Design of a closed-loop supply chain (CLSC) model using an interactive fuzzy goal programming

A closed-loop supply chain (CLSC) network is composed of both forward and reverse flows. An essential issue to be considered in designing any supply chain network is determination of number and locations of facilities in each layer of the network. Such a problem is a challenging job, since it contains sub-problems which are proven to be nondeterministic polynomial time complete. This paper proposes a CLSC distribution network design problem in which reverse flows are imported into forward model proposed by Selim and Ozkarahan (Int J Adv Manuf Technol 36:401–418, 1 ). Such a model is considered assuming forward covering (model I) and backward covering (model II) objectives, and then results are compared against the model incorporating covering of both forward and backward networks (model III). Our aim is to accentuate on the role of considering backward parameters in design of a CLSC network and to show how results differ from considering sub-problems separately. To model and solve the problem, a fuzzy goal programming approach is developed for network design in an interactive manner between decision maker and the model. To validate the presented model and the proposed solution approach, a test problem is presented and comparison of results is made using this problem. The results show that the proposed model can solve the CLSC problems in a manageable time. Moreover, outputs of the three models differ significantly. Therefore, the role of incorporating backward flows into the network design problem has been shown using our experiments.