The Humanitarian Pickup and Distribution Problem

Food rescue—the collection of perishable products from food suppliers who are willing to make donations, and their distribution to welfare agencies that serve individuals in need—has become increasingly widespread in recent years. This phenomenon is a result of economic crises, but it is also encouraged by the tax and good image it provides to donor companies. The problem we study in this paper focuses on the logistic challenges of a food bank that on a daily basis uses vehicles of limited capacity to distribute food collected from suppliers in the food industry to welfare agencies, under an imposed maximal traveling time. We model this problem as a routing resource allocation problem, with the aim of maintaining equitable allocations to the different agencies while delivering overall as much food as possible. We introduce an innovative objective function that satisfies desired properties of the allocation, that is easy to compute and implement within a mathematical formulation, and that balances effectiveness and equity acceptably. We present both an exact solution method and a heuristic approach, based on the large neighborhood search framework, which relies on the fact that a certain subproblem is easy to solve. Numerical experiments on several real-life and randomly generated data sets confirm that high-quality solutions may be obtained.