A heuristic for bi-objective vehicle routing with time window constraints

This paper is concerned with the bi-objective vehicle routing problem with time window constraints (BVRPTW). The BVRPTW is to determine the most favorable vehicle routes that minimize the total vehicle travel time and the total customer wait time which are, more often than not, conflicting. We construct a linear goal programming (GP) model for the BVRPTW and propose a heuristic algorithm to relieve a computational burden inherent to the application of the GP model. The heuristic algorithm consists of a parallel insertion method for clustering and a sequential linear goal programming procedure for routing. The results of computational experiments showed that the proposed algorithm finds successfully the more favorable solutions in more cases than the Potvin and Rousseau's method that is known as a very good heuristic for the VRPs with time window constraints. The proposed algorithm was capable of generating numerous nondominated solutions through the change of the target values of the two objectives and the decision maker's preference on the objectives expressed as α.