Abstract
In this paper, we develop a multi-item inventory model with stochastic demand, and the demand is considered as a random variable following a power demand pattern. A cumulative cycle demand is first identified for each product, and then the demand is gradually released to the inventory system by the power patterns within a cycle. The replenishment schedule is predetermined and well-known. Shortages are permitted but partially backlogged, and the rest are taken as lost sales. An effective inventory policy is utilized to reduce the total expected cost per unit of time by acquiring the optimal amount of stock to be stored at the start of the inventory cycle, which may protect against excessive lost sales and also avoid overstocking. This model is better suited for use in online purchases and the offline market where the buyer is assured that the goods will be shipped within a few days rather than at the time of purchase. We evaluated the system with items deteriorating instantaneously, which makes it appropriate to have a larger initial demand with a power pattern index greater than one. Numerical illustrations and sensitivity analysis provide an efficient tool for the insights of the theoretical solutions over the managerial foundation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adaraniwon, A. O., & Omar, M. B. (2019). An inventory model for delayed deteriorating items with power demand considering shortages and lost sales. Journal of Intelligent and Fuzzy Systems, 36(6), 5397–5408. https://doi.org/10.3233/JIFS-181284
Ali, H., Nasreen, R., Arneja, N., & Jaggi, C. K. (2024). Periodic inventory model with controllable lead time and back-order discount for decaying items. Opsearch. https://doi.org/10.1007/s12597-023-00738-w
Cárdenas-Barrón, L. E., & Sana, S. S. (2015). Multi-item EOQ inventory model in a two-layer supply chain while demand varies with promotional effort. Applied Mathematical Modelling, 39(21), 6725–6737. https://doi.org/10.1016/j.apm.2015.02.004
Chuang, C. H., & Chiang, C. Y. (2016). Dynamic and stochastic behaviour of coefficient of demand uncertainty incorporated with EOQ variables: An application in finished-goods inventory from General Motors× dealerships. International Journal of Production Economics, 172, 95–109. https://doi.org/10.1016/j.ijpe.2015.10.019
Dhaiban, A. K. (2022). Two models of inventory system with stochastic demand and deteriorating items: Case study of a local cheese factory. Opsearch, 59(1), 78–101. https://doi.org/10.1007/s12597-021-00532-6
Đorđević, L., Antić, S., Čangalović, M., & Lisec, A. (2017). A metaheuristic approach to solving a multiproduct EOQ-based inventory problem with storage space constraints. Optimization Letters, 11(6), 1137–1154. https://doi.org/10.1007/s11590-016-1009-5
Eynan, A., & Kropp, D. H. (2007). Effective and simple EOQ-like solutions for stochastic demand periodic review systems. European Journal of Operational Research, 180(3), 1135–1143. https://doi.org/10.1016/j.ejor.2006.05.015
Girlich, H.-J. (1990). Naddor’s demand patterns and the economic order quantity under uncertainty. Engineering Costs and Production Economics, 19(1–3), 327–331.
HormozzadehGhalati, H., Abbasi, A., & Sadeghi-Niaraki, A. (2019). Optimal multi-product supplier selection under stochastic demand with service level and budget constraints using learning vector quantization neural network. RAIRO—Operations Research, 53(5), 1709–1720. https://doi.org/10.1051/ro/2018096
Keshavarzfard, R., Makui, A., Tavakkoli-Moghaddam, R., & Taleizadeh, A. A. (2019). Optimization of imperfect economic manufacturing models with a power demand rate dependent production rate. Sādhanā, 44, 1–19. https://doi.org/10.1007/s12046-019-1171-4S
Khouja, M., Christou, E., & Stylianou, A. (2020). A heuristic approach to in-season capacity allocation in a multi-product newsvendor model. Omega, 95, 102252. https://doi.org/10.1016/j.omega.2020.102252
Krishnaraj, R. B., & Ramasamy, K. (2012). An inventory model with power demand pattern, weibull distribution deterioration and without shortages. The Bulletin of Society for Mathematical Services and Standards, 2, 33–37. https://doi.org/10.18052/www.scipress.com/bsmass.2.33
Liao, H., & Deng, Q. (2018). EES-EOQ model with uncertain acquisition quantity and market demand in dedicated or combined remanufacturing systems. Applied Mathematical Modelling, 64, 135–167. https://doi.org/10.1016/j.apm.2018.07.026
Maddah, B., & Noueihed, N. (2017). EOQ holds under stochastic demand, a technical note. Applied Mathematical Modelling, 45, 205–208. https://doi.org/10.1016/j.apm.2016.12.026
Malik, A. I., & Sarkar, B. (2018). Optimizing a multi-product continuous-review inventory model with uncertain demand, quality improvement, setup cost reduction, and variation control in lead time. IEEE Access, 6, 36176–36187. https://doi.org/10.1109/ACCESS.2018.2849694
Mishra, R. K., & Mishra, V. K. (2022). An optimum sustainable inventory model for non-instantaneous deterioration and quality assessment under carbon emissions and complete backordering shortage. Arabian Journal for Science and Engineering, 47(3), 3929–3944. https://doi.org/10.1007/s13369-021-06402-z
Mishra, S., Raju, L. K., Misra, U. K., & Misra, G. (2012). A study of EOQ model with power demand of deteriorating items under the influence of inflation. General Mathematics Notes, 10(1), 41–50.
Misra, U. K., Raju, L. K., Mishra, S., & Misra, G. (2012). An inventory model with quadratic demand pattern and deterioration with shortages under the influence of inflation. Mathematical Finance Letters, 1(1), 57–67.
