A multi objective approach for vehicle routing problem with backhauls under fuzzy enviroment and an application

In Vehicle Routing Problem with Backhauls (VRPB), customers are divided into two categories as linehaul customers and backhaul customer. A vehicle that starts from depot deliveries all good to linehaul customers, then bring goods from backhaul customers and finally return to depot. A method that consists of two phase is proposed to solve the problem with mathematical programming in this study. Customers are clustered to vehicles with proposed multi objective mathematical programming in the first phase that is named as ?clustering phase? and fuzzy approaches are used to solve the model. A method that is a modification of Belenson and Kapur?s two-person zero-sum game theory based approach with using fuzzy sets is proposed to determine weights of objectives. Constructing routes are converted into traveling salesman problem with backhauls (TSPB) after clustering. Every vehicle routes is obtained by proposed mathematical model of TSPB that is a modification of Goetschalckx ve Jacobs-Belcha?s model for VRPB in the second phase that is named as routing phase. Finally local search is used to improve the routes that are generated after two phases. Test problems from literature are solved by the proposed method and the solutions are compared with best known solutions in literature. Also weekly routing problem for a firm that produces ceramic sanitary ware , is solved by the proposed method. Demand nodes that exceed vehicle capacity are divided due to vehicle capacity and artificial nodes are generated so demand of all nodes are provided to be less or equal to vehicle capacity.