closed loop supply chain planning with vehicle routing

in the recent decade, special attention is paid to reverse logistic due to economic benefits of recovery and recycling of used products as well as environmental legislation and social concerns. on the other hand، many researches claim that separately and sequential planning of forward and reverse logistic causes sub-optimality. effective transport activities are also one of the most important components of a logistic system and it needs an accurate planning. in this study, a mixed integer linear programming model is proposed for integrated forward / reverse supply chain as well as vehicles routing. logistic network which is used in this paper is a multi-echelon integrated forward /reverse logistic network which is comprised capacitated facility, common facilities of production/recovery and distribution/collection, disposal facilities and customers. the proposed model is multi-period and multi-product with the ability to consider several facilities in each level. various types of vehicle routing models are also included such as multi-period routing, multi-depot, multi-products, routing with simultaneous delivery and pick-up, flexible depot assignment and split delivery. the model results present the product flow between the various facilities in forward and reverse direction throughout the planning horizon with the objective minimization of total cost. numerical example for solving the model using gams shows that the proposed model could reach the optimal solution in reasonable time for small and medium real world’s problems.