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To avert unmanageable surges in COVID-19 hospitalizations and to mitigate pandemic mortality, states across the U. S. have implemented stay-at-home (or shelter-in-place) orders to enforce social distancing in March. In May, several states relaxed the restrictions and some businesses could reopen, such as manufactures. To balance the potential overwhelming healthcare surges and the costly lockdowns, governments need to decide when, where, and to which degree to reopen businesses. For example, Michigan published the "Michigan Safe Start Plan to Re-Engage the Economy," and New York published "New York Forward", which contain the metrics to safely reopen [1, 2].
Overview
Overview
In this work, we design three Excel macro-based games. These games consider one risk category ("Risk Index") and two benefit categories ("Economic Benefit Index" and "Employment Index"). In these three games, players determine which states or workforce industries to reopen for:
In this work, we design three Excel macro-based games. These games consider one risk category ("Risk Index") and two benefit categories ("Economic Benefit Index" and "Employment Index"). In these three games, players determine which states or workforce industries to reopen for:
(a) Reopening Game: Balancing the benefit and the risk.
(a) Reopening Game: Balancing the benefit and the risk.
(b) Feasibility Game: Maximizing the difference between the benefit and the risk.
(b) Feasibility Game: Maximizing the difference between the benefit and the risk.
(c) Optimization Game: Optimizing the risk while satisfying the constraints for the benefit (vise versa).
(c) Optimization Game: Optimizing the risk while satisfying the constraints for the benefit (vise versa).
We recommend to teach this game to potential audiences who do not have optimization or decision-making background but understand the tradeoff between multiple objectives (e.g., risk and benefit) associated with reopening or closedown decisions. This game is suitable for teaching K-12 students about how mathematics can be used to guide the governments' decisions of gradually reopen economy in different industries or states.
We recommend to teach this game to potential audiences who do not have optimization or decision-making background but understand the tradeoff between multiple objectives (e.g., risk and benefit) associated with reopening or closedown decisions. This game is suitable for teaching K-12 students about how mathematics can be used to guide the governments' decisions of gradually reopen economy in different industries or states.
The problems in these three games can be formulated as general 0-1 Knapsack problems [3] with binary variables and can be solved optimistically. The technical details can be found in our [report].
The problems in these three games can be formulated as general 0-1 Knapsack problems [3] with binary variables and can be solved optimistically. The technical details can be found in our [report].
How to Play
How to Play
The player decides how to begin the relaxing restrictions put in place to prevent the spread of the virus. We provide a PlayerManual for each game, which includes:
The player decides how to begin the relaxing restrictions put in place to prevent the spread of the virus. We provide a PlayerManual for each game, which includes:
- Detailed introduction
- Demonstration of risk and benefit categories
- Guide for playing
- Interpretation of the scores and results
Both the Excel macro-based game sheet and player-manual can be downloaded below for each game.
Both the Excel macro-based game sheet and player-manual can be downloaded below for each game.
Reopening Game
Reopening Game
You have the option to choose either three states or three workforce industries to reopen. Use the provided evaluations of selected criteria (the potential economic benefits, added employment, and risk of increased infections) to determine the optimal combination. After deciding which three states or industries to reopen, you will receive a final score that measures how well your combination is able to reduce the risk of new infections while maintaining economic viability. The score is presented as a percentage and 100% reflects the ideal outcome.
You have the option to choose either three states or three workforce industries to reopen. Use the provided evaluations of selected criteria (the potential economic benefits, added employment, and risk of increased infections) to determine the optimal combination. After deciding which three states or industries to reopen, you will receive a final score that measures how well your combination is able to reduce the risk of new infections while maintaining economic viability. The score is presented as a percentage and 100% reflects the ideal outcome.
Feasibility Game
Feasibility Game
You have the option to choose which states or workforce industries to reopen. Use the provided evaluations of selected criteria (the potential economic benefits, added employment, and risk of increased infections) to determine optimal combinations. An optimal combination reduces the risk of new infections while maintaining economic viability; the cumulative risk index should be the minimum of the three cumulative index scores. The outcome will be evaluated as either a “fail,” if the potential risk outweighs the potential benefit, or a “success” if the potential risk does not.
