Modeling for the Equitable and Effective Food Distribution under Capacity Constraints

We present and analyze a number of models to support the equitable and effective distribution of donated food by a food bank among the population at risk for hunger. In this environment, supply is donated; demand typically exceeds supply and is proportional to the population in poverty in the service area. Equitable food distribution seeks to provide each individual in the service area with equal access to the donated food such that no individual is at a disadvantage compared to others. However, this objective often conflicts with the desire to maximize the amount of distributed food. We develop deterministic, capacity-constrained network flow models for maximizing effectiveness in food distribution while maintaining a specified level of equity. We then study the effect of distribution capacities on the optimal food distribution and identify optimal policies for the allocation of additional capacity in the service region. We illustrate our results using real data from a large food bank in North Carolina.