Mathematical Formulation and Solving of Green Closed-Loop Supply Chain Planning Problem With Production, Distribution and Transportation Reliability

In this paper, developed a new multi-product, multi-period, and multi-level closed-loop green supply chain planning model under uncertain conditions. the formulated model consists of five objective functions, which minimize the cost of the supply chain, minimize the co2 emission of transportation vehicles, maximize the reliability of manufacturing and distribution centers, maximize the reliability of the transportation system, and maximize the level of service provided. therefore, the problem of model formulated as a multi-objective mixed integer nonlinear programming. also, since the proposed model is complex and np-hard in large size, therefore, for the investigation of the results, we have used a non-dominated sorting genetic ii algorithm (nsga-ii). in addition, the small of size results of the problem achieved by gams software. therefore, we try to solve these problems by analyzing and comparing them with the help of these algorithm. for this purpose, various size has been considered.