conservation Measures",
+ "description": "Assess the implementation of water and electricity conservation measures within the model to enhance sustainability."
+ },
+ {
+ "category": "Independence from Historical Agreements",
+ "description": "Ensure the solution is independent of historical agreements or political influences, focusing solely on mathematical and practical considerations."
+ },
+ {
+ "category": "Communication and Presentation",
+ "description": "Evaluate the clarity and effectiveness of the one- to two-page article for 'Drought and Thirst' magazine, ensuring it communicates the solution succinctly and effectively."
+ }
+ ]
+ }
+ },
+ "2023_Dandelions:_Friend?_Foe?": {
+ "year": "2023",
+ "title": "Dandelions: Friend? Foe? Both? Neither?",
+ "level": "High School",
+ "source": "HiMCM",
+ "link": "Problems/2023/HIMCM-A/index.html",
+ "question": "2023_HiMCM_Problem_A.pdf 2023_HiMCM_Problem_A.pdf Dandelions: Friend? Foe? Both? Neither?\n\n### Text in the PDF File: 2023_HiMCM_Problem_A.pdf\n\n**2023 HiMCM Problem A: Dandelions: Friend? Foe? Both? Neither?**\n\n**Overview:**\n- **Dandelion (Taraxacum officinale):** A plant native to Eurasia, now found worldwide. Recognizable by its yellow flowers and puffball seed head, which aids in wind dispersal.\n\n**Tasks:**\n\n1. **Spread Prediction Model:**\n - Develop a mathematical model to predict dandelion spread over 1, 2, 3, 6, and 12 months.\n - Consider climatic conditions: temperate, arid, and tropical climates.\n\n2. **Impact Factor Model for Invasive Species:**\n - Create a model to determine an 'impact factor' for invasive species, considering plant characteristics and environmental harm.\n - Test the model with dandelions.\n - Apply the model to two other invasive plant species, specifying the region where they are invasive.\n\n**Submission Requirements:**\n- max 25 pages, including:\n - One-page Summary Sheet\n - Complete solution\n\n**Glossary:**\n- **Invasive Species:** Non-native species causing or likely to cause harm to the economy, environment, or human health.\n\n**References:**\n1. [Dandelion Information](https://anpc.ab.ca/wp-content/uploads/2015/01/dandelion.pdf)\n2. [Dandelion Article](https://hort.extension.wisc.edu/articles/dandelion-taraxacum-officinale/)\n3. [Invasive Species Information](https://www.invasivespeciesinfo.gov/what-are-invasive-species)",
+ "requirements": [
+ {
+ "category": "Spread Prediction Model",
+ "description": "Develop a mathematical model to predict the spread of dandelions over specified time frames (1, 2, 3, 6, and 12 months)."
+ },
+ {
+ "category": "Spread Prediction Model",
+ "description": "Incorporate climatic conditions (temperate, arid, and tropical) into the spread prediction model."
+ },
+ {
+ "category": "Spread Prediction Model",
+ "description": "Evaluate the model's accuracy and reliability in predicting dandelion spread across different climates and time frames."
+ },
+ {
+ "category": "Impact Factor Model",
+ "description": "Create a model to determine an 'impact factor' for invasive species, considering plant characteristics and environmental harm."
+ },
+ {
+ "category": "Impact Factor Model",
+ "description": "Test the impact factor model specifically with dandelions to ensure its applicability and accuracy."
+ },
+ {
+ "category": "Impact Factor Model",
+ "description": "Apply the impact factor model to two other invasive plant species, specifying the region where they are invasive, and evaluate the model's adaptability."
+ },
+ {
+ "category": "Assumptions and Justifications",
+ "description": "Identify and justify any assumptions made in the development of both models, ensuring they are reasonable and well-supported."
+ },
+ {
+ "category": "Model Validation",
+ "description": "Provide validation for both models, using data or logical reasoning to support the models' effectiveness and accuracy."
+ },
+ {
+ "category": "Clarity and Completeness",
+ "description": "Ensure the solution is clearly presented and complete, with all necessary components and explanations included within the page limit."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires the development of mathematical models to predict the spread of dandelions and to calculate an impact factor for invasive species. This involves formulating equations and systems that can accurately represent biological and environmental processes.",
+ "details": "As a mathematician, you are adept at creating and analyzing mathematical models. Your expertise in differential equations, probability, and statistical analysis will be crucial in developing models that predict the spread of dandelions under various climatic conditions. You should focus on ensuring the mathematical rigor and validity of the models, checking for assumptions, and verifying the solutions' accuracy."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves handling and analyzing data related to climatic conditions and plant characteristics, which is essential for building predictive models and calculating impact factors.",
+ "details": "As a data scientist, your skills in data collection, cleaning, and analysis are vital. You will need to work with datasets that include climatic variables and plant characteristics to inform the models. Your expertise in machine learning and statistical methods will help in refining the models and ensuring they are data-driven. Pay attention to the quality and relevance of the data used, and ensure that the models are robust and generalizable."
+ },
+ {
+ "name": "Ecologist",
+ "thoughts": "Understanding the ecological impact of dandelions and other invasive species is crucial for developing accurate models. An ecologist can provide insights into plant behavior, interactions with the environment, and ecological consequences.",
+ "details": "As an ecologist, your knowledge of plant ecology and invasive species dynamics is essential. You should evaluate the models for their ecological validity, ensuring they accurately reflect biological processes and interactions. Consider the ecological roles of dandelions and other species, and assess the potential environmental impacts predicted by the models."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem requires assessing the environmental impact of invasive species, which involves understanding environmental systems and the potential harm caused by these species.",
+ "details": "As an environmental scientist, your expertise in environmental systems and impact assessment is crucial. You should review the models for their ability to predict environmental harm and assess the broader implications of dandelion spread and other invasive species. Focus on the environmental factors included in the models and ensure they are comprehensive and realistic in representing potential impacts."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Spread Prediction Model",
+ "description": "Develop a mathematical model to predict the spread of dandelions over specified time frames (1, 2, 3, 6, and 12 months)."
+ },
+ {
+ "category": "Spread Prediction Model",
+ "description": "Incorporate climatic conditions (temperate, arid, and tropical) into the spread prediction model."
+ },
+ {
+ "category": "Spread Prediction Model",
+ "description": "Evaluate the model's accuracy and reliability in predicting dandelion spread across different climates and time frames."
+ },
+ {
+ "category": "Impact Factor Model",
+ "description": "Create a model to determine an 'impact factor' for invasive species, considering plant characteristics and environmental harm."
+ },
+ {
+ "category": "Impact Factor Model",
+ "description": "Test the impact factor model specifically with dandelions to ensure its applicability and accuracy."
+ },
+ {
+ "category": "Impact Factor Model",
+ "description": "Apply the impact factor model to two other invasive plant species, specifying the region where they are invasive, and evaluate the model's adaptability."
+ },
+ {
+ "category": "Assumptions and Justifications",
+ "description": "Identify and justify any assumptions made in the development of both models, ensuring they are reasonable and well-supported."
+ },
+ {
+ "category": "Model Validation",
+ "description": "Provide validation for both models, using data or logical reasoning to support the models' effectiveness and accuracy."
+ },
+ {
+ "category": "Clarity and Completeness",
+ "description": "Ensure the solution is clearly presented and complete, with all necessary components and explanations included within the page limit."
+ }
+ ]
+ }
+ },
+ "2023_Drought-Stricken_Plant_Communities": {
+ "year": "2023",
+ "title": "Drought-Stricken Plant Communities",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2023/MCM-A/index.html",
+ "question": "2023_MCM_Problem_A.pdf Drought-Stricken Plant Communities\n\n### Text in the PDF File: 2023_MCM_Problem_A.pdf\n\n**2023 MCM Problem A: Drought-Stricken Plant Communities**\n\n**Background**\n\nPlant species respond differently to environmental stresses like droughts, which vary in frequency and severity. Observations suggest that plant communities with more species adapt better to drought conditions over generations. This raises questions about the minimal number of species needed for effective adaptation, how this scales with more species, and implications for long-term community survival.\n\n**Task Overview**\n\nYour task is to explore the relationship between drought adaptability and species diversity in plant communities. Specifically, you should:\n\n1. **Develop a Mathematical Model**: \n - Predict changes in a plant community over time under irregular weather cycles, including droughts.\n - Account for species interactions during drought cycles.\n\n2. **Explore Conclusions**:\n - Determine the minimum number of species required for community benefit and the effects of increasing species numbers.\n - Assess how species types affect outcomes.\n - Evaluate the impact of increased drought frequency and variation on community dynamics.\n - Consider the effects of less frequent droughts on species impact.\n - Analyze the influence of pollution and habitat reduction on your conclusions.\n - Recommend actions for ensuring long-term plant community viability and environmental impacts.\n\n**Submission Requirements**\n\nYour solution should be no more than 25 pages, including:\n\n- One-page Summary Sheet\n- Complete Solution",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Develop a robust mathematical model that predicts changes in plant communities over time under irregular weather cycles, including droughts, and accounts for species interactions."
+ },
+ {
+ "category": "Species Diversity Analysis",
+ "description": "Determine the minimum number of species required for community benefit and analyze the effects of increasing species numbers on community adaptability."
+ },
+ {
+ "category": "Species Type Impact",
+ "description": "Assess how different types of species affect the outcomes of the model and community adaptability."
+ },
+ {
+ "category": "Drought Frequency and Variation",
+ "description": "Evaluate the impact of increased drought frequency and variation on community dynamics and species interactions."
+ },
+ {
+ "category": "Less Frequent Droughts",
+ "description": "Consider and analyze the effects of less frequent droughts on the impact of species within the community."
+ },
+ {
+ "category": "Environmental Factors",
+ "description": "Analyze the influence of pollution and habitat reduction on the conclusions drawn from the model."
+ },
+ {
+ "category": "Recommendations",
+ "description": "Provide actionable recommendations for ensuring long-term plant community viability and mitigating environmental impacts."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires developing a mathematical model to predict changes in plant communities under varying drought conditions, which involves complex equations and interactions between species.",
+ "details": "You are a mathematician with expertise in formulating and solving mathematical models related to ecological systems. You should focus on ensuring the model accurately represents species interactions and environmental variables. Pay attention to the assumptions made in the model and their implications on the results. Your skills in differential equations, probability, and optimization will be crucial in evaluating the robustness and validity of the proposed solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to plant species diversity, drought frequency, and environmental impacts, which requires advanced data processing and statistical analysis.",
+ "details": "You are a data scientist skilled in handling large datasets and extracting meaningful insights from them. You should evaluate the data sources used in the model, the methods of data analysis, and the statistical techniques applied. Your expertise in machine learning and data visualization will be essential in assessing how well the model predicts real-world scenarios and in identifying patterns or trends in the data that support the conclusions."
+ },
+ {
+ "name": "Ecologist",
+ "thoughts": "The problem is deeply rooted in ecological principles, requiring an understanding of plant species interactions, community dynamics, and environmental stress responses.",
+ "details": "You are an ecologist with a deep understanding of plant communities and their responses to environmental changes. You should review the biological assumptions and ecological theories applied in the model. Your knowledge of species adaptation, biodiversity, and ecosystem resilience will be vital in assessing the ecological validity of the model and its conclusions. Pay attention to how well the model incorporates ecological concepts and the potential real-world implications of the proposed solutions."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem involves assessing the impact of environmental factors such as pollution and habitat reduction on plant communities, requiring expertise in environmental science.",
+ "details": "You are an environmental scientist with expertise in evaluating the effects of environmental changes on ecosystems. You should focus on the environmental variables included in the model and their representation. Your skills in environmental impact assessment and sustainability will be crucial in evaluating the long-term viability of the plant communities and the recommended actions for environmental conservation. Pay attention to how the model addresses pollution, habitat loss, and other environmental stressors, and ensure the solutions are feasible and sustainable."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Develop a robust mathematical model that predicts changes in plant communities over time under irregular weather cycles, including droughts, and accounts for species interactions."
+ },
+ {
+ "category": "Species Diversity Analysis",
+ "description": "Determine the minimum number of species required for community benefit and analyze the effects of increasing species numbers on community adaptability."
+ },
+ {
+ "category": "Species Type Impact",
+ "description": "Assess how different types of species affect the outcomes of the model and community adaptability."
