A goal programming model for vehicle routing problem with backhauls and soft time windows

The vehicle routing problem with backhauls (VRPB) as an extension of the classical vehicle routing problem (VRP) attempts to define a set of routes which services both linehaul customers whom product are to be delivered and backhaul customers whom goods need to be collected. A primary objective for the problem usually is minimizing the total distribution cost. Most real-life problems have other objectives addition to this common primary objective. This paper describes a multi-objective model for VRPB with time windows (VRPBTW) and some new assumptions. We present a goal programming approach and a heuristic algorithm to solve the problem. Computational experiments are carried out and performance of developed methods is discussed.