The design for the integration of the forward reverse logistics network has attracted growing attention with the stringent pressures from environmental and social requirements in order to increase operational efficiency and support sustainable operations. Generally, decisions about reverse logistics network configurations are made on a long-term basis. In light of this, we consider the Dynamic Facility in the closed chain. A mixed integer non-linear program (MINLP) of a single type of forward product and single type of returned product, through a set of facilities whose location is determined based on whether they serve as forward, reverse or joint facilities dealing with products from both directions is proposed. Minimizing the total costs, which include fixed location, fixed ordering, inventory holding, transportation as well as reprocessing costs, the latter referring to returned products is the objective function. In order to get rid of the non-linearity phrases, the linearization constraints are proposed. Afterwards, a Benders decomposition method is developed to efficiently solve the problem. The computational results introduce several random generated problems to be solved with Benders algorithm and demonstrate that this algorithm can efficiently solve the proposed model.