+ },
+ {
+ "category": "Drought Frequency and Variation",
+ "description": "Evaluate the impact of increased drought frequency and variation on community dynamics and species interactions."
+ },
+ {
+ "category": "Less Frequent Droughts",
+ "description": "Consider and analyze the effects of less frequent droughts on the impact of species within the community."
+ },
+ {
+ "category": "Environmental Factors",
+ "description": "Analyze the influence of pollution and habitat reduction on the conclusions drawn from the model."
+ },
+ {
+ "category": "Recommendations",
+ "description": "Provide actionable recommendations for ensuring long-term plant community viability and mitigating environmental impacts."
+ }
+ ]
+ }
+ },
+ "2023_Light_Pollution": {
+ "year": "2023",
+ "title": "Light Pollution",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2023/ICM-E/index.html",
+ "question": "2023_ICM_Problem_E.pdf Light Pollution\n\n### Text in the PDF File: 2023_ICM_Problem_E.pdf\n\n**Problem E: Light Pollution**\n\n**Background**\nLight pollution refers to the excessive or poor use of artificial light, manifesting as light trespass, over-illumination, and light clutter. It is often visible as a glow in the sky after sunset, especially in large cities, but can also occur in remote areas. Light pollution affects our view of the night sky, has environmental impacts, and influences health and safety. It can disrupt plant growth, wildlife migration, and human circadian rhythms, potentially leading to health issues and contributing to motor vehicle accidents. \n\nIntervention strategies to mitigate light pollution must consider both positive and negative effects, which vary by location. Factors such as development level, population, biodiversity, geography, and climate influence the impacts of light pollution and the effectiveness of interventions.\n\n**Task**\nThe task is to support COMAP\u2019s Illumination Control Mission (ICM) by addressing the measurement and mitigation of light pollution effects, considering both human and non-human concerns. Specifically, you should:\n\n- Develop a metric to identify the light pollution risk level of a location.\n- Apply and interpret this metric for four types of locations:\n - Protected land\n - Rural community\n - Suburban community\n - Urban community\n\n- Choose two locations and determine the most effective intervention strategy for each using your metric. Discuss the impact of the strategy on the location's risk level.\n- Create a 1-page flyer promoting the most effective strategy for one location.\n\n**Submission Requirements**\nYour solution should be no more than 25 pages, including:\n- One-page Summary Sheet\n- Complete solution\n- One-page promotion flyer\n\n**Glossary**\n- **Artificial Light:** Non-natural light sources.\n- **Circadian Rhythms:** The natural 24-hour sleep-wake cycle.\n- **Glare:** Excessive brightness reducing visibility.\n- **Intervention Strategies:** Actions to mitigate light pollution.\n- **Light Clutter:** Excessive grouping of lights.\n- **Light Trespass:** Light entering unintended areas.\n- **Over-Illumination:** Excessive lighting intensity.\n- **Protected Land:** Areas protected for ecological, cultural, or natural importance.\n- **Rural Community:** Least densely populated areas, not easily accessible from urban areas.\n- **Suburban Community:** Moderately densely populated areas, accessible from urban areas.\n- **Urban Community:** Most densely populated areas.",
+ "requirements": [
+ {
+ "category": "Metric Development",
+ "description": "Develop a comprehensive and scientifically sound metric to assess light pollution risk, considering factors such as light intensity, duration, and impact on human and non-human entities."
+ },
+ {
+ "category": "Metric Application",
+ "description": "Accurately apply the developed metric to assess light pollution risk in four types of locations: protected land, rural community, suburban community, and urban community, providing clear interpretations for each."
+ },
+ {
+ "category": "Intervention Strategy Selection",
+ "description": "Select and justify the most effective intervention strategies for two chosen locations based on the metric results, considering local factors such as population density, biodiversity, and existing infrastructure."
+ },
+ {
+ "category": "Impact Analysis",
+ "description": "Analyze and discuss the potential impact of the chosen intervention strategies on the light pollution risk level of the selected locations, including both positive and negative effects."
+ },
+ {
+ "category": "Communication and Promotion",
+ "description": "Create a clear and persuasive 1-page flyer promoting the most effective intervention strategy for one location, effectively communicating the benefits and importance of the strategy to a general audience."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem of light pollution involves developing a metric to quantify risk levels, which requires a strong foundation in mathematical modeling and analysis. A mathematician can help in formulating the equations and models needed to accurately assess and interpret light pollution data.",
+ "details": "As a mathematician, you are adept at creating and analyzing mathematical models. Your expertise in differential equations, statistical analysis, and optimization techniques will be crucial in developing a robust metric for light pollution risk. You should focus on ensuring the mathematical soundness of the models and verify that the assumptions and simplifications made are valid and reasonable for the context of light pollution."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The task involves analyzing complex datasets related to light pollution, such as geographical, demographic, and environmental data. A data scientist is essential for processing this data, applying machine learning techniques, and deriving insights that inform the development of the light pollution metric.",
+ "details": "As a data scientist, your role is to handle large datasets, perform data cleaning, and apply statistical and machine learning methods to extract meaningful patterns. You should ensure that the data used in the models is accurate and representative of the different locations. Your skills in data visualization will also be important for interpreting and presenting the results clearly."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "Light pollution has significant environmental impacts, affecting ecosystems and wildlife. An environmental scientist can provide insights into how light pollution affects biodiversity and ecological processes, which is crucial for developing effective intervention strategies.",
+ "details": "As an environmental scientist, you bring expertise in understanding the ecological consequences of light pollution. You should evaluate how different levels of light pollution impact various species and ecosystems, and assess the effectiveness of proposed intervention strategies in mitigating these impacts. Your knowledge will be vital in ensuring that the solutions are environmentally sustainable and consider the broader ecological context."
+ },
+ {
+ "name": "Urban Planner",
+ "thoughts": "The problem involves assessing light pollution in various community settings, including urban, suburban, and rural areas. An urban planner can provide insights into how urban design and infrastructure contribute to light pollution and help develop location-specific intervention strategies.",
+ "details": "As an urban planner, your expertise in land use planning and community design is crucial for understanding how different urban layouts and lighting infrastructures contribute to light pollution. You should focus on evaluating how proposed interventions can be integrated into existing urban plans and policies, and ensure that they are feasible and effective in reducing light pollution while considering the needs of the community."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Metric Development",
+ "description": "Develop a comprehensive and scientifically sound metric to assess light pollution risk, considering factors such as light intensity, duration, and impact on human and non-human entities."
+ },
+ {
+ "category": "Metric Application",
+ "description": "Accurately apply the developed metric to assess light pollution risk in four types of locations: protected land, rural community, suburban community, and urban community, providing clear interpretations for each."
+ },
+ {
+ "category": "Intervention Strategy Selection",
+ "description": "Select and justify the most effective intervention strategies for two chosen locations based on the metric results, considering local factors such as population density, biodiversity, and existing infrastructure."
+ },
+ {
+ "category": "Impact Analysis",
+ "description": "Analyze and discuss the potential impact of the chosen intervention strategies on the light pollution risk level of the selected locations, including both positive and negative effects."
+ },
+ {
+ "category": "Communication and Promotion",
+ "description": "Create a clear and persuasive 1-page flyer promoting the most effective intervention strategy for one location, effectively communicating the benefits and importance of the strategy to a general audience."
+ }
+ ]
+ }
+ },
+ "2023_Preparing_for_Olympic": {
+ "year": "2023",
+ "title": "Preparing for Olympic Medal Ceremonies",
+ "level": "Middle School",
+ "source": "MidMCM",
+ "link": "Problems/2023/MidMCM-C/index.html",
+ "question": "2023_MidMCM_Problem_C.pdf Preparing for Olympic Medal Ceremonies\n\n### Text in the PDF File: 2023_MidMCM_Problem_C.pdf\n\n**2023 MidMCM Problem C: Preparing for Olympic Medal Ceremonies**\n\n**Overview:**\nThe International Olympic Committee (IOC) is preparing for the Paris 2024 Olympic Games, scheduled from July 26 to August 11, 2024. They need to order an appropriate number of medals and flags for the medal ceremonies to avoid shortages or excesses. Your task is to develop models to determine the necessary quantities.\n\n**Key Information:**\n- **Participating Countries:** Invitations have been sent to 203 National Olympic Committees (NOCs).\n- **Olympic Sports:** The 2024 Summer Olympics will feature 40 sports with 329 medal events.\n- **Medal Ceremonies:** Each event awards Gold, Silver, and Bronze medals. Flags of the winning countries are displayed.\n- **Venues:** The events will be held across 37 venues, primarily in and around Paris, with some overseas locations like Tahiti.\n\n**Task Requirements:**\n1. **Venue Selection and Analysis:**\n - Choose one venue: La D\u00e9fense Arena, Bercy Arena, or Stade de France.\n - Develop a schedule for medal ceremonies at the chosen venue.\n - Create a model to determine the number of medals (Gold, Silver, Bronze) needed.\n - Create a model to determine the number and types of flags needed.\n\n2. **Model Application:**\n - Apply your models to the other two venues.\n - Develop comprehensive models for medals and flags needed across all three venues.\n\n3. **Communication:**\n - Write a one- to two-page letter to the IOC explaining your model and its effectiveness in ensuring adequate medal and flag supplies.\n\n4. **Reflection:**\n - Consider the applicability of your model to all 37 venues and future Olympic Games, including Winter Olympics.\n\n**Submission Guidelines:**\n- Include a one-page summary, complete solution, and letter to the IOC\n- The solution document should not exceed 25 pages.\n\n**References:**\n- [1] Olympic Games Paris 2024 Information: https://olympics.com/ioc/news/one-year-to-go-ioc-invites-nocs-and-their-best-athletes-to-the-olympic-games-paris-2024\n- [2] Olympic Sports Overview: https://olympics.com/en/sports/summer-olympics#paris-2024\n- [3] Paris 2024 Schedule: https://olympics.com/en/news/olympic-games-paris-2024-full-schedule-and-day-by-day-competitions\n- [4] Paris Olympics Venues: https://www.parisdigest.com/sports/paris-olympics-2024.htm\n- [5] Venue Concept: https://www.paris2024.org/en/competition-venue-concept/",
+ "requirements": [
+ {
+ "category": "Venue Selection and Analysis",
+ "description": "Selection of one venue and development of a detailed schedule for medal ceremonies at that venue."
+ },
+ {
+ "category": "Medal Quantity Model",
+ "description": "Creation of a model to accurately determine the number of Gold, Silver, and Bronze medals needed for the selected venue."
+ },
+ {
+ "category": "Flag Quantity Model",
+ "description": "Creation of a model to determine the number and types of flags needed for the selected venue, considering the diversity of participating countries."
+ },
+ {
+ "category": "Model Application to Other Venues",
+ "description": "Application of the developed models to the other two specified venues and evaluation of their effectiveness."
+ },
+ {
+ "category": "Comprehensive Model Development",
+ "description": "Development of comprehensive models for medals and flags needed across all three venues, ensuring scalability and adaptability."
+ },
+ {
+ "category": "Communication",
+ "description": "Effectiveness of the one- to two-page letter to the IOC, explaining the model and its effectiveness in ensuring adequate medal and flag supplies."
+ },
+ {
+ "category": "Model Scalability and Reflection",
+ "description": "Consideration of the model's applicability to all 37 venues and future Olympic Games, including Winter Olympics, demonstrating scalability and adaptability."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to accurately predict the number of medals and flags needed for the Olympic ceremonies. This involves understanding probability, statistics, and optimization techniques to ensure the models are robust and reliable.",
+ "details": "As a mathematician, you are skilled in developing and analyzing mathematical models. You should focus on ensuring the models are mathematically sound, using appropriate statistical methods to predict medal counts and flag requirements. Pay attention to the assumptions made in the models and verify their validity. Your expertise in optimization can help refine the models to minimize costs and avoid shortages or excesses."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves handling large datasets related to Olympic events, participating countries, and historical data. A data scientist can leverage data analysis and machine learning techniques to enhance the accuracy of the models.",
+ "details": "As a data scientist, you are adept at processing and analyzing complex datasets. You should focus on extracting relevant data from historical Olympic events to inform the models. Use machine learning algorithms to predict outcomes and trends, ensuring the models are data-driven. Your expertise in data visualization can help communicate the model's predictions effectively to the IOC."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem involves logistical planning and resource allocation, which are key areas of operations research. An operations research analyst can optimize the scheduling and distribution of medals and flags across venues.",
+ "details": "As an operations research analyst, you specialize in optimizing processes and resource allocation. You should focus on developing models that efficiently schedule medal ceremonies and distribute medals and flags across venues. Pay attention to constraints such as venue capacity and timing. Your expertise in linear programming and simulation can help ensure the models are practical and implementable."
