An Inventory Model for Obsolescence Items with Consideration of Permissible Delay in Payments (Case Study of Obsolete Medicines in Pharmacies)

Background and Objectives: In the real world, the obsolescence items are some items that lose their value over time due to the emergence of new technology. Because of rapid changes in technology, inventory management of such items is considered in recent years. Moreover, suppliers try to encourage the retailers for purchasing an item before it is outmoded with some policies such as discounts, rebates, bonus backs, and delayed payment and so on. Given the speed of medical advances in pharmaceutical industries and the successive release of new products to the market, and also the fact that delay in payment is the main marketing issue in selling the medicine products to the pharmacies in Iran, in this paper, the delay in payment policy for obsolescence items is studied and an inventory control model is developed to respond to these conditions.   Methods: The model minimizes total inventory cost to achieve the optimal cycle time with respect to the constant demand rate and sudden obsolescence with exponential distribution over time. Numerical examples referring to a real case study in the pharmaceutical industry like drugstores are given to demonstrate the performance of the model in different states of delay in payment.   Findings: Based on the results, according to the considered permissible payment period based on the actual market situation, the length of the optimal ordering cycle is usually smaller than that of the payment cycle. Besides, with the reduction of the expected lifetime, the inventory costs are concurrently reduced and on the other hand, the increase in the expected lifetime raises the inventory costs. Moreover, there is no exact relationship between credit time due date (i.e. payment time) and inventory cost; which shows the high sensitivity of this parameter in finding the optimal solutions.   Conclusions: An inventory control model for obsolescence items in the pharmaceutical retailing industry is introduced under delay in payment policy. In the presented model, after determining the inventory cost functions regarding obsolescence, holding and delay in payment costs, which are related to the pharmaceutical supply chain, the total cost function is introduced during the lifetime of items and the optimality is checked by convexity test through the second derivative in two cases of delay in payment in the model.