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 prob-lem (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.