An assignment-based heuristic for vehicle routing with time windows

In this paper, we consider the typical vehicle routing problem with time window constraints (VRPTW). The problem is approached via mathematical decomposition and solved using a three-stage method. First, we formulate the generalized assignment problem, which provides an approximation to the sequencing of customers that partially respects the time windows and apply the Hungarian method to obtain optimal solutions. Subsequently, we address the split of infeasible routes resulting from the assignment solution using a simple, time window-based decomposition heuristic. The best of these routes, in terms of traveling and vehicle waiting times, form part of the final solution, which is completed by the routes provided by a look-ahead heuristic applied to the remainder of the customers. The proposed method is applied to a standard literature data set, and provides very good results with respect to both the number of vehicles and the total travel time. Furthermore, the approach offers useful insights on the effect of employing optimal travel time solutions resulting from the assignment relaxation to derive partial route sets of VRPTW.