a benders decomposition method to solve an integrated logistics network designing problem with multiple capacities

in this paper, a new model is proposed for the integrated logistics network designing problem. in many research papers in this area, it is assumed that there is only one option for the capacity of each facility in the network. however, this is not a realistic assumption because generally there may be many possible options for the capacity of the facility that is being established. usually the cost of establishing a facility depends on its capacity. moreover, of the majority of the research done in the field of logistics network designing problem only a limited number of options for product recovery is addressed. specifically, in most of the research papers only one option, i.e. remanufacturing, has been considered. therefore, a mathematical formulation with multiple options for capacities and product recovery is addressed in this research to obviate this gap. 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.