Development of pricing model for deteriorating items with constant deterioration rate considering replacement

Document Type : Research Paper


School of Inddustrial Engineering, Iran University of Science & Technology, Tehran, I.R. Iran


Proper inventory control policy and the optimal price for the items has always been one of the main topics of scientific research and industry. On the other hand, there are many products in the market witch are classified as deteriorating items. Therefore the problem of determining optimal price and optimal inventory policy for this type of items is very important. In this paper a 3 echelon supply chain consisting of a manufacturer, a distributor and a retailer is considered. There is only a single type of item with constant deterioration. Demand is deterministic and replenishment is instantaneous. The purpose of this study is to increase the total profit by determining the optimum values of the product price (p) and ordering cycle (T) of distributor. Since the products are deteriorating, some part of the initial stored inventory is lost. Therefore, distributor disposes the spoiled items and replaces them with the same amount of sound items. The replacement in the storehouse of the distributor is also instantaneous. Finally, numerical examples are presented to elaborate the model and sensitivity analysis is performed on the values of some parameters.


Main Subjects

  1.  Polatoglu, L. H. (1991). “Optimal order quantity and pricing decisions in single-period inventory systems.” International Journal of ProductionEconomics, 23, 175-185.
  2.  Chen, F. Y., Wang, T., and Xu, T. Z. (2005). “Integrated inventory replenishment and temporal shipment consolidation: A comparison of quantity-based and time-based models.” Annals of Operations Research, 135, 197-210.
  3.  Sajadieh, M. S. and Jokar, M. R. A. (2009). “Optimizing shipment, ordering and pricing policies in a two-stage supply chain with price- sensitive demand.” Transportation Research-Part E, 45, 564-571.
  4.  Huang, Y., Huang, G. Q., and Newman, S. T. (2011). “Coordinating pricing and inventory decisions in a multi-level supply chain: A game theoric approach.” Transportation Research Part E, 47, 115-129.
  5.  Bahari-Kashani, H. (1989). “Replenishment schedule for deteriorating items with time-proportional demand.” Journal of the Operational Research Society, 40, 75-81.
  6.  Chung, K. J. and Lin, C. N. (2001). “Optimal inventory replenishment madels for deteriorating items taking account of time discounting.” Computer & Operations Research, 28, 67-83.
  7.  Rau, H., Wu, M. Y., and Wee, H. M. (2004). “Deteriorating item inventory model with shortage due to supplier in an integrated supply chain.” International Journal of Systems Science, 35:5, 293-303.
  8.  Hou, K. L. (2006). “An inventory model for deteriorating items with stock-dependent consumption rate and shortage under inflation and time discounting.” European Journal of Operation Research, 168, 463-474.
  9.  Lee, C. F. and Chung, C. P. (2012). “An inventory model for deteriorating items in a supply chain with system dynamics analysis.” Procedia- Social and Behavioral Sciences, 40, 41-51.
  10.  Chung, C. J. (2013). “Investigating imperfect process and demand effects on inspection scheduling and supply chain replenishment policy.” Computer & Industrial Engineering, 64, 31-44.
  11.  Wee, H. M. (1999). Deteriorating inventory model with quantity discount, pricing and partial backordering.” International Journal of Production Economics, 59, 511-518.
  12.  Yang, P. C. (2004). “Pricing strategy for deteriorating items using quantity discount when demand is price sensitive.” European Journal of Operational Research, 157, 389-397.
  13.  Dye, C. Y., Ouyang, L.Y., andHsieh, T. P. (2007). “Inventory and pricing strategies for deteriorating items with shortages: A discounted cash flow approach.” Computer & Industrial Engineering, 52, 29-40.
  14.  Tsao, Y. C. and Sheen, G. J. (2008). “Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments.” Computer & Operations Research, 35, 3562-3580.
  15.  Huang, C. K. (2010). “An integrated inventory model under conditions of order processing cost reduction and permissible delay in payments.” Applied Mathematical Modeling, 34, 1352-1359.
  16.  Dye, C. Y. (2012). “A finite horizon deteriorating inventory model with two-phase pricing and time-varying demand and cost under trade credit financing using particle swarm optimization.” Swarm and Evolutionary Computation, 5, 37-53.
  17.  Maihami, R. and Nakhai, I. (2012). “Joint control of inventory and its pricing for non-instantaneously deteriorating items under permissible delay in payments and partial backlogging.” Mathematical and Computer Modeling, 55, 1722-1733.
  18.  DehayemNodem, F. I., Kenne, J. P., and Gharbi, A. (2011). “Simultaneous control of production, repair/replacement and preventive maintenance of deteriorating manufacturing systems.” International Journal of Production Economics, 134, 271-282.
  19.  Sivazlian, B. D. and Danusaputro, S. L. (1989). “Economic inventory and replacement management of a system in which components are subject to failure.” Microelectronics Reliability, 29, 861-881.
  20.  Chang, C. C. (2014). “Optimum preventive maintenance policies for systems subject to random working times, replacement, and minimal repair.” Computer & Industrial Engineering, 67, 185-194.
  21.  Rivera-Gomes, H., Gharbi, A., and Kenne, J. P. (2013). “Joint production and major maintenance planning policy of a manufacturing system with deteriorating quality.” International Journal of Production Economics, 146, 575-587.
  22.  Khanh Nguyen, T. P., Yeung, Th. G., and Castanier, B. (2013). “Optimal maintenance and replacement decisions under technological change with consideration of spare parts inventories.” International Journal of Production Economics, 143, 472-477.
  23.  Jain, M. and Gupta, R. (2013). “Optimal replacement policy for a repairable system with multiple vacations and imperfect fault coverage.” Computers & Industrial Engineering, 66, 710-719
  24.  Cheng, G. Q. and Li, L. (2014). “An optimal replacement policy for a degenerative system with two-types of failure states.” Journal of Computational and Applied Mathematics, 261, 139-145.