+ },
+ {
+ "name": "Event Planner",
+ "thoughts": "The problem involves planning and executing medal ceremonies, which requires expertise in event management. An event planner can provide insights into the logistical and practical aspects of organizing ceremonies.",
+ "details": "As an event planner, you have experience in organizing large-scale events. You should focus on the practical aspects of the models, ensuring they align with the realities of event management. Consider factors such as venue layout, timing, and coordination with other events. Your expertise in contingency planning can help address potential issues such as delays or unexpected changes in the schedule."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Venue Selection and Analysis",
+ "description": "Selection of one venue and development of a detailed schedule for medal ceremonies at that venue."
+ },
+ {
+ "category": "Medal Quantity Model",
+ "description": "Creation of a model to accurately determine the number of Gold, Silver, and Bronze medals needed for the selected venue."
+ },
+ {
+ "category": "Flag Quantity Model",
+ "description": "Creation of a model to determine the number and types of flags needed for the selected venue, considering the diversity of participating countries."
+ },
+ {
+ "category": "Model Application to Other Venues",
+ "description": "Application of the developed models to the other two specified venues and evaluation of their effectiveness."
+ },
+ {
+ "category": "Comprehensive Model Development",
+ "description": "Development of comprehensive models for medals and flags needed across all three venues, ensuring scalability and adaptability."
+ },
+ {
+ "category": "Communication",
+ "description": "Effectiveness of the one- to two-page letter to the IOC, explaining the model and its effectiveness in ensuring adequate medal and flag supplies."
+ },
+ {
+ "category": "Model Scalability and Reflection",
+ "description": "Consideration of the model's applicability to all 37 venues and future Olympic Games, including Winter Olympics, demonstrating scalability and adaptability."
+ }
+ ]
+ }
+ },
+ "2023_Prioritizing_the_UN": {
+ "year": "2023",
+ "title": "Prioritizing the UN Sustainability Goals",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2023/ICM-D/index.html",
+ "question": "2023_ICM_Problem_D.pdf Prioritizing the UN Sustainability Goals\n\n### Text in the PDF File: 2023_ICM_Problem_D.pdf\n\n**2023 ICM Problem D: Prioritizing the UN Sustainability Goals**\n\n**Background**\nThe United Nations (UN) has established 17 Sustainable Development Goals (SDGs) aimed at improving global living conditions. These goals are interconnected, meaning progress in one can affect others positively or negatively. Achieving these goals is complex due to funding limitations, technological advances, global pandemics, climate change, regional conflicts, and refugee movements.\n\n**Task Overview**\n1. **Network Creation**: Develop a network illustrating the relationships between the 17 SDGs.\n2. **Priority Setting**: Use the network to prioritize goals that can most effectively advance the UN's mission. Evaluate the effectiveness of each priority and project achievable outcomes over the next decade.\n3. **Impact of Achievements**: Analyze how achieving one SDG (e.g., no poverty or zero hunger) would alter the network and affect priorities. Consider proposing additional goals to the UN.\n4. **Influence of Global Factors**: Discuss how technological advances, pandemics, climate change, wars, and refugee movements impact the network and priorities.\n5. **Application to Other Organizations**: Explain how this network approach can assist other entities in setting their goals.\n\n**UN Sustainable Development Goals**\n1. No Poverty\n2. Zero Hunger\n3. Good Health and Well-being\n4. Quality Education\n5. Gender Equality\n6. Clean Water and Sanitation\n7. Affordable and Clean Energy\n8. Decent Work and Economic Growth\n9. Industry, Innovation, and Infrastructure\n10. Reduced Inequality\n11. Sustainable Cities and Communities\n12. Responsible Consumption and Production\n13. Climate Action\n14. Life Below Water\n15. Life on Land\n16. Peace and Justice Strong Institutions\n17. Partnerships to achieve the Goal\n\n**Submission Requirements**\n- A solution document of up to 25 pages, including:\n - One-page Summary Sheet\n - Complete solution\n\n**Glossary**\n- **United Nations (UN)**: An intergovernmental organization focused on maintaining peace, fostering friendly relations, and promoting international cooperation.\n- **Sustainable Development Goals (SDGs)**: A set of 17 interconnected objectives serving as a blueprint for global peace and prosperity.\n\n**References**\n- Transforming Our World: The 2030 Agenda for Sustainable Development. UN General Assembly, A/RES/70/1, 2015.",
+ "requirements": [
+ {
+ "category": "Network Creation",
+ "description": "Evaluate the accuracy and completeness of the network illustrating the relationships between the 17 SDGs, ensuring all goals and their interconnections are represented."
+ },
+ {
+ "category": "Priority Setting",
+ "description": "Assess the method used to prioritize the SDGs based on the network, including the rationale and criteria for determining which goals can most effectively advance the UN's mission."
+ },
+ {
+ "category": "Effectiveness Evaluation",
+ "description": "Examine the evaluation of the effectiveness of each prioritized goal and the projected achievable outcomes over the next decade."
+ },
+ {
+ "category": "Impact Analysis",
+ "description": "Analyze how achieving one specific SDG alters the network and affects the priorities, including any proposed additional goals to the UN."
+ },
+ {
+ "category": "Global Factors Influence",
+ "description": "Discuss how global factors such as technological advances, pandemics, climate change, wars, and refugee movements impact the network and the prioritization of goals."
+ },
+ {
+ "category": "Application to Other Organizations",
+ "description": "Evaluate the explanation of how the network approach can assist other entities in setting their goals, including adaptability and potential benefits."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves creating a network to illustrate the relationships between the 17 Sustainable Development Goals (SDGs), which requires a strong foundation in graph theory and mathematical modeling. A mathematician's expertise is crucial in developing and analyzing the network structure to ensure it accurately represents the complex interconnections between the goals.",
+ "details": "As a mathematician, you are adept at constructing and analyzing complex networks. Your skills in graph theory will be essential in developing a robust model that captures the intricate relationships between the SDGs. When reviewing the modeling solutions, pay close attention to the mathematical rigor and validity of the network structure. Ensure that the relationships are logically sound and that the model can effectively prioritize the goals based on their interdependencies."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The task requires analyzing large datasets to evaluate the effectiveness of prioritizing certain SDGs and projecting outcomes. A data scientist's expertise in data analysis, statistical methods, and machine learning is vital for processing and interpreting the data to inform decision-making.",
+ "details": "As a data scientist, your role is to analyze the data related to the SDGs and their interconnections. You should focus on using statistical methods and machine learning techniques to derive insights from the data, which will help in setting priorities and projecting outcomes. When reviewing the solutions, ensure that the data analysis is thorough and that the conclusions drawn are supported by the data. Look for the use of appropriate models and algorithms that can handle the complexity and scale of the data involved."
+ },
+ {
+ "name": "Systems Analyst",
+ "thoughts": "The problem involves understanding and modeling complex systems, which is the core expertise of a systems analyst. Their ability to see the big picture and understand how different components interact within a system is crucial for developing a comprehensive model of the SDGs network.",
+ "details": "As a systems analyst, you are skilled in examining and modeling complex systems. Your expertise will be invaluable in understanding how the SDGs interact and influence each other. When reviewing the solutions, focus on the system's dynamics and ensure that the model accurately reflects the real-world complexities of the SDGs. Pay attention to how well the model can adapt to changes in global factors such as technological advances and climate change."
+ },
+ {
+ "name": "Policy Analyst",
+ "thoughts": "The task involves evaluating the impact of achieving certain SDGs and proposing additional goals, which requires a deep understanding of policy implications and global development strategies. A policy analyst's expertise is crucial in assessing the feasibility and impact of different priorities and strategies.",
+ "details": "As a policy analyst, your role is to evaluate the policy implications of prioritizing certain SDGs and achieving specific outcomes. You should focus on understanding the broader context of global development and how different goals align with international policies and agendas. When reviewing the solutions, ensure that the proposed priorities and strategies are realistic and consider the potential impact on global and regional policies. Look for solutions that are not only theoretically sound but also practically feasible in the context of current and future global challenges."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Network Creation",
+ "description": "Evaluate the accuracy and completeness of the network illustrating the relationships between the 17 SDGs, ensuring all goals and their interconnections are represented."
+ },
+ {
+ "category": "Priority Setting",
+ "description": "Assess the method used to prioritize the SDGs based on the network, including the rationale and criteria for determining which goals can most effectively advance the UN's mission."
+ },
+ {
+ "category": "Effectiveness Evaluation",
+ "description": "Examine the evaluation of the effectiveness of each prioritized goal and the projected achievable outcomes over the next decade."
+ },
+ {
+ "category": "Impact Analysis",
+ "description": "Analyze how achieving one specific SDG alters the network and affects the priorities, including any proposed additional goals to the UN."
+ },
+ {
+ "category": "Global Factors Influence",
+ "description": "Discuss how global factors such as technological advances, pandemics, climate change, wars, and refugee movements impact the network and the prioritization of goals."
+ },
+ {
+ "category": "Application to Other Organizations",
+ "description": "Evaluate the explanation of how the network approach can assist other entities in setting their goals, including adaptability and potential benefits."
+ }
+ ]
+ }
+ },
+ "2023_The_Future_of": {
+ "year": "2023",
+ "title": "The Future of the Olympics",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2023/ICM-Z/index.html",
+ "question": "2023_ICM_Problem_Z.pdf The Future of the Olympics\n\n### Text in the PDF File: 2023_ICM_Problem_Z.pdf\n\n**The Future of the Olympics**\n\n**Background:**\nThe International Olympic Committee (IOC) is experiencing a decline in bids to host the Olympics, both Summer and Winter Games. Historically, hosting the Olympics was seen as prestigious, but recent host cities/nations have faced various negative impacts. To address these challenges, innovative solutions are being considered, such as establishing permanent locations for the Games or dividing the sports into four smaller seasonal events (Winter, Spring, Summer, and Fall) to reduce the hosting burden.\n\n**Task:**\nThe Interdisciplinary Committee on Modern Games (ICMG) seeks creative strategies to ensure the Olympics remain successful and continue to unite the world through sport. Recommendations should include metrics for evaluating the impacts of hosting the Games from perspectives such as economic, land use, human satisfaction (athletes and spectators), travel, future opportunities, and host city/nation prestige. Consider the feasibility, implementation timeline, and impact of potential strategies on these metrics. A one-page memorandum to the IOC should outline your strategy and policy recommendations.\n\n**Submission Requirements:**\n- A one-page Summary Sheet detailing your approach and key conclusions.\n- Complete solution.\n- One-page memorandum.\n\n**Reference:**\nMatheson, V. and Zimbalist, A. (2021, April 19). \"Why Cities No Longer Clamor to Host the Olympic Games.\" Georgetown Journal of International Affairs. Available at: [Georgetown Journal](https://gjia.georgetown.edu/2021/04/19/why-cities-no-longer-clamor-to-host-the-olympic-games/).",
+ "requirements": [
+ {
+ "category": "Strategy Development",
+ "description": "Evaluate the creativity and innovation of the proposed strategies to ensure the Olympics remain successful and appealing to host cities."
+ },
+ {
+ "category": "Metric Identification",
+ "description": "Assess the identification and justification of metrics used to evaluate the impacts of hosting the Olympics, including economic, land use, human satisfaction, travel, future opportunities, and prestige."
+ },
+ {
+ "category": "Feasibility Analysis",
+ "description": "Examine the feasibility of the proposed strategies, including the practicality of implementation and the timeline for execution."
+ },
+ {
+ "category": "Impact Assessment",
+ "description": "Evaluate the analysis of potential impacts of the strategies on the identified metrics, considering both short-term and long-term effects."
+ },
+ {
+ "category": "Policy Recommendations",
+ "description": "Review the clarity and persuasiveness of the policy recommendations provided in the one-page memorandum to the IOC."
