Family Meal Planning under COVID-19 Scarcity Constraints: A Linear Programming Approach

Abstract

The “Diet Problem” originated in the 1940s when researchers were tasked with determining the lowest-cost subsistence diet for a U.S. soldier. Originally, the task was accomplished through basic heuristics, but later the problem was solved using the simplex algorithm-the basis for modern linear programming. Enhancements to computing technology enabled further constraint consideration, including environmental and palatability constraints. In late 2019, the COVID-19 pandemic began to sweep the planet, resulting in the unavailability of staple food products in the United States, coupled with stay-at-home requirements. This study aimed to add scarcity constraints (food availability and time) to the Diet Problem to demonstrate that, even during a pandemic, healthy eating can be maintained, visits to the supermarket can be limited to reduce exposure, and this can be done relatively inexpensively. A diversified meal plan for a hypothetical family of four was identified at a total monthly cost of $641.51. This study not only demonstrates that healthy eating can be cost-effectively maintained by consumers during a global pandemic but also that shopping trips can be limited to reduce exposure and maintain social distance. Additionally, linear programming-not normally considered by academic researchers-is showcased as a methodology that can be used by other researchers to solve novel problems.