optimization of closed-loop supply chain, multi-level , multi-product , multi -period to reduce costs in supply chain

today, due to the direct and reverse logistics plays an important role in reducing the costs in supply chain. in this paper, in order to provide a closed-loop supply chain network including supply centers, production, distribution, collection, recycling and disposal of a used linear mixed integer programming. this paper to consider multi-period and multi-product in multi-level supply chain and processing costs are taken into account in place and returned goods that can be improved will be transferred entirely to the production and distribution centers in the logistics process directly reach the hands of consumers. the model objective centers rent cost reduction in the supply chain and the cost of transportation between the centers and the processing cost is in centers. the proposed model using software cplex 12.3 in the form of a case study solved. model based on some samples tested and analyzed based on the number of different products, and in the end conclusion was presented.