+ },
+ {
+ "category": "Assumptions and Justifications",
+ "description": "Check the identification and justification of any assumptions made in the modeling process."
+ },
+ {
+ "category": "Integration of Reference Material",
+ "description": "Assess the integration and application of insights from the referenced article by Matheson and Zimbalist in the development of the solution."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a strong foundation in mathematical modeling to develop and analyze metrics for evaluating the impacts of hosting the Olympics. This includes creating models to assess economic impacts, land use, and other quantifiable factors.",
+ "details": "As a mathematician, you are adept at formulating mathematical models that can simulate various scenarios related to hosting the Olympics. Your expertise in optimization, statistical analysis, and predictive modeling will be crucial in evaluating the feasibility and impact of proposed strategies. When reviewing the solutions, pay attention to the mathematical rigor and validity of the models used, ensuring they are robust and applicable to real-world scenarios."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets to derive insights into the impacts of hosting the Olympics. This includes processing data related to economic factors, human satisfaction, and travel logistics.",
+ "details": "As a data scientist, your skills in data analysis, machine learning, and statistical methods are essential for interpreting complex datasets. You will need to evaluate the data-driven aspects of the proposed solutions, ensuring that the data is accurately processed and that the conclusions drawn are supported by the data. Your role involves verifying the integrity of the data sources and the appropriateness of the analytical techniques used."
+ },
+ {
+ "name": "Urban Planner",
+ "thoughts": "The problem involves significant considerations of land use and urban development, which are critical when planning for large-scale events like the Olympics. An urban planner's perspective is vital in assessing the long-term impacts on host cities.",
+ "details": "As an urban planner, you bring expertise in sustainable development, infrastructure planning, and community impact assessment. Your role is to evaluate how the proposed strategies align with urban development goals and the potential long-term benefits or drawbacks for host cities. Pay attention to the integration of land use planning with the proposed solutions and ensure that they promote sustainable and efficient urban growth."
+ },
+ {
+ "name": "Economist",
+ "thoughts": "The economic implications of hosting the Olympics are a central concern, requiring an economist's expertise to evaluate the financial viability and potential economic benefits or risks associated with different strategies.",
+ "details": "As an economist, your focus is on analyzing the economic models and assumptions used in the proposed solutions. You will assess the cost-benefit analyses, economic impact studies, and financial projections to ensure they are realistic and comprehensive. Your role involves scrutinizing the economic feasibility of the strategies and their potential to enhance or detract from the host city's or nation's economic health."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Strategy Development",
+ "description": "Evaluate the creativity and innovation of the proposed strategies to ensure the Olympics remain successful and appealing to host cities."
+ },
+ {
+ "category": "Metric Identification",
+ "description": "Assess the identification and justification of metrics used to evaluate the impacts of hosting the Olympics, including economic, land use, human satisfaction, travel, future opportunities, and prestige."
+ },
+ {
+ "category": "Feasibility Analysis",
+ "description": "Examine the feasibility of the proposed strategies, including the practicality of implementation and the timeline for execution."
+ },
+ {
+ "category": "Impact Assessment",
+ "description": "Evaluate the analysis of potential impacts of the strategies on the identified metrics, considering both short-term and long-term effects."
+ },
+ {
+ "category": "Policy Recommendations",
+ "description": "Review the clarity and persuasiveness of the policy recommendations provided in the one-page memorandum to the IOC."
+ },
+ {
+ "category": "Assumptions and Justifications",
+ "description": "Check the identification and justification of any assumptions made in the modeling process."
+ },
+ {
+ "category": "Integration of Reference Material",
+ "description": "Assess the integration and application of insights from the referenced article by Matheson and Zimbalist in the development of the solution."
+ }
+ ]
+ }
+ },
+ "2024_Reducing_Illegal_Wildlife": {
+ "year": "2024",
+ "title": "Reducing Illegal Wildlife Trade",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2024/ICM-F/index.html",
+ "question": "2024_ICM_Problem_F.pdf Reducing Illegal Wildlife Trade\n\n### Text in the PDF File: 2024_ICM_Problem_F.pdf\n\n**2024 ICM Problem F: Reducing Illegal Wildlife Trade**\n\n**Overview:**\nIllegal wildlife trade is a significant global issue, estimated to involve up to $26.5 billion annually, making it the fourth largest illegal trade worldwide. The task is to develop a data-driven 5-year project aimed at significantly reducing this trade. The project should be tailored to a specific client capable of implementing it.\n\n**Key Sub-Questions:**\n1. **Client Selection:**\n - Identify a client with the necessary powers, resources, and interest to execute the project.\n - Justify why this client is suitable for the proposed project.\n\n2. **Project Suitability:**\n - Use research and data analysis to support the project choice.\n - Convince the client of the project's viability and importance.\n\n3. **Resource Requirements:**\n - Determine additional powers and resources needed for project execution.\n\n4. **Impact and Analysis:**\n - Predict the measurable impact on illegal wildlife trade if the project is implemented.\n - Conduct analysis to support these predictions.\n\n5. **Project Feasibility:**\n - Assess the likelihood of achieving the project's goals.\n - Perform a sensitivity analysis to identify conditions that may affect the project's success.\n\n**Complex Systems Approach:**\n- Consider illegal wildlife trade as part of a larger system, potentially integrating efforts from other domains like climate change or other forms of trafficking.\n- Justify the use of a complexity framework, discussing its benefits and drawbacks.\n\n**Submission Requirements:**\n- A 1-page memo for the client, summarizing the project proposal and its alignment with the client's mission.\n- A solution of up to 25 pages, including:\n - One-page summary sheet.\n - Complete solution.\n - One-page client memo.\n\n**Judging Criteria:**\n- Creativity in client and project selection.\n- Strong connections between the client and the project.\n- Clear ties between data analysis and project design.\n\n**Reference:**\n- Wildlife Conservancy Society. (2021). Why Should we Care about Wildlife Trafficking? Retrieved from WCS Wildlife Trade",
+ "requirements": [
+ {
+ "category": "Client Selection",
+ "description": "Identify a suitable client with the necessary powers, resources, and interest to execute the project, and provide a strong justification for this choice."
+ },
+ {
+ "category": "Project Suitability",
+ "description": "Use research and data analysis to support the choice of the project, ensuring it aligns with the client's mission and objectives."
+ },
+ {
+ "category": "Resource Requirements",
+ "description": "Determine and justify the additional powers and resources needed for the successful execution of the project."
+ },
+ {
+ "category": "Impact and Analysis",
+ "description": "Predict the measurable impact on illegal wildlife trade if the project is implemented, supported by thorough analysis and data."
+ },
+ {
+ "category": "Project Feasibility",
+ "description": "Assess the likelihood of achieving the project's goals, including a sensitivity analysis to identify conditions that may affect success."
+ },
+ {
+ "category": "Complex Systems Approach",
+ "description": "Justify the use of a complexity framework, discussing its benefits and drawbacks in the context of the illegal wildlife trade."
+ },
+ {
+ "category": "Creativity and Innovation",
+ "description": "Demonstrate creativity in the selection of the client and the design of the project, ensuring strong connections between the client and the project."
+ },
+ {
+ "category": "Data Analysis and Project Design",
+ "description": "Ensure clear ties between data analysis and project design, demonstrating how data informs and supports the project proposal."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to understand the dynamics of illegal wildlife trade and predict the impact of interventions. Mathematical models can help simulate scenarios and assess the effectiveness of different strategies.",
+ "details": "As a mathematician, you are skilled in developing models that can simulate complex systems like illegal wildlife trade. You should focus on creating models that incorporate various factors influencing the trade, such as economic incentives, enforcement levels, and social dynamics. Pay attention to the assumptions made in the models and ensure they are realistic and grounded in empirical data. Your expertise in differential equations, optimization, and statistical analysis will be crucial in evaluating the proposed solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets to identify patterns and trends in illegal wildlife trade. Data scientists can leverage machine learning and statistical techniques to extract insights and inform the project's design.",
+ "details": "As a data scientist, you are adept at handling and analyzing complex datasets. You should focus on identifying key data sources related to wildlife trade, such as trade records, enforcement actions, and market prices. Use your skills in data cleaning, feature engineering, and predictive modeling to uncover insights that can guide the project's strategy. Pay attention to the quality and reliability of the data, and ensure that the analysis is robust and reproducible. Your expertise in data visualization will also be important in communicating findings to stakeholders."
+ },
+ {
+ "name": "Environmental Economist",
+ "thoughts": "The problem requires understanding the economic drivers of illegal wildlife trade and evaluating the cost-effectiveness of proposed interventions. Environmental economists can assess the economic impact of the trade and the potential benefits of reducing it.",
+ "details": "As an environmental economist, you are skilled in analyzing the economic aspects of environmental issues. You should focus on evaluating the economic incentives that drive illegal wildlife trade and the potential economic benefits of reducing it. Consider the costs and benefits of different interventions, and assess their feasibility from an economic perspective. Pay attention to the trade-offs between economic growth and conservation efforts, and ensure that the proposed solutions are economically viable. Your expertise in cost-benefit analysis and economic modeling will be crucial in evaluating the project's impact."
+ },
+ {
+ "name": "Conservation Biologist",
+ "thoughts": "The problem involves understanding the ecological impact of illegal wildlife trade and designing interventions that protect biodiversity. Conservation biologists can provide insights into the species affected and the ecological consequences of the trade.",
+ "details": "As a conservation biologist, you are knowledgeable about the ecological aspects of wildlife trade. You should focus on identifying the species most affected by the trade and assessing the ecological impact of their exploitation. Consider the role of biodiversity in ecosystem services and the potential consequences of species loss. Pay attention to the ecological interactions and dependencies that may be disrupted by the trade, and ensure that the proposed solutions are ecologically sound. Your expertise in species conservation and habitat management will be important in evaluating the project's ecological impact."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Client Selection",
+ "description": "Identify a suitable client with the necessary powers, resources, and interest to execute the project, and provide a strong justification for this choice."
+ },
+ {
+ "category": "Project Suitability",
+ "description": "Use research and data analysis to support the choice of the project, ensuring it aligns with the client's mission and objectives."
+ },
+ {
+ "category": "Resource Requirements",
+ "description": "Determine and justify the additional powers and resources needed for the successful execution of the project."
+ },
+ {
+ "category": "Impact and Analysis",
+ "description": "Predict the measurable impact on illegal wildlife trade if the project is implemented, supported by thorough analysis and data."
+ },
+ {
+ "category": "Project Feasibility",
+ "description": "Assess the likelihood of achieving the project's goals, including a sensitivity analysis to identify conditions that may affect success."
+ },
+ {
+ "category": "Complex Systems Approach",
+ "description": "Justify the use of a complexity framework, discussing its benefits and drawbacks in the context of the illegal wildlife trade."
+ },
+ {
+ "category": "Creativity and Innovation",
+ "description": "Demonstrate creativity in the selection of the client and the design of the project, ensuring strong connections between the client and the project."
+ },
+ {
+ "category": "Data Analysis and Project Design",
+ "description": "Ensure clear ties between data analysis and project design, demonstrating how data informs and supports the project proposal."
+ }
+ ]
+ }
+ },
+ "2024_Resource_Availability_and": {
+ "year": "2024",
+ "title": "Resource Availability and Sex Ratios",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2024/MCM-A/index.html",
+ "question": "2024_MCM_Problem_A.pdf Resource Availability and Sex Ratios\n\n### Text in the PDF File: 2024_MCM_Problem_A.pdf\n\n**2024 MCM Problem A: Resource Availability and Sex Ratios**\n\n**Overview:**\nThe problem focuses on the adaptive sex ratio variation in animal species, particularly sea lampreys, and how these ratios are influenced by environmental factors such as food availability. The task is to develop a model to understand the ecological impacts of these variations.\n\n**Key Points:**\n\n- **Adaptive Sex Ratio Variation:** Some species, like the American alligator, have sex ratios influenced by environmental factors (e.g., nest temperature). Sea lampreys' sex ratios are influenced by larval growth rates, which depend on food availability.\n\n- **Sea Lampreys:** These are jawless fish found in coastal and freshwater habitats. They are both parasites and a food source in various regions.\n\n- **Sex Ratio Influence:** \n - Low food availability leads to slower growth rates, resulting in approximately 78% males.\n - High food availability results in about 56% males.\n\n**Questions to Explore:**\n\n1. **Ecological Impact:** How does the ability of lampreys to alter their sex ratio affect the larger ecosystem?\n2. **Population Dynamics:** What are the advantages and disadvantages for lampreys in altering their sex ratio?\n3. **Ecosystem Stability:** How do changes in lamprey sex ratios impact ecosystem stability?\n4. **Ecosystem Benefits:** Can variable sex ratios in lampreys offer advantages to other ecosystem members, such as parasites?\n\n**Submission Requirements:**\n\n- A complete solution with a one-page summary.",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "The model should accurately represent the relationship between food availability and sex ratio variations in sea lampreys."
