Interactive fuzzy programming approaches to the strategic and tactical planning of a closed-loop supply chain under uncertainty

In this paper, a closed-loop supply chain (CLSC) network model consisting of various conflicting decisions of forward and reverse facilities is considered. The proposed model integrates the strategic and tactical decisions to avoid the sub-optimalities led from separated design in both chain networks. The strategic-level decisions relate to the amounts of goods flowing on the forward and reverse chains whereas the tactical-level decisions concern balancing disassembly lines, collection and refurbishing activities in the reverse chain. First, a fuzzy multi-objective mixed-integer non-linear programming model that considers the imprecise nature of critical parameters such as cost coefficients, capacity levels, market demands and reverse rates is proposed. Then, proposed fuzzy model is converted into an auxiliary crisp multi-objective mixed-integer non-linear programming (MOMINP) model by applying two different approaches. Finally, different fuzzy interactive programming approaches are applied to solve this MOMINP model to find a satisfactory solution for the network that is considered. The proposed model with the solution approaches is validated through a realistic numerical example. Computational results indicate that our proposed model and solution approaches can effectively be used in CLSC network problems.