Routing and resource allocation in non-profit settings with equity and efficiency measures under demand uncertainty

Motivated by food distribution operations for non-profit organizations, we study a variant of the stochastic routing-allocation problem under demand uncertainty, in which one decides the assignment of trucks for demand nodes, the sequence of demand nodes to visit (i.e., truck route), and the allocation of food supply to each demand node. We propose three stochastic mixed-integer programming (SMIP) models representing different performance measures important to food banks, namely maximizing efficiency, maximizing equity, and maximizing efficiency and equity simultaneously. To solve practical large-scale instances, we develop an original matheuristic based on adaptive large-scale neighborhood search. Using real-world data based on real-life instances, we conduct an extensive numerical experiment to assess the computational performance of our approach and derive insights relevant to food banks. The proposed matheuristic produces high-quality solutions quickly with an optimality gap never exceeding 4.11% on tested instances. We also demonstrate the performance of the three models in terms of service levels, food waste, and equity.