Three-echelon supply chain model in an imperfect production system with inspection error, learning effect, and return policy under fuzzy environment

This article presents a three-echelon supply chain (SC) model, incorporating a single supplier, a single manufacturer, and a single wholesaler under fuzzy system. Three scenarios have been considered: (a) the learning effect (LE) of the employees on the production cost as well as the return contract (RC) between the supplier and an outside supplier and also between the manufacturer and the wholesaler, (b) without considering the LE on the manufacturing expenses and (c) without the RC between the SC players. The goal of this paper is to study the effect of the LE and the RC on total profit of the SC for centralised and decentralised cases. To adopt flexibility of the demand parameters of the entire process, we develop a fuzzy mathematical model of the proposed SC problem. To discuss the novelty of the proposed model, we insert a table of authors' contribution and also perform numerical illustrations with the help of LINGO software and make a comparative study between the optimal results of the existing method and the proposed fuzzy approach. Sensitivity analysis and graphical illustrations have also been done for better realisation of the model followed by conclusion.