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Dr. Anita Pal – Abstract

A study of fuzzy and neutrosophic economic order quantity model allowing delay in payment.

The inventory control problem is one of the most fundamental and well-known optimization problems in operation research. In this study, we develop two inventory control models under the assumption of trade credit policy. Firstly, we consider an interval type-2 fuzzy inventory control model that involves a delay in payment on the premise of a tacit agreement between retailer and supplier to obtain an entire trade credit order. In this model, we include time dependent deterioration rate. We have also introduced a fuzzy method to find maximum profit in the retailer’s inventory policy for deteriorating items in a supply chain. Finally, a sensitivity analysis is carried out to get the sensitiveness of the tolerance of different input parameters. Later, we establish a neutrosophic economic order quantity (EOQ) inventory model, assuming that the market demand is sensitive to the retail price and promotional effort. The supplier and retailer both adopt a partial trade credit policy. We include preservation technology to restrict the normal deterioration. We analyse the crisp model first, and then neutrosophic logic is implemented in the proposed model, considering demand, retail cost, ordering cost, carrying cost, promotional cost, and cost for preservation technology as a triangular neutrosophic number. De-neutrosophication of total neutrosophic profit has been done based on the removal area method. The present investigation shows that the de-neutrosophic and defuzzification values of the total profit function are convex, which assures the existence of unique solution. Mathematical theorems are developed to determine the optimal inventory policy for the retailer efficiently. Finally, numerical illustrations are also provided to justify the models, and the results in this study generalize some already published results in the crisp sense.