An optimal approach to the multiple-depot heterogeneous vehicle routing problem with time window and capacity constraints

Abstract

The vehicle routing problem (VRP) has become a crucial industrial issue for its impact on product distribution costs. Though quite important in practice, the time-constrained version of the VRP accounting for several types of vehicles and m- depots, called the extended VRP with time windows (m-VRPTW), has received less attention. Since it is an NP-hard problem, most of the current approaches to m-VRPTW are heuristic, thus providing good but not necessarily optimal solutions. This work presents a novel MILP mathematical framework for the m-depot heterogeneous-fleet VRPTW problem. The new optimization approach permits to find both the optimal vehicle route/schedule and the fleet size by choosing the best set of preceding nodes for each pick-up point. To get a significant reduction on the problem size to tackle larger m-VRPTW problems, some elimination rules have been embedded in the MILP framework. When applied to a pair of examples, it was observed a remarkable saving in computer costs with regards to prior VRPTW optimization methods.