Two-objective optimization model of costs and carbon dioxide in closed loop supply chain

In recent years, due to the reverse logistics and particularly integration with direct Logistics is considered important in reducing supply chain costs. In this paper, a closed supply chain with multi-objective, multi-product and multi-period is designed. The objective functions consists of minimizing transportation costs between centers and processing cost within centers and centers construction and also the minimization of carbon dioxide is published within centers and carbon dioxide is published of transportation between centers. For this purpose, a mixed integer programming model is used and the problem is NP Hard. This model is superior to previous models,Considering multi-product and multi-period in relevant two objectives and also the relevant model constraints Production carbon dioxide between centers and within centers consideration. In order to integrate the supply chain's two goals the same phase and by multi-objective planning became an object. In order to validate the model and the influence of objective functions Weights several problem is designed and is solved with CPLEX 12.3 and in the end, the results are analyzed.