A facility location model for bidirectional flows

Recent research on reverse logistics and closed-loop supply chains has produced a number of specialized network design models. We develop three generic facility location models for the integrated distribution and collection of products that accommodate a variety of applications and industries. These models quantify the value of integrated decision making in the design of forward and reverse logistics networks throughout different stages of a product's life cycle. The formulations extend the uncapacitated fixed-charge location model to include the location of used product collection centers and the assignment of product return flows to these centers. In addition, we develop a Lagrangian relaxation-based solution algorithm that is both quick and effective. We measure the implications of integrated decision making by comparing the total facility and transportation costs of our joint optimization models with the cost of solutions in which forward and reverse facility location decisions are made sequentially or independently of one another. In addition, we discuss the implications of integrated decision making on network configuration and introduce a new network similarity measure to quantify this analysis. Computational results are also presented.