+ },
+ {
+ "category": "Ecological Impact Analysis",
+ "description": "Evaluate how changes in sex ratios affect the larger ecosystem, including predator-prey relationships and resource competition."
+ },
+ {
+ "category": "Population Dynamics",
+ "description": "Analyze the advantages and disadvantages for sea lampreys in altering their sex ratio, considering factors like survival, reproduction, and competition."
+ },
+ {
+ "category": "Ecosystem Stability",
+ "description": "Assess how variations in lamprey sex ratios influence the stability and resilience of the ecosystem."
+ },
+ {
+ "category": "Ecosystem Benefits",
+ "description": "Investigate potential advantages that variable sex ratios in lampreys might offer to other ecosystem members, such as parasites or other species."
+ },
+ {
+ "category": "Assumptions and Justifications",
+ "description": "Identify and justify any assumptions made in the model, particularly those related to environmental factors and biological processes."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct a sensitivity analysis to determine how changes in key parameters affect the model's outcomes."
+ },
+ {
+ "category": "Validation and Testing",
+ "description": "Provide evidence of model validation and testing against real-world data or established ecological theories."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to understand the relationship between environmental factors and sex ratio variations in sea lampreys. This involves formulating equations and models that can predict changes in sex ratios based on resource availability.",
+ "details": "You are a mathematician with expertise in ecological modeling and differential equations. Your role is to develop and analyze mathematical models that describe the sex ratio dynamics in sea lampreys. Pay attention to the assumptions made in the models and ensure they accurately reflect biological processes. Your skills in mathematical analysis will be crucial in evaluating the stability and sensitivity of the models to changes in environmental parameters."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to sea lamprey populations, environmental conditions, and sex ratios. A data scientist can help in processing and interpreting this data to inform the model and validate its predictions.",
+ "details": "You are a data scientist with expertise in data analysis and machine learning. Your role is to gather and analyze data on sea lamprey populations and environmental factors such as food availability. Use statistical methods to identify patterns and correlations that can be incorporated into the model. Pay attention to data quality and ensure that the data used in the model is reliable and representative of real-world conditions."
+ },
+ {
+ "name": "Ecologist",
+ "thoughts": "Understanding the ecological impact of sex ratio variations requires expertise in ecology. An ecologist can provide insights into how changes in sex ratios affect population dynamics and ecosystem stability.",
+ "details": "You are an ecologist with expertise in population dynamics and ecosystem interactions. Your role is to evaluate the ecological implications of sex ratio variations in sea lampreys. Consider how these changes affect predator-prey relationships, competition, and overall ecosystem health. Pay attention to the broader ecological context and ensure that the model captures the complexity of interactions within the ecosystem."
+ },
+ {
+ "name": "Marine Biologist",
+ "thoughts": "A marine biologist can provide specific insights into the biology and behavior of sea lampreys, which are crucial for understanding how environmental factors influence their sex ratios.",
+ "details": "You are a marine biologist with expertise in the biology and life cycle of sea lampreys. Your role is to provide biological insights that inform the model, such as the impact of larval growth rates on sex determination. Pay attention to the biological accuracy of the model and ensure that it reflects the physiological and behavioral characteristics of sea lampreys. Your understanding of marine ecosystems will be valuable in assessing the model's predictions and implications for ecosystem stability."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "The model should accurately represent the relationship between food availability and sex ratio variations in sea lampreys."
+ },
+ {
+ "category": "Ecological Impact Analysis",
+ "description": "Evaluate how changes in sex ratios affect the larger ecosystem, including predator-prey relationships and resource competition."
+ },
+ {
+ "category": "Population Dynamics",
+ "description": "Analyze the advantages and disadvantages for sea lampreys in altering their sex ratio, considering factors like survival, reproduction, and competition."
+ },
+ {
+ "category": "Ecosystem Stability",
+ "description": "Assess how variations in lamprey sex ratios influence the stability and resilience of the ecosystem."
+ },
+ {
+ "category": "Ecosystem Benefits",
+ "description": "Investigate potential advantages that variable sex ratios in lampreys might offer to other ecosystem members, such as parasites or other species."
+ },
+ {
+ "category": "Assumptions and Justifications",
+ "description": "Identify and justify any assumptions made in the model, particularly those related to environmental factors and biological processes."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Conduct a sensitivity analysis to determine how changes in key parameters affect the model's outcomes."
+ },
+ {
+ "category": "Validation and Testing",
+ "description": "Provide evidence of model validation and testing against real-world data or established ecological theories."
+ }
+ ]
+ }
+ },
+ "2024_Searching_for_Submersibles": {
+ "year": "2024",
+ "title": "Searching for Submersibles",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2024/MCM-B/index.html",
+ "question": "2024_MCM_Problem_B.pdf Searching for Submersibles\n\n### Text in the PDF File: 2024_MCM_Problem_B.pdf\n\n**2024 MCM Problem B: Searching for Submersibles**\n\n**Overview:**\nMaritime Cruises Mini-Submarines (MCMS), based in Greece, builds submersibles for deep-sea exploration. They plan to offer tourist adventures in the Ionian Sea to explore shipwrecks. To gain regulatory approval, they need to develop safety procedures for scenarios like loss of communication or mechanical failures, including propulsion loss.\n\n**Tasks:**\n\n1. **Locate:**\n - Develop a model to predict the submersible's location over time.\n - Identify uncertainties in predictions.\n - Determine what information the submersible can send to the host ship to reduce uncertainties and the equipment needed.\n\n2. **Prepare:**\n - Recommend additional search equipment for the host ship, considering costs, maintenance, and readiness.\n - Suggest equipment a rescue vessel might need.\n\n3. **Search:**\n - Create a model to recommend initial deployment points and search patterns to minimize the time to locate a lost submersible.\n - Calculate the probability of finding the submersible over time and with accumulated search results.\n\n4. **Extrapolate:**\n - Expand the model for other tourist destinations like the Caribbean Sea.\n - Adapt the model for multiple submersibles in the same area.\n\n**Report Requirements:**\n- Maximum of 25 pages.\n- Include a one-page summary, complete solution, and one- to two-page memo to the Greek government.\n\n**Glossary:**\n- **Submersible:** An underwater vehicle supported by a larger watercraft, unlike self-supporting submarines.\n- **Neutral Buoyancy:** When an object's density equals the fluid's density, causing it to neither sink nor rise.",
+ "requirements": [
+ {
+ "category": "Location Prediction Model",
+ "description": "Evaluate the model's ability to accurately predict the submersible's location over time, including the mathematical approach and assumptions made."
+ },
+ {
+ "category": "Uncertainty Analysis",
+ "description": "Assess how well the solution identifies and quantifies uncertainties in the location predictions and the strategies proposed to mitigate these uncertainties."
+ },
+ {
+ "category": "Communication Strategy",
+ "description": "Examine the proposed information and equipment needed for the submersible to communicate with the host ship to reduce uncertainties."
+ },
+ {
+ "category": "Search Equipment Recommendations",
+ "description": "Evaluate the recommendations for additional search equipment for the host ship, considering cost, maintenance, and readiness."
+ },
+ {
+ "category": "Rescue Vessel Equipment",
+ "description": "Assess the suggested equipment for a rescue vessel, ensuring it is practical and effective for the intended purpose."
+ },
+ {
+ "category": "Search Strategy Model",
+ "description": "Analyze the model for recommending initial deployment points and search patterns, focusing on its effectiveness in minimizing search time."
+ },
+ {
+ "category": "Probability Calculation",
+ "description": "Evaluate the method used to calculate the probability of finding the submersible over time and with accumulated search results."
+ },
+ {
+ "category": "Model Extrapolation",
+ "description": "Assess the adaptability of the model for other tourist destinations and for scenarios involving multiple submersibles."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires developing mathematical models to predict the submersible's location, calculate probabilities, and adapt models for different scenarios. This involves complex equations and understanding of mathematical principles.",
+ "details": "You are a mathematician with expertise in formulating and solving mathematical models. Your role is crucial in ensuring the accuracy and reliability of the models used to predict the submersible's location and search patterns. Pay attention to the assumptions made in the models, the mathematical techniques used, and the robustness of the solutions. Your expertise in differential equations, probability theory, and optimization will be essential in evaluating the modeling solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data to reduce uncertainties in predictions and to inform search strategies. This requires expertise in data analysis, statistical methods, and machine learning.",
+ "details": "You are a data scientist skilled in processing and analyzing complex datasets. Your role is to evaluate how data is used to improve the accuracy of the models and reduce uncertainties. Focus on the data sources, data quality, and the methods used to analyze and interpret the data. Your knowledge in data visualization, statistical analysis, and predictive modeling will be key in assessing the effectiveness of the solutions."
+ },
+ {
+ "name": "Marine Engineer",
+ "thoughts": "The problem involves understanding the mechanical and operational aspects of submersibles, including potential failures and the equipment needed for search and rescue operations.",
+ "details": "You are a marine engineer with expertise in the design and operation of submersibles. Your role is to assess the technical feasibility of the proposed solutions, particularly in terms of the equipment and procedures recommended for search and rescue. Pay attention to the mechanical reliability, safety protocols, and the practicality of the equipment suggested. Your understanding of marine technology and engineering principles will be vital in evaluating the solutions' effectiveness and safety."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "The problem requires optimizing search patterns and deployment strategies to minimize the time to locate a lost submersible, which involves operations research techniques.",
+ "details": "You are an operations research analyst with expertise in optimization and decision-making processes. Your role is to evaluate the efficiency and effectiveness of the search strategies proposed. Focus on the optimization models used, the assumptions made, and the decision-making criteria. Your skills in linear programming, simulation, and resource allocation will be crucial in assessing the solutions' ability to minimize search time and maximize the probability of success."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Location Prediction Model",
+ "description": "Evaluate the model's ability to accurately predict the submersible's location over time, including the mathematical approach and assumptions made."
+ },
+ {
+ "category": "Uncertainty Analysis",
+ "description": "Assess how well the solution identifies and quantifies uncertainties in the location predictions and the strategies proposed to mitigate these uncertainties."
+ },
+ {
+ "category": "Communication Strategy",
+ "description": "Examine the proposed information and equipment needed for the submersible to communicate with the host ship to reduce uncertainties."
+ },
+ {
+ "category": "Search Equipment Recommendations",
+ "description": "Evaluate the recommendations for additional search equipment for the host ship, considering cost, maintenance, and readiness."
+ },
+ {
+ "category": "Rescue Vessel Equipment",
+ "description": "Assess the suggested equipment for a rescue vessel, ensuring it is practical and effective for the intended purpose."
+ },
+ {
+ "category": "Search Strategy Model",
+ "description": "Analyze the model for recommending initial deployment points and search patterns, focusing on its effectiveness in minimizing search time."
+ },
+ {
+ "category": "Probability Calculation",
+ "description": "Evaluate the method used to calculate the probability of finding the submersible over time and with accumulated search results."
+ },
+ {
+ "category": "Model Extrapolation",
+ "description": "Assess the adaptability of the model for other tourist destinations and for scenarios involving multiple submersibles."
