Modeling for the equitable and effective distribution of donated food under capacity constraints

Mathematical models are presented and analyzed to facilitate a food bank's equitable and effective distribution of donated food among a population at risk for hunger. Typically exceeding the donated supply, demand is proportional to the poverty population within the food bank's service area. The food bank seeks to ensure a perfectly equitable distribution of food; i.e., each county in the service area should receive a food allocation that is exactly proportional to the county's demand such that no county is at a disadvantage compared to any other county. This objective often conflicts with the goal of maximizing effectiveness by minimizing the amount of undistributed food. Deterministic network-flow models are developed to minimize the amount of undistributed food while maintaining a user-specified upper bound on the absolute deviation of each county from a perfectly equitable distribution. An extension of this model identifies optimal policies for the allocation of additional receiving capacity to counties in the service area. A numerical study using data from a large North Carolina food bank illustrates the uses of the models. A probabilistic sensitivity analysis reveals the effect on the models' optimal solutions arising from uncertainty in the receiving capacities of the counties in the service area.