A joint replenishment problem with the (T,ki) policy under obsolescence

Abstract: Companies are frequently confronted with the need to order different types of items from a single supplier or to manufacture the items in a production line. Indeed, coordinated ordering of multiple items may lead to important savings whenever a family of items can be ordered from a common supplier, produced in a common facility, or use a common mode of transportation. The Joint Replenishment Problem (JRP) tackles the coordinated replenishment of multiple items by minimizing the total cost, composed of ordering (or setup) costs and holding costs, while satisfying the demand. On the other hand, when items are subject to obsolescence, they may face an abrupt decline in demand as they are no longer needed. This decline can be caused by reasons such as rapid advancements in technology, going out of fashion, or ceasing to be economically viable. The present article develops an extension of the JRP where the items may suddenly become obsolete during an infinite planning horizon. The point at which an item becomes obsolete is uncertain. The lifetimes of the items are assumed to follow independent negative exponential distributions. A model is proposed by using the total expected discounted cost as the minimization criterion. The time value of money is considered through an appropriate discount rate. Extensive tests were performed to assess the impact of obsolescence rates and discount rates on the ordering policies. The progressive increase of the obsolescence rates determines smaller periods between successive replenishments, while the progressive increase of the discount rate determines smaller lot sizes.

How to cite this paper

 Afonso, R., Godinho, P & Costa, J. (2023). A joint replenishment problem with the (T,ki) policy under obsolescence.International Journal of Industrial Engineering Computations , 14(3), 523-538.

Refrences

Afonso, R., Godinho, P., & Costa, J. P. (2022). Discounted costs and obsolescence with the joint replenishment problem. International Journal of Industrial Engineering Computations, 13(1), 51–66.
Arcelus, F. J., Pakkala, T. P. M., & Srinivasan, G. (2002). A myopic policy for the gradual obsolescence problem with price-dependent demand. Computers & Operations Research, 29(9), 1115–1127.
Axsäter, S. (2015). Coordinated ordering. In C. C. Price, J. Zhu, & F. S. Hillier (Eds.), Inventory Control (3rd ed., Vol. 225, pp. 121–145). Springer International Publishing Switzerland.
Bakker, M., Riezebos, J., & Teunter, R. H. (2012). Review of inventory systems with deterioration since 2001. European Journal of Operational Research, 221(2), 275–284.
Bartels, B., Ermel, U., Sandborn, P., & Pecht, M. G. (2012). Strategies to the prediction, mitigation and management of product obsolescence (A. P. Sage (ed.)). John Wiley & Sons, Inc.
Bastos, L., Mendes, M., Nunes, D., Melo, A., & Carneiro, M. (2017). A systematic literature review on the joint replenishment problem solutions: 2006-2015. Production, 27(e20162229), 1–11.
Berk, E., & Gurler, U. (2017). Inventory theory. In J. Sengupta, Raghu; Gupta, Aparna; Dutta (Ed.), Decision Sciences Theory and Practice (pp. 349–411). CRC Press - Taylor & Francis Group.
Brown, G. W., Lu, J. Y., & Wolfson, R. J. (1964). Dynamic modeling of inventories subject to obsolescence. Management Science, 11(1), 51–63.
Covert, R. P., & Philip, G. C. (1973). An EOQ model for items with Weibull distribution deterioration. A I I E Transactions, 5(4), 323–326.
Dagpunar, J. S. (1982). Formulation of a multi item single supplier inventory problem. Journal of the Operational Research Society, 33(3), 285–286.
Dohi, T., & Osaki, S. (1995). Optimal inventory policies under product obsolescent circumstance. Computers & Mathematics with Applications, 29(3), 23–30.
Goyal, S. K., & Giri, B. C. (2001). Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 134(1), 1–16.
Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management, 10(2), 135–136, 152.
Holmbom, M., & Segerstedt, A. (2014). Economic order quantities in production: from Harris to economic lot scheduling problems. International Journal of Production Economics, 155, 82–90.
Joglekar, P., & Lee, P. (1993). An exact formulation of inventory costs and optimal lot size in face of sudden obsolescence. Operations Research Letters, 14(5), 283–290.
Khanlarzade, N., Yegane, B. Y., Kamalabadi, I. N., & Farughi, H. (2014). Inventory control with deteriorating items: a state-of-the-art literature review. International Journal of Industrial Engineering Computations, 5(2), 179–198.
Khouja, M., & Goyal, S. K. (2008). A review of the joint replenishment problem literature: 1989-2005. European Journal of Operational Research, 186(1), 1–16.
Masters, J. M. (1991). A Note on the effect of sudden obsolescence on the optimal lot size. Decision Sciences, 22(5), 1180–1186.
Nahmias, S. (2011). Perishable inventory systems. In International Series in Operations Research & Management Science, Vol. 160 (1st ed.). Springer US.
Pahl, J., & Voβ, S. (2014). Integrating deterioration and lifetime constraints in production and supply chain planning: a survey. European Journal of Operational Research, 238(3), 654–674.
Sandborn, P. (2013). Design for obsolescence risk management. Procedia CIRP, 11, 15–22.
Silver, E. A., Pyk, D. F., & Thomas, D. J. (2017). Coordinated replenishments at a single stocking point. In Inventory and Production Management in Supply Chains (4th ed., Vol. 1, pp. 437–485). CRC Press - Taylor & Francis Group.
Song, J.-S., & Zipkin, P. H. (1996). Managing inventory with the prospect of obsolescence. Operations Research, 44(1), 215–222.
Taft, E. W. (1918). The most economical production lot. The Iron Age, 101(18), 1410–1412.
van Delft, C., & Vial, J. P. (1996). Discounted costs, obsolescence and planned stockouts with the EOQ formula. International Journal of Production Economics, 44(3), 255–265.
Wee, H.-M. (1997). A replenishment policy for items with a price-dependent demand and a varying rate of deterioration. Production Planning & Control, 8(5), 494–499.