A branch and efficiency algorithm to design a sustainable two-echelon supply chain network considering traffic congestion and uncertainty

This work aims to design a sustainable two-echelon supply chain not only based on the widely used cost perspective, but also based on the efficient use and preservation of limited resources. For this purpose, a branch and efficiency (B&E) algorithm is developed, which includes an optimization model and an evaluation model. The proposed tri-objective optimization model simultaneously minimizes the total cost of the supply chain, maximizes the sustainability score, and minimizes inequity among customers. The solutions obtained from the optimization model are then evaluated by extended data envelopment analysis (EDEA) models based on common criteria (i.e., cost and service) and traffic congestion criterion. To take into account real-world conditions, parameters related to labor and demand are assumed under uncertainty. Since the presented models consist of more than one objective function, fuzzy goal programming (FGP) method is utilized to tread the multi-objectiveness. The obtained results from tackling a case study problem demonstrate that considering sustainability issues can positively affect both the economic and social aspects of the problem. Furthermore, the developed B&E algorithm is able to reduce costs in each iteration; this is what supply chain managers are interested in. On the other hand, this algorithm can provide more services to applicants compared to one of the competing algorithms.