A New Facility Location Model to Design a Closed-loop Apparel Supply Chain Network Under Uncertainty

Utilizing a Closed-Loop Supply Chain (CLSC) network to manage the apparel wastes is of utmost importance for the health of our planet, our environment, and our species. In this study, a Mixed-Integer Linear Programming (MILP) model is developed to design a new apparel CLSC to minimize the total cost. The uncertainty of demand and different types of returns are considered in the model for the first time. In addition, a new hybrid robust possibilistic flexible programming method is applied to tackle the uncertainty of parameters and flexibility of soft constraints. Hexagonal fuzzy membership functions are utilized to represent the uncertain parameters for the first time. The application of the model for a Canadian company is also discussed. The results show that considering the hexagonal fuzzy numbers, to present the uncertain parameters, leads to obtaining more reliable solutions in comparison to the triangular fuzzy numbers.