Improving expected shortage estimations in the base-stock policy by accounting for undershoots
Submitted: 2024-07-04
|Accepted: 2024-11-23
|Published: 2025-01-31
Copyright (c) 2025 Eugenia Babiloni, Ester Guijarro
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Downloads
Keywords:
inventory, Continuous review, Expected shortage per replenishment cycle, Lost sales, Undershoots
Supporting agencies:
Abstract:
Shortage events are inevitable random phenomena in inventory systems when dealing with real demand. For inventory managers, knowing the size of these shortages becomes crucial to deciding the optimal policy for the inventory system. Therefore, the Expected Shortage per Replenishment Cycle, ESPCR, is an essential indicator in inventory management for several reasons. On the one hand, it gives information about the number of units not served in each cycle, and on the other hand, it is fundamental in determining service levels or shortage costs. Therefore, ESPCR estimation for the continuous review base-stock policy (s, S) is traditionally based on the assumption that inventory levels reach exactly the reorder point, i.e., inventory levels are never below the reorder point, and undershoots are not considered. This paper shows that the traditional estimation based on neglecting undershoots is biased and proposes a new and unbiased approximation, ESPCRW. This approach is based on estimating the probability vector of the stock levels at the reorder point considering the presence of undershoots. Results of this paper show that our approach outperforms the biased nature of the traditional approximation, which may have significant practical implications for the inventory systems.
References:
Adegbola, A. E., Adegbola, M. D., Amajuoyi, P., Benjamin, L. B., & Adeusi, K. B. (2024). Advanced financial modeling techniques for reducing inventory costs: A review of strategies and their effectiveness in manufacturing. Finance & Accounting Research Journal, 6(6), 801-824. https://doi.org/10.51594/farj.v6i6.1180
Babai, M. Z., Jemai, Z., & Dallery, Y. (2011). Analysis of order-up-to-level inventory systems with compound Poisson demand. European Journal of Operational Research, 210(3), 552-558. https://doi.org/10.1016/j.ejor.2010.10.004
Babiloni, E., & Guijarro, E. (2020). Fill rate: from its definition to its calculation for the continuous (s, Q) inventory system with discrete demands and lost sales. Central European Journal of Operarions Research, 28(1), 35-43. https://doi.org/10.1007/s10100-018-0546-7
Babiloni, E., Guijarro, E., & Trapero, J. R. (2023). Stock control analytics: a data-driven approach to compute the fill rate considering undershoots. Operational Research, 23(1), 18. https://doi.org/10.1007/s12351-023-00748-y
Babiloni, E., Guijarro, E., & Trapero, J. R. (2020). A Non-parametric Enhancement of the Fill Rate Estimation. In Advances in Engineering Networks: Proceedings of the 12th International Conference on Industrial Engineering and Industrial Management (pp. 129-135). Springer International Publishing, Cham. https://doi.org/10.1007/978-3-030-44530-0_16
Bijvank, M., & Johansen, S. G. (2012). Periodic review lost-sales inventory models with compound Poisson demand and constant lead times of any length. European Journal of Operational Research, 220(1), 106-114. https://doi.org/10.1016/j.ejor.2012.01.041
Bijvank, M., Bhulai, S., & Huh, W. T. (2015). Parametric replenishment policies for inventory systems with lost sales and fixed order cost. European Journal of Operational Research, 241(2), 381-390. https://doi.org/10.1016/j.ejor.2014.09.018
Chikán, A., Kovács, E., Matyusz, Z., Sass, M., Vakhal, P., Chikán, A., ... & Vakhal, P. (2018). Introduction: The Nature and Structure of the Inventory Problem. Inventories in National Economies: A Cross-Country Analysis of Macroeconomic Data, 1-12. https://doi.org/10.1007/978-1-4471-7371-7_1
Dhaiban, A. K., & Aziz, N. (2019). Stochastic demand of production-inventory system with shortage. In AIP Conference Proceedings (Vol. 2138, No. 1). AIP Publishing. https://doi.org/10.1063/1.5121034
De, P. K., Paul, A. C., & Debnath, M. (2018). Mathematical Modeling of Economic Order Quantity in a Fuzzy Inventory Problem Under Shortages. In Smart and Innovative Trends in Next Generation Computing Technologies: Third International Conference, NGCT 2017, Dehradun, India, October 30-31, 2017, Revised Selected Papers, Part I 3 (pp. 617-622). Springer Singapore. https://doi.org/10.1007/978-981-10-8657-1_47
Disney, S. M., Gaalman, G. J., Hedenstierna, C. P. T., & Hosoda, T. (2015). Fill rate in a periodic review order-up-to policy under auto-correlated normally distributed, possibly negative, demand. International Journal of Production Economics 170, 501-512. https://doi.org/10.1016/j.ijpe.2015.07.019
