Fuzzy Inventory Model for Noninstantaneous Deteriorating Items With Delay Differentiation Process

In this article, we have devised an inventory model tailored for noninstantaneous deteriorating items, with an emphasis on partially backlogged shortages. In addition, the deterioration rate is considered to be inversely proportional to the length of the waiting time. Inventory costs cannot always be considered static or dynamic. In certain situations, the fuzzy nature of costs needs to be considered to account for uncertainty. Hence, cost components such as production cost, holding cost per unit time, ordering cost, unit backorder cost, and unit cost of lost sales are fuzzified using pentagonal fuzzy numbers. Cost components are fuzzified, and defuzzification is performed through the graded mean integration method in both systems. Our inventory model is designed to encompass both postponement and independent systems. Optimal solutions are obtained and numerical analysis is carried out. The effect of various parameters, such as deterioration rate, fresh product time, and backlogging parameter, on the total cost is investigated, and the findings are discussed. Our goal is to compare the overall inventory costs in both crisp and fuzzy sense for noninstantaneous deteriorating items, with shortages taken into consideration. Furthermore, an analysis has been carried out comparing the independent and postponement systems, incorporating fuzzy costs. To validate the proposed model, numerical examples, sensitivity analysis, managerial insights, conclusions, and future research directions are provided.