A chance-constraint optimization model for a multi-echelon multi-product closed-loop supply chain considering brand diversity: An accelerated Benders decomposition algorithm

The closed-loop supply chain (CLSC) network design has become one of the most critical issues due to the importance of resource optimization. Moreover, increasing competition in commercial markets leads to the diversity of a brand's product portfolio to meet the customer's demand. Hence, this paper develops a multi-period, multi-brand stochastic mixed-integer linear programming (MILP) model with direct and indirect distribution for the proposed CLSC network. Because of the uncertain nature of demand, the uncertainties for new and secondhand product demand are considered. Besides, a chance-constraint optimization (CCO) approach is applied to deal with uncertainty. Moreover, the accelerated Benders decomposition (BD) algorithm is designed to solve the proposed model. Several test problems are created and used to solve the accelerated BD compared with the conventional BD algorithm to investigate this model. Finally, the results are compared and described analytically, and some future research is suggested.