Escalona, P., Angulo, A., Weston, J., Stegmaier, R., & Kauak, I. (2019). On the effect of two popular service-level measures on the design of a critical level policy for fast-moving items. Computers & Operations Research, 107, 107-126. https://doi.org/10.1016/j.cor.2019.03.011
Escalona, P., Araya, D., Simpson, E., Ramirez, M., & Stegmaier, R. (2021). On the shortage control in a continuous review (Q, r) inventory policy using αL service-level. RAIRO-Operations Research, 55(5), 2785-2806. https://doi.org/10.1051/ro/2021125
Guijarro, E., Babiloni, E., Canós-Darós, M. J., Canós-Darós, L., & Estellés, S. (2020a). Fuzzy modeling approach to on-hand stock levels estimation in (R, S) inventory system with lost sales. Journal of Industrial Engineering and Management, 13(3), 464-474. https://doi.org/10.3926/jiem.3071
Guijarro, E., Cardós, M., & Babiloni, E. (2012). On the exact calculation of the fill rate in a periodic review inventory policy under discrete demand patterns. European Journal of Operational Research, 218(2), 442-447. https://doi.org/10.1016/j.ejor.2011.11.025
Guijarro, E., Canós Darós, M. J., Babiloni, E., & Canós-Darós, L. (2020b). Cálculo de los niveles del stock disponible al inicio del ciclo mediante un formalismo fuzzy. Rect@. Revista Electrónica de Comunicaciones y Trabajos de ASEPUMA, 21(1), 151-159. https://doi.org/10.24309/recta.2020.21.2.04
Guijarro, E., Babiloni, E., & Cardós, M. (2022). On the estimation of the fill rate for the continuous (s, S) inventory system for the lost sales context. Plos one, 17(2), e0263655. https://doi.org/10.1371/journal.pone.0263655
Gutgutia, A., & Jha, J. K. (2018). A closed-form solution for the distribution free continuous review integrated inventory model. Operational Research, 18, 159-186. https://doi.org/10.1007/s12351-016-0258-5
Jiang, Y., Shi, C., & Shen, S. (2019). Service level constrained inventory systems. Production and Operations Management, 28(9), 2365-2389. https://doi.org/10.1111/poms.13060
Korponai, J., Tóth, Á. B., & Illés, B. (2017). Context of the inventory management expenses in the case of planned shortages. Engineering Management in Production and Services, 9(1), 26-35. https://doi.org/10.1515/emj-2017-0003
Kuzucu, N., Kuzucu, S., (2023). Linking inventory management and financial performance of manufacturing industry companies. PressAcademia Procedia (PAP), 16, 207-208. https://doi.org/10.17261/Pressacademia.2023.1692
Lathasri, U., & Varadharajan, R. (2020). A study on fuzzy inventory model with lot size dependent ordering cost with shortages using graded mean integration representation method. In AIP Conference Proceedings (Vol. 2277, No. 1). AIP Publishing. https://doi.org/10.1063/5.0025996
Mirkhorsandi, S. S., & Pasandideh, S. H. R. (2020). A bi-objective multi-product multi-constraint EPQ model in a stochastic environment and partial shortage. Journal of Advanced Manufacturing Systems, 19(03), 567-587. https://doi.org/10.1142/S0219686720500274
Kuzucu, N., & Kuzucu, S. (2023). Linking inventory management and financial performance of manufacturing industry companies. PressAcademia Procedia (PAP), 16, 207-208. https://doi.org/10.17261/Pressacademia.2023.1692
Rama, B., & Rosario, G. M. (2019). Inventory model with penalty cost and shortage cost using fuzzy numbers. International Journal of Artificial Intelligence and Soft Computing, 7(1), 59-85. https://doi.org/10.1504/IJAISC.2019.105002
Rosling, K. (2002). Inventory cost rate functions with nonlinear shortage costs. Operations Research, 50(6), 1007-1017. https://doi.org/10.1287/opre.50.6.1007.346
Sah, G. G., & Furedi-Fulop, J. (2022). The effects of proper inventory management on the profitability of SMEs. Technium Social Sciences Journal, 32, 340. https://doi.org/10.47577/tssj.v32i1.6634
Selmi, M. H., Jemai, Z., Grégoire, L., & Dallery, Y. (2019). Literature Review on Shortage Cost Modeling in Inventory Management. ICORES, 322-329. https://doi.org/10.5220/0007370203220329
Sen, N., & Malakar, S. (2015). A fuzzy inventory model with shortages using different fuzzy numbers. American Journal of Mathematics and Statistics, 5(5), 238-248.
Silver, E. A., Pyke, D. F., & Thomas, D. J. (2017) Inventory and Production Management in Supply Chains, 4th edn. Taylor and Francis Group. https://doi.org/10.1201/9781315374406
Tan, Y., Paul, A. A., Deng, Q., & Wei, L. (2017). Mitigating inventory overstocking: Optimal order-up-to level to achieve a target fill rate over a finite horizon. Production and Operations Management, 26(11), 1971-1988. https://doi.org/10.1111/poms.12750
Tempelmeier, H., & Fischer, L. (2019). A procedure for the approximation of the waiting time distribution in a discrete-time (r, S) inventory system. International Journal of Production Research, 57(5), 1413-1426. https://doi.org/10.1080/00207543.2018.1489157
Xu, F. (2017). Statistical measurement of the inventory shortage cost. Journal of Applied Statistics, 44(4), 642-648. https://doi.org/10.1080/02664763.2016.1182129
