This paper considers the vehicle routing problem with soft time windows (VRPSTW) constraints, in which vehicles are allowed to service customers before and after the earliest and latest time windows bounds. This relaxation comes at the expense of appropriate penalties that time windows violations affect on the customers’ satisfaction. In this paper, a non-linear mathematical model is proposed. Due to the complexity of such an NP-hard problem, the linearization of the above model is presented and solved by an efficient meta-heuristic method. A number of instance problems are carried out and solve by the proposed method. Finally, the associated results are compared with the Lingo software to prove the efficiency method.
کلید واژگان :
vehicle routing problem with soft time windows,VRPSTW