You have the option to choose which states or workforce industries to reopen. Use the provided evaluations of selected criteria (the potential economic benefits, added employment, and risk of increased infections) to determine optimal combinations. An optimal combination reduces the risk of new infections while maintaining economic viability; the cumulative risk index should be the minimum of the three cumulative index scores. The outcome will be evaluated as either a “fail,” if the potential risk outweighs the potential benefit, or a “success” if the potential risk does not.
Optimization Game
Optimization Game
You have the option to focus on optimizing either the risk or the benefit. That is, you will have the option to find:
You have the option to focus on optimizing either the risk or the benefit. That is, you will have the option to find:
• The lowest possible risk for a given minimum expected economic benefit.
• The lowest possible risk for a given minimum expected economic benefit.
• The greatest possible economic benefit for a given maximum expected risk.
• The greatest possible economic benefit for a given maximum expected risk.
The evaluations of selected criteria (the potential economic benefits and the potential risk of increased infections) are provided. An optimal combination reduces the risk of new infections while maintaining economic viability; the cumulative risk index should be less than the cumulative economic benefit index. The selected states or industries will be highlighted in purple and listed in the game window.
The evaluations of selected criteria (the potential economic benefits and the potential risk of increased infections) are provided. An optimal combination reduces the risk of new infections while maintaining economic viability; the cumulative risk index should be less than the cumulative economic benefit index. The selected states or industries will be highlighted in purple and listed in the game window.
Knapsack Problem Formulation
Knapsack Problem Formulation
The problems considered in these three games can be formulated as Knapsack problems and can be solved optimally. The Knapsack problems consider adding a set of items to a knapsack with a limited capacity to maximize the total values of the added items [1]. Here, we can use binary variables to represent the decisions of reopening the states or the industries, where 1 means reopen and 0 otherwise. The "total values" can be expressed as a linear combination of these binary variables and the weights are the risk or benefits indices. The "capacity" can be viewed as (i) the number of reopening states or industries or (ii) the specific requirements on the benefit or the risk.
The problems considered in these three games can be formulated as Knapsack problems and can be solved optimally. The Knapsack problems consider adding a set of items to a knapsack with a limited capacity to maximize the total values of the added items [1]. Here, we can use binary variables to represent the decisions of reopening the states or the industries, where 1 means reopen and 0 otherwise. The "total values" can be expressed as a linear combination of these binary variables and the weights are the risk or benefits indices. The "capacity" can be viewed as (i) the number of reopening states or industries or (ii) the specific requirements on the benefit or the risk.
References
References
[1] Michigan Safe Start: A Plan to Re-Engage Michigan’s Economy. https://www.michigan.gov/documents/whitmer/MI_SAFE_START_PLAN_689875_7.pdf. Accessed 7 May, 2020.
[1] Michigan Safe Start: A Plan to Re-Engage Michigan’s Economy. https://www.michigan.gov/documents/whitmer/MI_SAFE_START_PLAN_689875_7.pdf. Accessed 7 May, 2020.
[2] Metrics to Guide Reopening New York. https://forward.ny.gov/metrics-guide-reopening-new-york. Accessed 1 June, 2020.
[2] Metrics to Guide Reopening New York. https://forward.ny.gov/metrics-guide-reopening-new-york. Accessed 1 June, 2020.
[3] Garey, M. R., & Johnson, D. S. (1979). Computers and intractability (Vol. 174). San Francisco: Freeman.
[3] Garey, M. R., & Johnson, D. S. (1979). Computers and intractability (Vol. 174). San Francisco: Freeman.
Student Contributor:
Student Contributor:
Ryan DaCosta
Ryan DaCosta
Major in Industrial and Operations Engineering
Major in Industrial and Operations Engineering
Minors in International Engineering, Mathematics, and Supplemental Studies in Sustainable Engineering
Minors in International Engineering, Mathematics, and Supplemental Studies in Sustainable Engineering
University of Michigan at Ann Arbor
University of Michigan at Ann Arbor
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