In recent years, one of the goals of any company is to increase overall production and process reliability. Hereupon supply chain reliability has been gaining growing attention and provides a technical framework for quantifying supply chain risks and uncertainties. In this paper, supply chain reliability was investigated in a two-stage stochastic programming model to design reliable closed-loop green four-echelon forward/backward supply chain networks. The purpose of this model was to maximize the total reliability of the supply chain based on the structural reliability theory. Our proposed model also minimized the cost of the supply chain by definition of recycling centres and the cost of penalizing unauthorized carbon emission and damages. The model optimized the locations of factories, warehouses, and recycling centres considering stochastic modes for demands and carbon price, as well as the flow between different sectors and the optimal orders. As the proposed model was a mixed-integer nonlinear problem, both e-constraint method and the metaheuristic algorithm (NSGA-II) were used in different scales and the sensitivity analysis was performed for critical parameters.
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