An integrated supply chain network design problem for bidirectional flows

•We propose an integrated facility location and product distribution–collection model for bidirectional flows.•We develop an efficient Lagrangian relaxation-based heuristic to address the proposed model.•We apply the heuristic in an industrial case study.•Several interesting managerial insights are reported from numerous computational experiments. Coordination among supply chains has elicited considerable attention in both academia and industry. This paper investigates an integrated supply chain network design problem that involves the determination of the locations for distribution centers and the assignment of customers and suppliers to the corresponding distribution centers. The problem simultaneously involves the distribution of products from the manufacturer to the customers and the collection of components from the suppliers to the manufacturer via cross-docking at distribution centers. The co-location of different types of distribution centers and coordinated transportation are introduced to achieve cost savings. A Lagrangian relaxation-based algorithm is then developed. Extensive computational experiments show that the proposed algorithm has stable performance and outperforms CPLEX for large-scale problems. An industrial case study is considered and sensitivity analysis is conducted to explore managerial insights. Finally, conclusions are drawn, and future research directions are outlined.