Abstract: Considering the vehicle routing problem with soft time windows, customer points are often accompanied by dual demands for pick-up and delivery. For these problems, the soft time window, the time relationship of vehicle on the route and the combination between them are described, and a mixed integer nonlinear programming (MINLP) model is built by considering the vehicle travelling distance, vehicle number, total time of the soft time windows being violated and customer satisfaction. The corresponding multi-objective optimization algorithm is designed, and the objective function is transformed by using ideal point method, and the multi-objective optimization problem is transformed into single-objective optimization problem, and combining the set of test problems, each global optimal solution of test problems is solved by the global solver of LINGO 17.0. The results show that the model and algorithm of vehicle routing problem with simultaneous pick-up and delivery and soft time windows (VRPSPDSTW) are effective and feasible.

Key words: logistics engineering, vehicle routing problem, simultaneous pick-up and delivery, soft time window, ideal point method