Multi-objective programming for multi-period multi-product closed-loop supply chain network design: a fuzzy robust optimization approach

Closed-loop supply chain network design (CLSCND) is one of the important strategic decisions for the sustainability of many business organizations. A multi-objective mixed integer linear programming (MMILP) model is formulated for the multi-period multi-product CLSCND problem. The objectives of the model are to minimize the total costs, minimize the total CO2 emissions and maximize the job opportunities. The decisions made in the multi-period multi-product CLSCND problem include supplier selection, facility location, transportation mode selection, optimal flows between facilities and inventory levels. A fuzzy robust optimization approach with flexible constraints is applied to the MMILP model to convert it to a fuzzy robust multi-objective optimization (FRMO) model in order to cope with uncertainties in the periodic customer demands, transportation costs, facility opening/closing costs and operating costs of all the facilities on the reverse flow. Flexible constraints allow for the best balance between penalty costs and constraint violations, i.e., unsatisfied demands and overloaded facilities. The FRMO model is solved to find non-dominated solutions for the multi-period multi-product CLSCND problem. The proposed FRMO model and solution approach can be used by decision makers to make trade-offs among the objectives so as to identify a final and optimal solution. Numerical experiments demonstrate the superior performance of the proposed model over the deterministic, i.e., the MMILP, model. Sensitivity analyses are performed to examine the impacts of the major uncertain parameters on the performances. Some meaningful insights into the strategic decisions are provided for business firms and their managers facing multi-period multi-product CLSCND problems.