A novel multi-objective robust possibilistic flexible programming to design a sustainable apparel closed-loop supply chain network.

Designing a sustainable Closed-Loop Supply Chain (CLSC) network is imperative for the apparel industry, given its escalating adverse effects on economic, environmental, and social dimensions. In this study, a novel tri-objective location-allocation optimization model is specifically developed for designing a sustainable apparel CLSC, incorporating the industry's unique facilities. The aim of the model is to simultaneously minimize the costs and negative environmental impacts while maximizing social benefits under demands and returns uncertainty. A notable research contribution lies in addressing the unique challenges of treating different types of returns, including commercial, End Of Use (EOU) and End Of Life (EOL) returns due to their uncertain quality and quantity. Additionally, the model optimizes the environmental performance levels of production facilities, a novel aspect in the apparel CLSC research. Moreover, the flexibility of constraints related to the demand fulfilment is considered. To cope with such flexibility and uncertainties, a new hybrid robust possibilistic flexible programming model is developed, by extending the previous methodologies. A core innovation of this solution approach lies in the pioneering utilization of hexagonal fuzzy numbers for uncertain epistemic parameters, making a significant advancement in the field of CLSC. Comparative analysis with the similar studies demonstrates the superiority of the proposed model, incorporating hexagonal fuzzy numbers over the method using triangular fuzzy numbers. Furthermore, AUGMECON method using lexicographic optimization is applied to handle the multi-objective model. The application of the proposed model is shown focusing on Southwestern Ontario in Canada. The results reveal that commercial and EOU returns have a more detrimental impact on economic, environmental, and social sustainability aspects compared to EOL returns.