periodic vehicle routing problem in reverse logistics with qualified customers

one of the important issues in transportation and logistics systems is vehicle routing problem (vrp). the vehicle routing problem is concerned with finding efficient routes of minimum total cost, beginning and ending at a central depot, for a fleet of vehicles to serve a number of customers. on the other hand, as a result of the increasing environmental concerns, economic problems and pressure of laws, reverse logistics (rl) has received increasing attention during recent years. reverse logistics includes all the activities in supply chain that happen as reverse manner. one of the critical issues in the development of reverse logistics at the operational level is routing problem. in this regard, the present study introduced a periodic vehicle routing with circumstance to supply of customer (collection centers) goods as a qualification condition for serving them. for this problem, a mixed integer nonlinear programming model is proposed. finally, to validate the proposed model, some examples have been solved by gams software.