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

Document Type : Research Paper


School of Industrial Engineering, Iran University of Science and Technology (IUST)


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.


Food and Drug Administration,
Tsolakisa N, Srai JS. Inventory planning and control in ‘green’ pharmacies supply chains – A System Dynamics modeling perspective, Computer Aided Chemical Engineering. 2017; 40: 1285-1290.
Saedi S, Kundakcioglu OE, Henry AC. Mitigating the Impact of Drug Shortages for a Healthcare Facility: An Inventory Management Approach, European Journal of Operational Research. 2016; 251: 107-123.
Stecca G, Baffo I, Kaihara T. Design and operation of strategic inventory control system for drug delivery in healthcare industry, IFAC 2016; 49: 904-909.
Joglekar P, Lee P. An exact formulation of inventory costs and optimal lot size in face of sudden obsolescence. Operations Research Letters. 1993; 14: 283-290
Cobbaert K, Oudheusden, DV. Inventory models for fast moving spare parts subject to “sudden death” obsolescence. International Journal of Production Economics. 1996; 44: 239- 248.
Wang K, Tung CT. Construction of a model towards EOQ and pricing strategy for gradually obsolescent products, Applied Mathematics and Computation. 2011; 217:6926–6933
Song Y, Lau HC. A periodic-review inventory model with application to the continuous-review obsolescence problem. European Journal of Operational Research. 2004; 159: 110–120.
Persona A, Grassi A, Catena M. Consignment stock of inventories in the presence of obsolescence. International Journal of Production Research. 2005; 43:4969-4988
Mahata GC. An EPQ-based inventory model for exponentially deteriorating items under retailer partial trade credit policy in supply chain. Expert Systems with Applications. 2012; 39(3):3537-3550.
Majumder P, Bera UK, Maiti M. An EPQ Model of Deteriorating Items under Partial Trade Credit Financing and Demand Declining Market in Crisp and Fuzzy Environment. Procedia Computer Science. 2015; 45:780-789.
Shabani S, Mirzazadeh A, Sharifi E. A two-warehouse inventory model with fuzzy deterioration rate and fuzzy demand rate under conditionally permissible delay in payment. Industrial and Production Engineering. 2015; 33(2):134-142
Sharma BK. An EOQ model for retailer’s partial permissible delay in payment linked to order quantity with shortages. Mathematics and Computers in Simulation. 2016; 125: 99–112.
Pourmohammad Zia N, Taleizadeh AA. A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment. Transportation Research Part E. 2016; 82:19–37.
Kumar S, Kumar N, Liu S.  An inventory model for deteriorating items under inflation and permissible delay in payments by genetic algorithm. Cogent Business & Management 2016; 3(1): 1-15.
Liao JJ, Lee WCH, Huang KN, Huang YG.  Optimal ordering policy for a two-warehouse inventory model use of two-level trade credit. Journal of Industrial & Management Optimization. 2017; 13 (4):1661-1683.
Tsao YC. Ordering policy for non-instantaneously deteriorating products under price adjustment and trade credits. Journal of Industrial & Management Optimization. 2017; 13(1): 329-347.
Nematollahi M, Hosseini-Motlagh SM, Ignatius J, Goh M, Saghafi Nia M. Coordinating a socially responsible pharmaceutical supply chain under periodic review replenishment policies. Journal of Cleaner Production. 2018; 172: 2876-2891.
Ebrahimi S, Hosseini‑Motlagh SM, Nematollahi M. Proposing a delay in payment contract for coordinating a two-echelon periodic review supply chain with stochastic promotional effort dependent demand. International Journal of Machine Learning and Cybernetics. 2018; In press.
Shah NH, Patel DG, Shah DB. Optimal policies for deteriorating items with maximum lifetime and two-level trade credits. International Journal of Mathematics and Mathematical Sciences. 2014: 1- 5.
Johari M, Hosseini-Motlagh SM, Nematollahi M, Goh M, Ignatius J. Bi-level credit period coordination for periodic review inventory system with price-credit dependent demand under time value of money. Transportation Research Part E: Logistics and Transportation Review. 2018; 114: 270-291.
Chen SC, Teng J T. Retailer’s optimal ordering policy for deteriorating items with maximum lifetime under supplier’s trade credit financing. Applied Mathematical Modelling. 2014; 38(15-16): 4049-4061.