A closed-loop supply chain model with carbon emission and pricing decisions under an intuitionistic fuzzy environment

This paper explores the issues involved in delivering an item from a manufacturer to a retailer in a closed-loop two-echelon supply chain model. Two types of safety factors are maintained in the hands of the retailer to avoid stock-outs during the lead time. This model considers carbon emission from material production and supply chain-related transportation. If products are found to be defective during the inspection or screening process, they are returned to the manufacturer, and the defective items are reworked for resale. Moreover, the transportation costs incurred during the return of such defective items found through the screening process are added to the manufacturer as a penalty. All essential inventory costs of the supply chain are considered uncertain. Furthermore, this uncertainty is handled with an intuitionistic triangular fuzzy number and the corresponding defuzzification process is dealt with the signed distance method. The main objective of this research is to maximize the total expected profit of the supply chain with realistic factors. Distinct from the existing literature, two different solution techniques are employed to provide the optimal solution for the decision variables. In addition, two special cases are specialized in this study. Three numerical experiments are considered to validate the proposed model. Finally, sensitivity analysis, managerial insights, and conclusions are provided.