Mitra, S. (2018). Newsvendor problem with clearance pricing. European Journal of Operational Research, 268(1), 193–202. https://doi.org/10.1016/j.ejor.2018.01.023
Placido dos Santos, F. S., & Oliveira, F. (2019). An enhanced L-shaped method for optimizing periodic-review inventory control problems modeled via two-stage stochastic programming. European Journal of Operational Research, 275(2), 677–693. https://doi.org/10.1016/j.ejor.2018.11.053
Qin, Y., Wang, R., Vakharia, A. J., Chen, Y., & Seref, M. M. H. (2011). The newsvendor problem: Review and directions for future research. European Journal of Operational Research, 213(2), 361–374. https://doi.org/10.1016/j.ejor.2010.11.024
Roozbeh Nia, A., Hemmati Far, M., & Niaki, S. T. A. (2015). A hybrid genetic and imperialist competitive algorithm for green vendor managed inventory of multi-item multi-constraint EOQ model under shortage. Applied Soft Computing Journal, 30, 353–364. https://doi.org/10.1016/j.asoc.2015.02.004
Sana, S. S. (2015). An EOQ model for stochastic demand for limited capacity of own warehouse. Annals of Operations Research, 233(1), 383–399. https://doi.org/10.1007/s10479-013-1510-5
Sana, S. S. (2020). Price competition between green and non-green products under corporate social responsible firm. Journal of Retailing and Consumer Services, 55, 102118. https://doi.org/10.1016/j.jretconser.2020.102118
Sana, S. S. (2022a). A structural mathematical model on two echelon supply chain system. Annals of Operations Research, 315(2), 1997–2025. https://doi.org/10.1007/s10479-020-03895-z
Sana, S. S. (2022b). Sale through dual channel retailing system—A mathematical approach. Sustainability Analytics and Modeling, 2, 100008. https://doi.org/10.1016/j.samod.2022.100008
Sana, S. S. (2023). The effects of greenhouse gas costs on optimal pricing and production lotsize in an imperfect production system. RAIRO—Operations Research, 57(4), 2209–2230. https://doi.org/10.1051/ro/2023115
San-José, L. A., Sicilia, J., & Alcaide-López-de-Pablo, D. (2018). An inventory system with demand dependent on both time and price assuming backlogged shortages. European Journal of Operational Research, 270(3), 889–897. https://doi.org/10.1016/j.ejor.2017.10.042
San-José, L. A., Sicilia, J., Cárdenas-Barrón, L. E., & Gutiérrez, J. M. (2019a). Optimal price and quantity under power demand pattern and non-linear holding cost. Computers and Industrial Engineering, 129, 426–434. https://doi.org/10.1016/j.cie.2019.01.054
San-José, L. A., Sicilia, J., González-De-la-Rosa, M., & Febles-Acosta, J. (2017). Optimal inventory policy under power demand pattern and partial backlogging. Applied Mathematical Modelling, 46, 618–630. https://doi.org/10.1016/j.apm.2017.01.082
San-José, L. A., Sicilia, J., González-De-la-Rosa, M., & Febles-Acosta, J. (2019b). Analysis of an inventory system with discrete scheduling period, time-dependent demand and backlogged shortages. Computers and Operations Research, 109, 200–208. https://doi.org/10.1016/j.cor.2019.05.003
San-José, L. A., Sicilia, J., González-De-la-Rosa, M., & Febles-Acosta, J. (2020). Best pricing and optimal policy for an inventory system under time-and-price-dependent demand and backordering. Annals of Operations Research, 286(1–2), 351–369. https://doi.org/10.1007/s10479-018-2953-5
Sarkar, S., Giri, B. C., & Sarkar, A. K. (2020). A vendor-buyer inventory model with lot-size and production rate dependent lead time under time value of money. RAIRO—Operations Research, 54(4), 961–979. https://doi.org/10.1051/ro/2019030
Sicilia, J., González-De-La-Rosa, M., Febles-Acosta, J., & Alcaide-López-De-Pablo, D. (2014). An inventory model for deteriorating items with shortages and time-varying demand. International Journal of Production Economics, 155, 155–162. https://doi.org/10.1016/j.ijpe.2014.01.024
Sicilia, J., San-José, L. A., Alcaide-López-de-Pablo, D., & Abdul-Jalbar, B. (2022). Optimal policy for multi-item systems with stochastic demands, backlogged shortages and limited storage capacity. Applied Mathematical Modelling, 108, 236–257. https://doi.org/10.1016/j.apm.2022.03.025
Singh, S. P., & Sehgal, V. K. (2011). An EOQ inventory model for Weibull distributed deteriorating items with power demand pattern and shortages. JP Journal of Mathematical Sciences, 1(2), 99–110.
Zhang, G. (2010). The multi-product newsboy problem with supplier quantity discounts and a budget constraint. European Journal of Operational Research, 206(2), 350–360. https://doi.org/10.1016/j.ejor.2010.02.038
Zhang, R. Y., Liu, Q., & Wang, C. X. (2019). Inventory optimization of building materials under the dual constraints of carbon emissions and stochastic demand. Systems Science and Control Engineering, 7(1), 146–157. https://doi.org/10.1080/21642583.2019.1585301
Acknowledgements
This research work is supported by the Council of Scientific and Industrial Research (CSIR-UGC) and is funded by the Ministry of Social Justice and Empowerment, Govt. of India, New Delhi through National Fellowship for Other Backward Classes (NFOBC). The authors wish to express their gratitude to the editor and anonymous reviewers for their constructive suggestions and comments that have helped in significantly shaping the manuscript.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
There is no known existing conflict of interest to the authors.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Gupta, S., Mishra, V.K. Multi-item stochastic inventory model for deteriorating items with power demand pattern under partial backlogging and joint replenishment. Ann Oper Res (2024). https://doi.org/10.1007/s10479-024-05997-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10479-024-05997-4