Multi-objective optimization for multi-echelon, multi-product, stochastic sustainable closed-loop supply chain

The closed-loop supply chain (CLSC) is the supply chain that includes various recovery plans for used products to be reused in the industry. Most of the previous stochastic CLSC studies considered the effect of uncertain parameter changes on the economic aspect only, while the other sustainability aspects were neglected. The purpose of this study is to develop a realistic mathematical model that represents and analyzes the impact of uncertainty in demand and recovery rate of products on the economic, environmental, and social sustainability aspects in the CLSC. The objective functions were optimized using the constrained optimization by linear approximation (COBYLA) algorithm along with preference-based Pareto optimal solution set algorithm at multiple computations to optimize various objectives simultaneously and efficiently. The results show a significant correlation between demand uncertainty, rate of return uncertainty, and the sustainability objectives in the CLSC using optimal inventory management settings.