Discounted costs and obsolescence with the Joint replenishment problem

Abstract: Real life inventory lot sizing problems are frequently challenged with the need to order different types of items within the same batch. The Joint Replenishment Problem (JRP) addresses this setting of coordinated ordering by minimizing the total cost, composed of ordering (or setup) costs and holding costs, while satisfying the demand. The complexity of this problem increases when some or all item types are prone to obsolescence. In fact, the items may experience an abrupt decline in demand because they are no longer needed, due to rapid advancements in technology, going out of fashion, or ceasing to be economically viable. This article proposes an extension of the Joint Replenishment Problem (JRP) where the items may suddenly become obsolete at some time in the future. The model assumes constant demand and the items’ lifetimes follow independent negative exponential distributions. The optimization process considers the time value of money by using the expected discounted total cost as the minimization criterion. The proposed model was applied to some test cases, and sensitivity analyses were performed, in order to assess the impact of obsolescence on the ordering policy. The increase in the obsolescence risk, through the progressive increase of the obsolescence rates of the item types, determines smaller lot sizes on the ordering policy. The increase in the discount rate causes smaller quantities to be ordered as well.

How to cite this paper

 Afonso, R., Godinho, P & Costa, J. (2022). Discounted costs and obsolescence with the Joint replenishment problem.International Journal of Industrial Engineering Computations , 13(1), 51-66.

Refrences

Ai, X.-Y., Zhang, J.-L., & Wang, L. (2017). Optimal joint replenishment policy for multiple non-instantaneous deteriorating items. International Journal of Production Research, 55(16), 4625–4642.
Andriolo, A., Battini, D., Grubbström, R. W., Persona, A., & Sgarbossa, F. (2014). A century of evolution from Harris’s basic lot size model: survey and research agenda. International Journal of Production Economics, 155, 16–38.
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.
Arcelus, F. J., Pakkala, T. P. M., & Srinivasan, G. (2006). The instant obsolescence problem with price-dependent demand. Information Systems and Operational Research, 44(4), 248–266.
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.
Cobbaert, K., & Van Oudheusden, D. (1996). Inventory models for fast moving spare parts subject to “sudden death” obsolescence. International Journal of Production Economics, 44(3), 239–248.
Cohen, T., & Yedidsion, L. (2015). The periodic joint replenishment problem is strongly NP-hard. Mathematics of Operations Research, 43(4).
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.
Emsermann, M., & Simon, B. (2007). Optimal control of an inventory with simultaneous obsolescence. Interfaces, 37(5), 445–454.
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.
Huang, C.-J. (2004). The convexity and bounds on optimal cycle time for the EOQ model with obsolescent items. Journal of Statistics and Management Systems, 7(2), 237–251.
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.
Khouja, M., Saydam, C., Vergara, F. E., & Rajagopalan, H. (2006). Optimal inventory policy under continuous unit cost decrease and risk of sudden obsolescence. International Journal of Operations & Quantitative Management, 12(2), 1–18.
Kouki, C., Babai, M. Z., Jemai, Z., & Minner, S. (2016). A coordinated multi-item inventory system for perishables with random lifetime. International Journal of Production Economics, 181, 226–237.
Lee, F.-C., & Yao, M.-J. (2003). A global optimum search algorithm for the joint replenishment problem under power-of-two policy. Computers & Operations Research, 30(9), 1319–1333.
Li, C., Xu, Xi., & Zhan, D. (2009). Solving joint replenishment problem with deteriorating items using genetic algorithm. Journal of Advanced Manufacturing Systems, 08(01), 47–56.
Masters, J. M. (1991). A Note on the effect of sudden obsolescence on the optimal lot size. Decision Sciences, 22(5), 1180–1186.
Menipaz, E. (1986). An inventory model with product obsolescence and its implications for high technology industry. IEEE Transactions on Reliability, 35(2), 185–187.
Nahmias, S. (1982). Perishable inventory theory: a review. Operations Research, 30(4), 680–708.
Nahmias, S. (2011). Perishable inventory systems. In International Series in Operations Research & Management Science, Vol. 160 (1st ed.). Springer US.
Oguji, N. (2018). Strategies for managing excess and dead inventories: a case study of spare parts inventories in the elevator equipment industry. In Operations and Supply Chain Management: An International Journal (Vol. 11).
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.
Pierskalla, W. P. (1969). An inventory problem with obsolescence. Naval Research Logistics Quarterly, 16(2), 217–228.
Porras, E., & Dekker, R. (2008). A solution method for the joint replenishment problem with correction factor. International Journal of Production Economics, 113(2), 834–851.
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.
Taleizadeh, A. A., Wee, H.-M., & Jolai, F. (2013). Revisiting a fuzzy rough economic order quantity model for deteriorating items considering quantity discount and prepayment. Mathematical and Computer Modelling, 57(5–6), 1466–1479.
Thompson, H. E. (1975). Inventory management and capital budgeting: a pedagogical note. Decision Sciences, 6(2), 383–398.
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.
Webb, I. R., Buzby, B. R., & Campbell, G. M. (1997). Cyclical schedules for the joint replenishment problem with dynamic demands. Naval Research Logistics (NRL), 44(6), 577–589.