Vehicle routing with stochastic demand, service and waiting times: The case of food bank collection problems

Food banks play an important role both in combating food waste, and in alleviating hunger. However, due to the many uncertainties that food banks face, they often struggle to effectively collect all food items that donors such as supermarkets are willing to provide. To tackle this problem, we introduce the capacitated vehicle routing problem with travel time restrictions and stochastic demand, service and waiting times, in which the uncertainties are dependent of each other. This problem can be generalized to a large variety of routing applications. The goal of the problem is to determine a minimum number of vehicles, and to plan cost-effective routes for these vehicles so that each route violates the vehicle capacity and the travel time limit with only a very small probability. The resulting problem is highly complex and thus solved by means of a matheuristic, which decomposes the problem into its natural decision components. Thus, it first determines the number of districts into which the service area should be partitioned, before allocating each customer to exactly one district and then plans a route for each district. A set of feedback mechanisms is activated whenever no feasible solution has been found through these steps. Extensive numerical experiments, involving both randomly generated and real-life instances, demonstrate the matheuristic's effectiveness in solving instances with up to 100 customers. When applying our matheuristic to real-life instances from Dutch and Canadian food banks, we furthermore gain managerial insights to assist in optimizing fleet size and route cost.