Retailer’s Optimal Ordering Policy for Deteriorating Inventory having Positive Lead Time under Pre-Payment Interim and Post-Payment Strategy

Management of inventory and its control for the retailers involves the procurement and storage of items for the smooth functioning of day-to-day business affairs. The procurement of goods depends on lead time and the payment mechanism. Thus, these components have a vital role in the optimal strategy for inventory control and management. As a result, these two components have a very high priority in recent developments on inventory models. However, a few researchers investigated such inventory problems with the integration of these components. Also, most of the researchers overlooked the impreciseness of different parameters while developing the inventory models. Thus, it is highly required to consider lead-time, payment strategy, and the impreciseness of parameters for inventory problems to provide an insight into real practice. Therefore, keeping these aspects in view, we develop two inventory models for Weibull deteriorating items having selling-price-dependent demand with positive lead-time in prepayment, interim payment, and post-payment scenarios. In the first model (crisp), the inventory constraints and costs are assumed to be deterministic. However, in the second model (fuzzy), only cost parameters are considered as imprecise, and the rest are all deterministic in nature. We first describe the solution strategies for obtaining the optimality of both crisp and fuzzy models. Subsequently, we perform numerical experiments with various sets of inventory constraints to investigate the efficiency of the proposed models. Finally, through sensitivity analysis of crucial parameters, we provide a ready reference to managerial insights making essential decisions in handling various circumstances which arise during the inventory cycle due to alteration of different constraints or parameters.