Monitoring agency health: Utility elicitation of charitable agencies in a food bank network

In the United States, food banks play an integral role in the hunger relief supply chain, partnering with charitable agencies to serve the food-insecure population. These agencies are autonomous entities like food pantries that distribute food donations received from their food bank partner to the food-insecure population within their area. Feeding America maintains the largest network of more than 200 food banks whose partner agencies vary widely in size, operating structure, and capacity. While food banks ultimately decide how much food to allocate to each agency, agencies are not passive recipients — agency requests, shaped by their own capacities and constraints, influence the allocation process. The utility an agency derives from each pound of food is heterogeneous and may have a non-linear relationship with the total amount of food. This agency utility characterizes how much food an agency ultimately receives and impacts food flow through a hunger relief network. This complex but critical relationship has received little attention in the food bank operations literature. We address this gap by developing a nonlinear programming model that learns from an agency’s historical actions to identify its utility function. We use data from our collaborating food bank’s partner agencies to illustrate our approach and find that the agencies’ utility functions and stability levels vary significantly within their food bank network. We also develop a linear regression model to characterize the relationship between agency utility and their operational ability, organizational stability, and local socio-economic factors. Further, we discuss managerial insights associated with heterogeneous agency behavior.