A multi-depot vehicle routing problem with time windows, split pickup and split delivery for surplus food recovery and redistribution

The problem faced by the food banks operating on the front-end model is the collection of surplus food from donation points and re-distribution of it to the demand points using a fleet of vehicles available at different volunteer locations/depots within specified time windows. Further, due to the limited vehicle capacity, demand splitting is allowed at the pickup as well and delivery points. Therefore, this problem can be seen as a rich variant of the vehicle routing problem (VRP) and named as a multi-depot VRP with time windows, split pickup and split delivery (MDVRP-TW-SP-SD). The problem is to determine the optimal number of vehicles from each depot to be hired and their optimal routes (sequence for visiting pickup and demand nodes) such that the total cost of hiring the vehicles, routing cost and penalty for unmet demand are minimized and it is formulated as a mixed-integer programming problem. To the best of our knowledge, this is the first attempt to formulate the MDVRP-TW-SP-SD. To efficiently and effectively solve the problem, an elitist GA and a GA hybridized with the local search are proposed. The performance of the proposed algorithms is tested through extensive computational experiments carried out on 180 modified benchmark problem instances from the literature. The results of computational experiments show the superiority of the GA hybridized with 3-opt local search. A case of the Robin Hood Army operating in the Lucknow city of India is also presented to demonstrate the applicability of the proposed model to practice.