Modeling the role of efficiency for the equitable and effective distribution of donated food

Food banks operate with an objective to serve as many of food-insecure people as possible with the limited supply available to them. This paper presents a mixed-integer programming model to identify the efficient assignment of demand zones (counties) to distribution centers (branches) and equitable allocation of donated food from the food bank branches to the demand zones. The model objective function minimizes the total cost of branch operation, the cost of receiving and distributing food, the cost of undistributed food while maintaining the maximum allowed deviation from perfect equity. Data from the Food Bank of Central and Eastern North Carolina (FBCENC) are used to characterize the major attributes controlling the food distribution system of a food bank. Results from the optimization model using FBCENC data show that the optimal allocation under perfect equity follows a particular structure depending on the shipping cost and the cost of undistributed supply. Sensitivity analyses exploring the trade-offs between efficiency and effectiveness as a function of the cost of shipping, truck capacity, and a user-specified maximum inequity cap show that marginal sacrifice in equity can significantly improve effectiveness. The corresponding improvement in effectiveness is greater when comparatively larger trucks are used and the cost of shipping is relatively higher. The analyses also suggest that while efficiency is less sensitive to the allowable limit on the deviation from perfect equity, it is sensitive to truck size. A comparison of direct shipping to branches to operating a local hub suggests the former option to be more cost efficient.