+ }
+ ]
+ }
+ },
+ "2024_Sustainability_of_Property": {
+ "year": "2024",
+ "title": "Sustainability of Property Insurance",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2024/ICM-E/index.html",
+ "question": "2024_ICM_Problem_E.pdf Sustainability of Property Insurance\n\n### Text in the PDF File: 2024_ICM_Problem_E.pdf\n\n**Sustainability of Property Insurance**\n\n**Overview:**\nExtreme weather events are increasingly impacting property owners and insurers, with over $1 trillion in damages from more than 1,000 events recently. In 2022, insurance claims for natural disasters rose by 115% compared to the 30-year average. Climate change is expected to further increase these losses, with insurance premiums projected to rise by 30-60% by 2040. The insurance protection gap, the difference between economic losses and covered losses, averages 57% worldwide and is growing.\n\n**Challenges:**\n- Rising insurance costs and reduced availability as insurers adjust underwriting policies.\n- The dilemma of profitability for insurers versus affordability for property owners.\n- The need for a resilient insurance system to cover future claims while ensuring the long-term health of insurance companies.\n\n**Objectives:**\n1. Develop a model for insurance companies to determine underwriting policies in areas with increasing extreme weather events.\n2. Adapt the model to assess real-estate decisions, ensuring properties are resilient and services viable for growing communities.\n3. Create a preservation model for community leaders to protect culturally or historically significant buildings.\n\n**Tasks:**\n1. **Insurance Model Development:**\n - Determine conditions under which insurance companies should underwrite policies.\n - Identify actions property owners can take to influence underwriting decisions.\n - Demonstrate the model using two areas on different continents experiencing extreme weather.\n\n2. **Real-Estate Assessment:**\n - Adapt the insurance model to guide decisions on where and how to build resilient properties.\n\n3. **Preservation Model:**\n - Develop a model to help community leaders decide on preserving significant buildings.\n - Apply the model to a historic landmark (not Cape Hatteras Lighthouse) in an area prone to extreme weather.\n\n4. **Community Engagement:**\n - Compose a one-page letter to a community recommending a plan, timeline, and cost proposal for preserving a landmark based on the models.\n\n**Submission Requirements:**\n- A solution of up to 25 pages, including a summary sheet, complete solution, and community letter\n\n**References:**\n1. Boston Consulting Group. (2023, December 4). An Insurance Risk Framework for Climate Adaptation. Retrieved at: https://www.bcg.com/publications/2023/an-insurance-risk-framework-for-climate-adaptation\n2. Munich RE. (2022, January 10). Hurricanes, cold waves, tornadoes: Weather disasters in USA dominate natural disaster losses in 2021. Retrieved at: https://www.munichre.com/en/company/media-relations/media-information-and-corporate-news/media-information/2022/natural-disaster-losses-2021.html\n3. Union of Concerned Scientists. (2016, July 19). Saving an Icon: Moving the Cape Hatteras Lighthouse Away from the Shifting Shoreline. Retrieved at: https://www.ucsusa.org/resources/moving-cape-hatteras-lighthouse-away-shifting-shoreline \n\n**Glossary:**\n- **Insurance Protection Gap:** Difference between economic losses from natural disasters and covered losses.\n- **Underwrite:** Accept liability for guaranteeing payment in case of loss or damage.",
+ "requirements": [
+ {
+ "category": "Insurance Model Development",
+ "description": "Evaluate the model's ability to determine conditions for underwriting policies in areas with increasing extreme weather events, including the identification of key factors influencing these decisions."
+ },
+ {
+ "category": "Insurance Model Development",
+ "description": "Assess the model's capability to identify actions property owners can take to influence underwriting decisions, ensuring these actions are practical and evidence-based."
+ },
+ {
+ "category": "Insurance Model Development",
+ "description": "Examine the demonstration of the model using two areas on different continents, focusing on the model's adaptability and accuracy in different geographic and climatic contexts."
+ },
+ {
+ "category": "Real-Estate Assessment",
+ "description": "Evaluate how well the insurance model is adapted to guide real-estate decisions, particularly in terms of building resilience and ensuring service viability for growing communities."
+ },
+ {
+ "category": "Preservation Model",
+ "description": "Assess the development of a preservation model for community leaders, focusing on its ability to prioritize culturally or historically significant buildings in areas prone to extreme weather."
+ },
+ {
+ "category": "Preservation Model",
+ "description": "Evaluate the application of the preservation model to a historic landmark, ensuring the model's recommendations are feasible and contextually appropriate."
+ },
+ {
+ "category": "Community Engagement",
+ "description": "Review the one-page letter to a community, focusing on the clarity, persuasiveness, and practicality of the proposed plan, timeline, and cost proposal for preserving a landmark."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to develop robust insurance models that can predict and manage risks associated with extreme weather events. Mathematical expertise is crucial for formulating equations and algorithms that can simulate various scenarios and optimize underwriting policies.",
+ "details": "As a mathematician, you are skilled in creating and analyzing complex mathematical models. You should focus on ensuring the accuracy and reliability of the models used to predict insurance risks and assess real-estate decisions. Pay attention to the assumptions made in the models and the mathematical techniques used to solve them, such as differential equations, probability theory, and optimization methods. Your expertise will be vital in evaluating the mathematical soundness of the proposed solutions."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing large datasets related to weather patterns, insurance claims, and real-estate values. Data scientists are essential for processing this data, identifying trends, and using machine learning techniques to improve model predictions and decision-making processes.",
+ "details": "As a data scientist, you are adept at handling and interpreting complex datasets. You should focus on the data quality, the methods used for data analysis, and the application of machine learning algorithms to enhance model predictions. Your role involves ensuring that the data-driven insights are accurately integrated into the models and that the statistical methods used are appropriate for the problem at hand. Your expertise will be crucial in validating the data analysis components of the solutions."
+ },
+ {
+ "name": "Climate Scientist",
+ "thoughts": "Climate scientists are crucial for understanding the impact of climate change on extreme weather events and their subsequent effects on property insurance. Their expertise can provide insights into future climate scenarios and help refine models to account for these changes.",
+ "details": "As a climate scientist, you bring valuable knowledge about climate patterns and their implications for insurance and real-estate decisions. You should evaluate how well the models incorporate climate data and projections, ensuring that they accurately reflect the risks posed by climate change. Your expertise will be essential in assessing the environmental assumptions and predictions used in the models, ensuring they are grounded in scientific evidence."
+ },
+ {
+ "name": "Insurance Analyst",
+ "thoughts": "Insurance analysts have specialized knowledge in evaluating insurance policies, risk management, and financial implications. Their expertise is vital for assessing the feasibility and sustainability of the proposed insurance models.",
+ "details": "As an insurance analyst, you are skilled in analyzing insurance policies and financial risks. You should focus on the practicality and economic viability of the underwriting policies proposed in the models. Pay attention to the balance between profitability for insurers and affordability for property owners, ensuring that the models provide realistic solutions for the insurance industry. Your expertise will be crucial in evaluating the financial aspects and risk management strategies of the solutions."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Insurance Model Development",
+ "description": "Evaluate the model's ability to determine conditions for underwriting policies in areas with increasing extreme weather events, including the identification of key factors influencing these decisions."
+ },
+ {
+ "category": "Insurance Model Development",
+ "description": "Assess the model's capability to identify actions property owners can take to influence underwriting decisions, ensuring these actions are practical and evidence-based."
+ },
+ {
+ "category": "Insurance Model Development",
+ "description": "Examine the demonstration of the model using two areas on different continents, focusing on the model's adaptability and accuracy in different geographic and climatic contexts."
+ },
+ {
+ "category": "Real-Estate Assessment",
+ "description": "Evaluate how well the insurance model is adapted to guide real-estate decisions, particularly in terms of building resilience and ensuring service viability for growing communities."
+ },
+ {
+ "category": "Preservation Model",
+ "description": "Assess the development of a preservation model for community leaders, focusing on its ability to prioritize culturally or historically significant buildings in areas prone to extreme weather."
+ },
+ {
+ "category": "Preservation Model",
+ "description": "Evaluate the application of the preservation model to a historic landmark, ensuring the model's recommendations are feasible and contextually appropriate."
+ },
+ {
+ "category": "Community Engagement",
+ "description": "Review the one-page letter to a community, focusing on the clarity, persuasiveness, and practicality of the proposed plan, timeline, and cost proposal for preserving a landmark."
+ }
+ ]
+ }
+ },
+ "2024_The_Modeling_Musical": {
+ "year": "2024",
+ "title": "The Modeling Musical Tour",
+ "level": "Middle School",
+ "source": "MidMCM",
+ "link": "Problems/2024/MidMCM-C/index.html",
+ "question": "2024_MidMCM_Problem_C.pdf The Modeling Musical Tour\n\n### Text in the PDF File: 2024_MidMCM_Problem_C.pdf\n\n**2024 MidMCM Problem C: The Modeling Musical Tour**\n\n**Overview:**\nTaylor Swift's Eras Tour, concluding in December, included 152 shows, each lasting about 3.5 hours. In the US, each concert attracted approximately 72,000 fans, generating $13 million per show, making it the first tour to earn over $1 billion. Despite the success, ticket acquisition was challenging due to high demand and prices. Swift is known for her generosity towards her team, offering significant bonuses to crew members.\n\n**Task:**\nAs a tour manager at MidMCM Music Agency, you are tasked with planning a tour for a musical performer of your choice. Analyze the performer's past tours to develop a model for their next tour.\n\n**Steps to Follow:**\n\n1. **Familiarize with a Performer:**\n - Choose a performer with a past concert tour.\n - Investigate the reasons for their tour, its duration, number of shows, and locations.\n - Identify factors for planning a tour, such as single show logistics, multiple show coordination, and elements of a successful tour.\n\n2. **Develop a Model:**\n - Consider aspects like the number of concerts, venues, and ticket prices.\n - Determine the best plan to achieve goals such as maximizing attendance, venues, profits, or other objectives.\n\n3. **Apply the Model:**\n - Analyze a past tour using your model to identify strengths and weaknesses.\n - Plan a future tour, suggesting improvements and strategies based on your model.\n\n4. **Share Your Model:**\n - Write a one- to two-page letter to the performer, detailing a new tour plan and explaining how it meets their goals.\n\n5. **Reflect:**\n - Consider the model's applicability to other performers and its limitations.\n\n**Submission Requirements:**\n- A solution of up to 25 pages, including:\n - One-page Summary Sheet\n - Complete solution\n - One- to two-page letter",
+ "requirements": [
+ {
+ "category": "Performer Analysis",
+ "description": "Evaluate the depth of research and understanding of the chosen performer's past tours, including reasons for the tour, duration, number of shows, and locations."
+ },
+ {
+ "category": "Model Development",
+ "description": "Assess the comprehensiveness of the model developed for planning the tour, including factors like number of concerts, venue selection, ticket pricing, and logistical coordination."
+ },
+ {
+ "category": "Objective Alignment",
+ "description": "Examine how well the model aligns with the performer's goals, such as maximizing attendance, profits, or other specified objectives."
+ },
+ {
+ "category": "Model Application",
+ "description": "Analyze the application of the model to a past tour, identifying strengths and weaknesses, and how these insights are used to inform future tour planning."
+ },
+ {
+ "category": "Future Tour Planning",
+ "description": "Evaluate the proposed future tour plan, including suggested improvements and strategies based on the model, and how well these meet the performer's goals."
+ },
+ {
+ "category": "Communication",
+ "description": "Assess the clarity and persuasiveness of the one- to two-page letter to the performer, explaining the new tour plan and its benefits."
+ },
+ {
+ "category": "Model Generalization",
+ "description": "Consideration of the model's applicability to other performers and its limitations, demonstrating an understanding of the model's broader utility."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem involves creating a mathematical model to optimize various aspects of a musical tour, such as the number of concerts, venues, and ticket pricing. A mathematician's expertise is crucial in formulating and solving the equations and algorithms that will underpin the model.",
+ "details": "As a mathematician, you are adept at developing and analyzing mathematical models. Your role involves ensuring that the model is mathematically sound, identifying any assumptions or simplifications made, and verifying the accuracy of the calculations. You should pay attention to the logical structure of the model and its ability to predict outcomes based on different variables. Your expertise will be invaluable in refining the model to ensure it is robust and reliable."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The task requires analyzing past tour data to inform the model, making the role of a data scientist essential. You will need to handle large datasets, extract meaningful insights, and apply statistical methods to predict future trends.",
+ "details": "As a data scientist, you are skilled in data analysis, machine learning, and statistical modeling. Your role is to process and analyze historical tour data to identify patterns and trends that can inform the model. You should focus on the quality and relevance of the data used, ensuring that it is comprehensive and accurately reflects past performances. Your ability to apply predictive analytics will help in forecasting future tour success and optimizing the model accordingly."
