Mathematics Events

Location

Jones Hall, Room 301
200 Ukrop Way
Williamsburg, VA 23185Map this location

Abstract: Food insecurity has been an increasing threat to people's health status and quality of life. In the United States, local food banks serve the needy population to reduce food insecurity in their service area. We present and analyze several mathematical models to facilitate the equitable and effective distribution of donated food by a large local food bank among the population at risk for hunger. Demand typically exceeds the donated supply, and is proportional to the population in poverty within the service area. The food bank's supervising agencies and donors require that the food donations are distributed in an equitable manner in the food bank's service region, such that each person in poverty receives the same amount of food in each period. This objective conflicts with the goal of effectively distributing donated food by minimizing the amount of undistributed food. We first develop deterministic network-flow models to minimize the amount of undistributed food while maintaining a user-specified upper bound on the deviation from perfect equity and derive closed-form optimal solutions. These deterministic models show that locations with low capacity to demand ratios, bottlenecks, constrain the entire food distribution due to the need to distribute food equitably. Therefore, counties capacities, which in practice are uncertain, have a direct influence on the optimal solution. In order to address stochastic capacities, we first develop a robust optimization model allowing the capacity parameters to vary within a range. We obtain conservative yet realistic solutions which focus on the deviations at the bottleneck locations to achieve maximal influence on the objective. We also develop a two-stage stochastic programming model under which food distribution decisions are made before capacities at the receiving locations are known. In the second stage, capacities are realized and shipment decisions made in the first stage can be corrected at additional cost. We prove that this two-stage stochastic program has a newsvendor-type closed-form optimal solution which we use to develop a myopic heuristic for the multi-period problem. We illustrate our results using historical data from our collaborating food bank.

Contact

Sarah Day