development of closed-loop supply chain mathematical model (cost-benefit-environmental effects) under uncertainty conditions by approach of genetic algorithm

In the current world, the debate on the reinstatement and reuse of consumer products has become particularly important. since the supply chain of the closed loop is not only a forward flow but also a reverse one; therefore, companies creating integrity between direct and reverse supply chain are successful. the purpose of this study is to develop a new mathematical model for closed loop supply chain network. in the real world the demand and the maximum capacity offered by the supplier are uncertain which in this model; the fuzzy theory discussion was used to cover the uncertainty of the mentioned variables. the objective functions of the model include minimizing costs, increasing revenues of recycling products, increasing cost saving from recycling and environmental impacts. according to the np-hard, an efficient algorithm was suggested based on the genetic meta heuristic algorithm to solve it. twelve numerical problems were defined and solved using the nsga-ii algorithm to validate the model