+ },
+ {
+ "name": "Operations Research Analyst",
+ "thoughts": "Planning a tour involves logistical challenges, such as scheduling, routing, and resource allocation. An operations research analyst can apply optimization techniques to streamline these processes and improve efficiency.",
+ "details": "As an operations research analyst, you specialize in optimizing complex systems and processes. Your expertise in linear programming, simulation, and decision analysis will be crucial in developing a model that efficiently allocates resources and schedules concerts. You should evaluate the model's ability to handle logistical constraints and its effectiveness in minimizing costs while maximizing tour success. Your insights will help ensure that the tour plan is both practical and economically viable."
+ },
+ {
+ "name": "Marketing Strategist",
+ "thoughts": "The success of a musical tour is heavily influenced by marketing strategies, which affect ticket sales and audience engagement. A marketing strategist can provide insights into consumer behavior and promotional tactics.",
+ "details": "As a marketing strategist, you are experienced in developing and executing marketing campaigns. Your role involves analyzing market trends, audience demographics, and promotional channels to enhance the tour's visibility and appeal. You should assess the model's consideration of marketing factors, such as pricing strategies and advertising effectiveness. Your expertise will help ensure that the tour plan aligns with the performer's brand and maximizes audience reach and engagement."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Performer Analysis",
+ "description": "Evaluate the depth of research and understanding of the chosen performer's past tours, including reasons for the tour, duration, number of shows, and locations."
+ },
+ {
+ "category": "Model Development",
+ "description": "Assess the comprehensiveness of the model developed for planning the tour, including factors like number of concerts, venue selection, ticket pricing, and logistical coordination."
+ },
+ {
+ "category": "Objective Alignment",
+ "description": "Examine how well the model aligns with the performer's goals, such as maximizing attendance, profits, or other specified objectives."
+ },
+ {
+ "category": "Model Application",
+ "description": "Analyze the application of the model to a past tour, identifying strengths and weaknesses, and how these insights are used to inform future tour planning."
+ },
+ {
+ "category": "Future Tour Planning",
+ "description": "Evaluate the proposed future tour plan, including suggested improvements and strategies based on the model, and how well these meet the performer's goals."
+ },
+ {
+ "category": "Communication",
+ "description": "Assess the clarity and persuasiveness of the one- to two-page letter to the performer, explaining the new tour plan and its benefits."
+ },
+ {
+ "category": "Model Generalization",
+ "description": "Consideration of the model's applicability to other performers and its limitations, demonstrating an understanding of the model's broader utility."
+ }
+ ]
+ }
+ },
+ "2025_Cyber_Strong?": {
+ "year": "2025",
+ "title": "Cyber Strong?",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2025/ICM-F/index.html",
+ "question": "2025_ICM_Problem_F.pdf Cyber Strong?\n\n### Text in the PDF File: 2025_ICM_Problem_F.pdf\n\n**2025 ICM Problem F: Cyber Strong?**\n\n**Background:**\nThe increasing global connectivity through technology has enhanced productivity but also heightened vulnerability to cybercrime. Cybercrime is challenging to combat due to jurisdictional issues across borders and the reluctance of institutions to report breaches. Many countries have developed national cybersecurity policies, and the International Telecommunication Union (ITU) plays a key role in setting international standards and assessing cybersecurity status.\n\n**Objective:**\nIdentify patterns to inform the development and refinement of national cybersecurity policies based on effective existing policies. Develop a theory for strong national cybersecurity policy and support it with data-driven analysis.\n\n**Considerations:**\n- Analyze global cybercrime distribution: Identify countries with high cybercrime rates, successful defenses, reporting, and prosecution patterns.\n- Compare national security policies with cybercrime distribution to identify effective policy elements.\n- Consider national demographics (internet access, wealth, education) that correlate with cybercrime distribution and support your theory.\n\n**Data and Analysis:**\n- Use existing measures like ITU's Global Cybersecurity Index (GCI) and resources like the VERIS framework and Community Database (VCDB) for data collection.\n- Highlight limitations and concerns for policymakers when using your analysis to refine cybersecurity policies.\n\n**Deliverables:**\n- A 1-page memo for nontechnical policy experts at an ITU Summit, summarizing your work, theory, and key findings.\n- A solution of up to 25 pages, including a summary sheet, complete solution, and your memo.\n\n**References:**\n1. [ITU Global Cybersecurity Index 2024](https://www.itu.int/epublications/publication/global-cybersecurity-index-2024)\n2. [VERIS Framework](https://verisframework.org/index.html)\n3. [VERIS Community Database](https://verisframework.org/vcdb.html)\n\n**Glossary:**\n- **Cybercrime:** Criminal activities using digital devices/networks.\n- **Cybersecurity Incident:** Events compromising business operations and cybersecurity.\n- **Cybersecurity:** Tools, policies, and practices to protect the cyber environment and assets.",
+ "requirements": [
+ {
+ "category": "Data Analysis",
+ "description": "Effectiveness in analyzing global cybercrime distribution, identifying countries with high cybercrime rates, successful defenses, and patterns in reporting and prosecution."
+ },
+ {
+ "category": "Policy Comparison",
+ "description": "Ability to compare national cybersecurity policies with cybercrime distribution to identify effective policy elements."
+ },
+ {
+ "category": "Demographic Correlation",
+ "description": "Consideration of national demographics such as internet access, wealth, and education in relation to cybercrime distribution and their integration into the theory."
+ },
+ {
+ "category": "Theory Development",
+ "description": "Development of a coherent and data-supported theory for strong national cybersecurity policy."
+ },
+ {
+ "category": "Data Utilization",
+ "description": "Appropriate use of existing measures like the ITU's Global Cybersecurity Index and resources like the VERIS framework and Community Database for data collection."
+ },
+ {
+ "category": "Limitations and Concerns",
+ "description": "Identification and discussion of limitations and concerns for policymakers when using the analysis to refine cybersecurity policies."
+ },
+ {
+ "category": "Memo for Policy Experts",
+ "description": "Clarity and conciseness of the 1-page memo for nontechnical policy experts, summarizing the work, theory, and key findings."
+ },
+ {
+ "category": "Overall Solution Presentation",
+ "description": "Completeness and coherence of the solution, including the summary sheet, complete solution, and the memo, within the 25-page limit."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires a strong foundation in mathematical modeling to identify patterns and correlations between cybersecurity policies and cybercrime rates. A mathematician can develop and refine theoretical models that underpin the analysis of national cybersecurity policies.",
+ "details": "As a mathematician, you are adept at constructing and analyzing complex mathematical models. Your expertise in statistical analysis and pattern recognition is crucial for identifying effective elements of national cybersecurity policies. When reviewing the modeling solutions, pay attention to the mathematical rigor and validity of the models used, ensuring they are robust and accurately represent the data."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves handling and analyzing large datasets from various sources, such as the ITU's Global Cybersecurity Index and the VERIS Community Database. A data scientist is essential for processing this data and extracting meaningful insights to inform cybersecurity policy development.",
+ "details": "As a data scientist, your skills in data mining, machine learning, and statistical analysis are vital for uncovering patterns in cybercrime distribution and policy effectiveness. When reviewing the solutions, focus on the data preprocessing steps, the choice of analytical methods, and the interpretation of results. Ensure that the data-driven analysis is comprehensive and supports the proposed theory for strong national cybersecurity policies."
+ },
+ {
+ "name": "Cybersecurity Analyst",
+ "thoughts": "A cybersecurity analyst is crucial for understanding the practical aspects of cybersecurity policies and their implementation. They can provide insights into the effectiveness of different policy elements and how they translate into real-world defenses against cybercrime.",
+ "details": "As a cybersecurity analyst, you have a deep understanding of cybersecurity threats, defenses, and policy frameworks. Your role is to evaluate the practical applicability of the proposed models and theories, ensuring they align with current cybersecurity practices and challenges. Pay attention to how well the solutions address the nuances of cybersecurity incidents and the feasibility of policy recommendations."
+ },
+ {
+ "name": "Policy Advisor",
+ "thoughts": "A policy advisor is essential for bridging the gap between technical analysis and policy formulation. They can assess the implications of the proposed models and theories for national and international cybersecurity policy development.",
+ "details": "As a policy advisor, your expertise lies in understanding the policy landscape and the socio-political factors influencing cybersecurity strategies. When reviewing the solutions, consider the policy recommendations' alignment with existing frameworks and their potential impact on international cooperation and compliance. Ensure that the solutions are presented in a way that is accessible to nontechnical policy experts and can effectively inform decision-making at the ITU Summit."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Data Analysis",
+ "description": "Effectiveness in analyzing global cybercrime distribution, identifying countries with high cybercrime rates, successful defenses, and patterns in reporting and prosecution."
+ },
+ {
+ "category": "Policy Comparison",
+ "description": "Ability to compare national cybersecurity policies with cybercrime distribution to identify effective policy elements."
+ },
+ {
+ "category": "Demographic Correlation",
+ "description": "Consideration of national demographics such as internet access, wealth, and education in relation to cybercrime distribution and their integration into the theory."
+ },
+ {
+ "category": "Theory Development",
+ "description": "Development of a coherent and data-supported theory for strong national cybersecurity policy."
+ },
+ {
+ "category": "Data Utilization",
+ "description": "Appropriate use of existing measures like the ITU's Global Cybersecurity Index and resources like the VERIS framework and Community Database for data collection."
+ },
+ {
+ "category": "Limitations and Concerns",
+ "description": "Identification and discussion of limitations and concerns for policymakers when using the analysis to refine cybersecurity policies."
+ },
+ {
+ "category": "Memo for Policy Experts",
+ "description": "Clarity and conciseness of the 1-page memo for nontechnical policy experts, summarizing the work, theory, and key findings."
+ },
+ {
+ "category": "Overall Solution Presentation",
+ "description": "Completeness and coherence of the solution, including the summary sheet, complete solution, and the memo, within the 25-page limit."
+ }
+ ]
+ }
+ },
+ "2025_Making_Room_for": {
+ "year": "2025",
+ "title": "Making Room for Agriculture",
+ "level": "Undergraduate",
+ "source": "ICM",
+ "link": "Problems/2025/ICM-E/index.html",
+ "question": "2025_ICM_Problem_E.pdf Making Room for Agriculture\n\n### Text in the PDF File: 2025_ICM_Problem_E.pdf\n\n**Problem E: Making Room for Agriculture**\n\n**Situation:**\nA forest was cleared for agriculture, replacing a thriving ecosystem with crops. This led to soil depletion and pest invasions, prompting farmers to use chemicals, disrupting the natural balance. Over time, a new agricultural ecosystem emerged, including species like bats and birds.\n\n**Model and Analyze:**\nAs part of the Consideration of Mature Agricultural Practices (COMAP) group, you are tasked with modeling the transition from forest to farm. Your model should track ecosystem changes over time, considering both natural processes and human decisions.\n\n**Key Considerations:**\n\n- **Natural Processes:**\n - Develop a food web model for the new agricultural ecosystem, including producers, consumers, and the effects of agricultural cycles and chemical use.\n - Consider the reemergence of native species and their impact on the ecosystem.\n\n- **Human Decisions:**\n - Explore the effects of removing herbicides on ecosystem stability, incorporating bats as insectivores and pollinators.\n - Analyze the implications of organic farming methods, considering pest control, crop health, biodiversity, sustainability, and cost-effectiveness.\n\n**Share Your Insights:**\n- Write a one-page letter to a farmer exploring organic farming, advising on methods, economic trade-offs, and sustainability strategies.\n\n**Submission Requirements:**\n- A solution of up to 25 pages, including a summary sheet, complete solution, and one-page letter.\n\n**Glossary:**\n- **Converted Forest Area:** Land cleared from forest to agriculture.\n- **Food Web:** Network of feeding relationships in an ecosystem.\n- **Agricultural Ecosystem:** Complex interactions in food webs supporting ecological balance and crop production.\n- **Agriculture Cycle:** Stages from planting to consumption, including soil preparation, planting, growth, pest control, harvesting, and decomposition.\n- **Bats:** Beneficial species for pest control and pollination.\n- **Edge Habitats:** Buffer zones between agricultural fields and surrounding ecosystems.",
+ "requirements": [
+ {
+ "category": "Natural Processes",
+ "description": "Develop a comprehensive food web model for the new agricultural ecosystem, including producers, consumers, and the effects of agricultural cycles and chemical use."
