An accelerated benders decomposition algorithm for a bi-objective green closed loop supply chain network design problem

Abstract Recently, social awareness, governmental legislations and competitive business environment have spurred researchers to pay much attention to closed-loop supply chain network design. In order to support the arising trend, this paper presents a comprehensive mathematical model for a multi-period, multi-product, multi-modal and bi-objective green closed-loop supply chain. The objective of the model is to minimize the total cost and environmental emissions through making the best decisions on facility location, transportation amounts and inventory balances. According to the inherent complexity of the problem and considering multi-product, multi-period and multi- modality assumptions makes it hard to handle, and as for the solution approach, an effective accelerated benders decomposition algorithm is implemented. Then, computational results for a set of numerical example are discussed. Besides, the model and solution approach are applied on a wire-and-cable industry. Then, a sensitivity analysis is implemented in an effort to validate the model. Results reveal applicability of the proposed mathematical model and presented solution approach. Following the obtained results, it can be validly concluded that the suggested solution approach leads to more than 13 percent reduction in total cost for the studied case, and can be even employed for larger and more complex real-world industrial applications.