Exact and heuristic algorithms for finding envy-free allocations in food rescue pickup and delivery logistics

Food rescue organizations collect and re-distribute surplus perishable food for hunger relief. We propose novel approaches to address this humanitarian logistics challenge and find envy-free allocations of the rescued food together with least travel cost routes. We show that this food rescue and delivery problem is NP-hard and we present a cutting-plane algorithm based on Benders' decomposition for its exact solution. We introduce a novel heuristic algorithm that combines greedy and local search. We test our approaches using real data from food rescue organizations. Our results show that the proposed algorithms are able to efficiently provide envy-free and cost-effective solutions.