The Optimal Cycle Time for EPQ Inventory Model of Deteriorating Items under Trade Credit Financing in the Fuzzy Sense

 Normally, the real-world inventory control problems are imprecisely defined and human interventions are often required to solve these decision-making problems. In this paper, a realistic inventory model with imprecise inventory costs have been formulated for deteriorating items under trade credit policy within the economic production quantity (EPQ) framework. We assume that the supplier would offer the retailer a delay period and the retailer also adopts the trade credit policy to stimulate his/her customer demand to develop the retailer's replenishment model for deteriorating items under the replenishment rate is finite. Under these conditions, we model the retailer's inventory system for deteriorating items as a cost minimization problem to determine the retailer’s optimal inventory policy. We derive the expressions for the annual total inventory cost for the retailer both in the crisp and fuzzy sense. The total variable inventory cost in the fuzzy sense is defuzzified using Graded Mean Integration Representation method and it has been proved that there exists a unique optimal cycle time to minimize the annual total variable cost for the retailer. In addition, a theorem is developed to efficiently determine the optimal ordering policies for the retailer. For easy determination of optimal ordering policies, we have proposed three algorithms. Some previously published results of other authors will be special cases of this paper. Finally, numerical examples are used to illustrate all results obtained in this paper. Then, as well as, we obtain a lot of managerial insights from numerical examples.