+ },
+ {
+ "category": "Natural Processes",
+ "description": "Consider and model the reemergence of native species and their impact on the agricultural ecosystem."
+ },
+ {
+ "category": "Human Decisions",
+ "description": "Analyze the effects of removing herbicides on ecosystem stability, particularly focusing on the role of bats as insectivores and pollinators."
+ },
+ {
+ "category": "Human Decisions",
+ "description": "Evaluate the implications of adopting organic farming methods, considering aspects such as pest control, crop health, biodiversity, sustainability, and cost-effectiveness."
+ },
+ {
+ "category": "Insights and Recommendations",
+ "description": "Provide a well-reasoned one-page letter to a farmer exploring organic farming, advising on methods, economic trade-offs, and sustainability strategies."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem requires mathematical modeling to understand the complex interactions within the agricultural ecosystem, including food webs and the impact of human interventions.",
+ "details": "You are a mathematician with expertise in ecological modeling and systems analysis. Your role involves developing mathematical models to simulate the transition from forest to farm, focusing on the dynamics of food webs and the effects of agricultural practices. You should pay attention to the accuracy of equations representing natural processes and human decisions, ensuring they reflect real-world scenarios. Your evaluation should consider the robustness of the model in predicting ecosystem changes over time."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves analyzing data related to ecosystem changes, agricultural practices, and the impact of human decisions, requiring data-driven insights to inform the model.",
+ "details": "You are a data scientist skilled in data analysis, machine learning, and statistical methods. Your role is to process and analyze datasets related to soil health, pest populations, crop yields, and biodiversity. You should focus on identifying patterns and trends that can inform the model's assumptions and parameters. Your evaluation should ensure that the data used in the model is reliable and that the insights derived are actionable for improving agricultural practices."
+ },
+ {
+ "name": "Ecologist",
+ "thoughts": "The problem involves understanding the ecological impacts of converting forest to farmland, including species interactions and ecosystem stability.",
+ "details": "You are an ecologist with expertise in ecosystem dynamics and biodiversity. Your role is to assess the ecological implications of the transition from forest to agriculture, focusing on species interactions and the reemergence of native species. You should evaluate the model's representation of ecological processes, such as food webs and edge habitats, ensuring they accurately reflect the complexity of the agricultural ecosystem. Your insights should guide sustainable practices that enhance biodiversity and ecosystem resilience."
+ },
+ {
+ "name": "Agricultural Economist",
+ "thoughts": "The problem requires analyzing the economic trade-offs and sustainability of different farming methods, including organic practices and chemical use.",
+ "details": "You are an agricultural economist with expertise in evaluating the economic aspects of farming practices. Your role is to analyze the cost-effectiveness and sustainability of organic farming methods compared to conventional practices. You should assess the model's consideration of economic factors, such as pest control costs, crop health, and market dynamics. Your evaluation should provide insights into the economic viability of sustainable farming strategies, helping farmers make informed decisions that balance profitability and ecological health."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Natural Processes",
+ "description": "Develop a comprehensive food web model for the new agricultural ecosystem, including producers, consumers, and the effects of agricultural cycles and chemical use."
+ },
+ {
+ "category": "Natural Processes",
+ "description": "Consider and model the reemergence of native species and their impact on the agricultural ecosystem."
+ },
+ {
+ "category": "Human Decisions",
+ "description": "Analyze the effects of removing herbicides on ecosystem stability, particularly focusing on the role of bats as insectivores and pollinators."
+ },
+ {
+ "category": "Human Decisions",
+ "description": "Evaluate the implications of adopting organic farming methods, considering aspects such as pest control, crop health, biodiversity, sustainability, and cost-effectiveness."
+ },
+ {
+ "category": "Insights and Recommendations",
+ "description": "Provide a well-reasoned one-page letter to a farmer exploring organic farming, advising on methods, economic trade-offs, and sustainability strategies."
+ }
+ ]
+ }
+ },
+ "2025_Managing_Sustainable_Tourism": {
+ "year": "2025",
+ "title": "Managing Sustainable Tourism",
+ "level": "Undergraduate",
+ "source": "MCM",
+ "link": "Problems/2025/MCM-B/index.html",
+ "question": "2025_MCM_Problem_B.pdf Managing Sustainable Tourism\n\n### Text in the PDF File: 2025_MCM_Problem_B.pdf\n\n**Managing Sustainable Tourism in Juneau, Alaska**\n\n**Background:**\n- Juneau, Alaska, with a population of about 30,000, hosted 1.6 million cruise passengers in 2023, with up to 20,000 visitors on peak days.\n- Tourism revenue is approximately $375 million, but issues like overcrowding and environmental impact, such as the receding Mendenhall Glacier, are concerns.\n- Other attractions include whale watching and rainforests.\n\n**Challenges:**\n- Hidden costs of tourism include pressure on infrastructure, increased carbon footprint, and local population stress due to housing and overcrowding.\n- Measures like increased hotel taxes, visitor fees, and caps on daily visitors have been implemented to manage these issues.\n\n**Task:**\n1. **Model Development:**\n - Create a model for sustainable tourism in Juneau, considering visitor numbers, revenue, and stabilization measures.\n - Identify factors to optimize and constraints.\n - Plan expenditures from additional revenue to support sustainable tourism.\n - Conduct a sensitivity analysis to determine key factors.\n\n2. **Adaptation to Other Destinations:**\n - Demonstrate how the model can be adapted to other locations affected by overtourism.\n - Discuss the impact of location choice on the effectiveness of measures.\n - Use the model to promote less-visited attractions for better balance.\n\n3. **Memo to Tourist Council:**\n - Write a one-page memo outlining predictions, effects of measures, and advice for optimizing outcomes.\n\n**Submission Requirements:**\n- Include a one-page summary, complete solution, and one-page memo.\n\n**Glossary:**\n- **Sustainable Tourism:** Focuses on economic, social, and environmental issues, improving tourist experiences, and addressing host community needs.\n- **Carbon Footprint:** Measures greenhouse gas emissions, reported in CO2-equivalent tonnes.\n- **Infrastructure:** Physical and organizational structures needed for societal operation.\n\n**References:**\n- [1] Juneau's cruise ship limits: https://abc7.com/post/juneau-alaska-cruise-ship-limits-overtourism/15048713/\n- [2] Cruise impacts report: https://juneau.org/wp-content/uploads/2024/01/CBJ-Cruise-Impacts-2023-Report-1.22.24.pdf\n- [3] Mendenhall Glacier concerns: https://alaskapublic.org/2023/08/07/crammed-with-tourists-juneau-wonders-what-will-happen-as-mendenhall-glacier-recedes/\n- [4] Invisible burden of tourism: https://www.thetravelfoundation.org.uk/invisible-burden/",
+ "requirements": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the comprehensiveness and accuracy of the model developed for sustainable tourism in Juneau, including the consideration of visitor numbers, revenue, and stabilization measures."
+ },
+ {
+ "category": "Optimization and Constraints",
+ "description": "Assess the identification and justification of factors to optimize and constraints within the model, ensuring they align with sustainable tourism goals."
+ },
+ {
+ "category": "Expenditure Planning",
+ "description": "Grade the plan for allocating additional revenue towards supporting sustainable tourism, including the rationale and expected impact of proposed expenditures."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Evaluate the execution and findings of the sensitivity analysis, focusing on the identification of key factors that influence the model's outcomes."
+ },
+ {
+ "category": "Adaptation to Other Destinations",
+ "description": "Assess the demonstration of how the model can be adapted to other locations, including the discussion on the impact of location choice on the effectiveness of measures."
+ },
+ {
+ "category": "Promotion of Less-Visited Attractions",
+ "description": "Evaluate the use of the model to promote less-visited attractions, ensuring it contributes to a better balance in tourist distribution."
+ },
+ {
+ "category": "Memo to Tourist Council",
+ "description": "Grade the clarity, conciseness, and effectiveness of the one-page memo in outlining predictions, effects of measures, and advice for optimizing outcomes."
+ }
+ ],
+ "eval_roles": [
+ {
+ "name": "Mathematician",
+ "thoughts": "The problem of managing sustainable tourism in Juneau requires mathematical modeling to balance visitor numbers, revenue, and environmental impact. A mathematician can develop and analyze models to optimize these factors and constraints effectively.",
+ "details": "You are a mathematician with expertise in creating and analyzing mathematical models. Your skills in optimization, sensitivity analysis, and constraint management are crucial for developing a sustainable tourism model. Pay attention to the mathematical formulation of the problem, ensuring that all relevant factors are included and accurately represented. Your evaluation should focus on the robustness and adaptability of the model to different scenarios and locations."
+ },
+ {
+ "name": "Data Scientist",
+ "thoughts": "The problem involves handling large datasets related to visitor numbers, revenue, and environmental impact. A data scientist can analyze these datasets to inform the model and conduct sensitivity analyses to identify key factors affecting sustainable tourism.",
+ "details": "You are a data scientist skilled in data analysis, statistical methods, and machine learning. Your role is to process and analyze complex datasets to extract meaningful insights that inform the model. Pay attention to the quality and relevance of the data used in the model, ensuring that it accurately reflects the current situation in Juneau. Your evaluation should focus on the data-driven aspects of the model, including the accuracy of predictions and the effectiveness of measures based on data analysis."
+ },
+ {
+ "name": "Environmental Scientist",
+ "thoughts": "The problem involves significant environmental concerns, such as the impact of tourism on the Mendenhall Glacier and local ecosystems. An environmental scientist can provide insights into the ecological aspects of the model and suggest measures to mitigate negative impacts.",
+ "details": "You are an environmental scientist with expertise in assessing and mitigating environmental impacts. Your role is to ensure that the model incorporates ecological considerations and promotes sustainable practices. Pay attention to the environmental constraints and impacts included in the model, ensuring they are realistic and comprehensive. Your evaluation should focus on the ecological sustainability of the proposed solutions and their potential to preserve local ecosystems."
+ },
+ {
+ "name": "Urban Planner",
+ "thoughts": "The problem involves managing the infrastructure and societal impacts of tourism in Juneau. An urban planner can provide insights into the infrastructure needs and societal challenges, helping to develop a model that addresses these issues effectively.",
+ "details": "You are an urban planner with expertise in infrastructure development and societal impact assessment. Your role is to ensure that the model addresses the physical and organizational structures needed to support sustainable tourism. Pay attention to the infrastructure constraints and societal impacts included in the model, ensuring they are realistic and comprehensive. Your evaluation should focus on the feasibility and effectiveness of the proposed solutions in managing infrastructure and societal challenges."
+ }
+ ],
+ "decomposition": {
+ "grading_points": [
+ {
+ "category": "Model Development",
+ "description": "Evaluate the comprehensiveness and accuracy of the model developed for sustainable tourism in Juneau, including the consideration of visitor numbers, revenue, and stabilization measures."
+ },
+ {
+ "category": "Optimization and Constraints",
+ "description": "Assess the identification and justification of factors to optimize and constraints within the model, ensuring they align with sustainable tourism goals."
+ },
+ {
+ "category": "Expenditure Planning",
+ "description": "Grade the plan for allocating additional revenue towards supporting sustainable tourism, including the rationale and expected impact of proposed expenditures."
+ },
+ {
+ "category": "Sensitivity Analysis",
+ "description": "Evaluate the execution and findings of the sensitivity analysis, focusing on the identification of key factors that influence the model's outcomes."
+ },
+ {
+ "category": "Adaptation to Other Destinations",
+ "description": "Assess the demonstration of how the model can be adapted to other locations, including the discussion on the impact of location choice on the effectiveness of measures."
+ },
+ {
+ "category": "Promotion of Less-Visited Attractions",
+ "description": "Evaluate the use of the model to promote less-visited attractions, ensuring it contributes to a better balance in tourist distribution."
+ },
+ {
+ "category": "Memo to Tourist Council",
+ "description": "Grade the clarity, conciseness, and effectiveness of the one-page memo in outlining predictions, effects of measures, and advice for optimizing outcomes."
+ }
+ ]
+ }
+ }
+}
\ No newline at end of file