A robust fuzzy optimization model for designing close-loop green supply chain network under possibility chance constraint programming

Nowadays environmentalism has been become an important global issue. In recent years, the closed-loop green supply chain management has grown considerably and its result be important for managers. In this paper, we have proposed a mathematical optimization mixed-integer programming model for designing a single objective closed-loop green supply cahin network consisting of production and recovery centers, distribution centers, inspection centers,disposal centers and customers, which, in addition to reducing system costs includes the fixed cost of openning plant and distribution centers, the variable cost of product production with different technologies and shipping cost, taking into the carbon tax rate, the amount of carbon emissioned by production, transportation and establishing. Due to in real-world issue the parameters are uncertain. Moreover, the model has been developed using a robust fuzzy programming approach to examine the effects of uncertainties of production cost, remanufacturing cost,distribution process cost, inspection process cost and disposal process cost, amount carbon emission, facility capacity and the demand rate on the network design. Gams software has been used to obtain an optimal solution to the problem. The numerical results shows the proposed model is capable of controlling uncertainty and the robustness price is imposed on the system, therefore, the value of the objective function in a probability 5% is lower than the robust fuzzy possibilistic.