Optimizing a green supply chain with reverse logistics using the queuing system under uncertainties

Modernization affects social, environmental, and economic structures in ways that are both positive and negative, and it makes it impossible to maintain equilibrium in sustainable practices. In this context, optimization has received a lot of attention. Even though the comprehensive models that integrate queuing systems, uncertainty, and reverse logistics emphasize the necessity. This study considers a four-echelon closed-loop green supply chain including a third-party collector under a stochastic environment. The products are transported through fleets to different centers forming a queue system during loading/unloading time. The effective energy consumption and carbon emission occur at the time of production, transportation, waiting in the loading center, reverse logistics, disposal, etc. To reduce this environmental impact, a mathematical model has been developed under different collection strategies. A numerical example is considered for the proposed model, followed by a sensitivity analysis, to investigate the significant role of the parameters. The findings indicate that the extensive use of returned product can have a positive impact on the environment and influence all the supply chain decisions. Therefore, the management policy should place major emphasis on the best collection strategy that can benefit the ecological and economic environments.