The design for integrating the forward-reverse logistics network has attracted growing attention with the relentless pressures from environmental and social requirements to increase operational efficiency and support sustainable operations. Therefore, a dynamic facility in the closed chain is presented for the first time. In this problem, a set of facilities with determined locations are used based on whether they serve as forward-reverse, or joint facilities dealing with products from both directions. The objective is to minimize the total costs, including fixed location, fixed ordering, inventory holding, transportation, and reprocessing costs. In this paper, a mixed integer nonlinear program (MINLP) of a single type of forwarding product and a single type of returned product is proposed and a Benders decomposition method (BDM) is developed to solve the problem efficiently. The computational results on several randomly generated issues demonstrate that the proposed algorithm can efficiently solve the MINLP model compared to other algorithms.
