Decomposition of the vehicle routing problem with time windows on the time dimension

Abstract

The Vehicle Routing Problem with Time Windows (VRPTW) asks for the optimal set of routes to be performed by a fleet of vehicles to serve a set of customers within their assigned time windows. In this work, we propose a matheuristic for the VRPTW which utilizes the sub-problem constituted by optimizing only a selected time window of the VRPTW whereas the tours outside of this time window are regarded as fixed. We call this problem the Single Time Window Vehicle Routing Problem (STWVRP). For applying the STWVRP, we must assume that several customers are assigned to the same time window, i.e., the number of time windows is much smaller than the number of customers. An exact problem description of the STWVRP is given in the form of a Mixed-Integer Linear Programming formulation. We apply this exact formulation within a matheuristic for the VRPTW. The paper concludes with extensive computational experiments.