Multi-vehicle sequential resource allocation for a nonprofit distribution system

This article introduces a multi-vehicle sequential allocation problem that considers two critical objectives for nonprofit operations: providing equitable service and minimizing unused donations. This problem is motivated by an application in food redistribution from donors such as restaurants and grocery stores to agencies such as soup kitchens and homeless shelters. A set partitioning model is formulated that can be used to design vehicle routes; it primarily focuses on equity maximization and implicitly considers waste. The behavior of the model in clustering agencies and donors on routes is studied, and the impacts of demand variability and supply availability on route composition and solution performance are analyzed. A comprehensive numerical study is performed in order to develop insights on optimal solutions. Based on this study, an efficient decomposition-based heuristic for the problem that can handle an additional constraint on route length is developed and it is shown that the heuristic obtains high-quality solutions in terms of equity and waste.