Decision making in two-layer supply chain with doubt fuzzy set

In this article, we discuss the application of doubt fuzzy set in a pollution sensitive economic production quantity (EPQ) model. Here, we study some doubtful situations like proper, harmful, depressive and confident based on human decision-making behaviour of a life-long inventory process. Secondly, we construct two-layer supply chain model of profit a maximization problem with backlogging. In fact, in supply chain there exists so many processes uncertainty due to doubts of managerial decision making. These doubts are basically coming from the actual quantity to be ordered and that of backorder quantity in a specific cycle time. Therefore, considering several doubt fuzzy sets in the order quantity, we construct a doubt fuzzy model by taking a case study then solve it with the help of a novel approach. Finally, numerical illustrations, sensitivity analysis, comparative study and graphical explanations are done to justify the proposed work.