IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v309y2022i1d10.1007_s10479-021-04186-x.html
   My bibliography  Save this article

Inventory systems with stochastic and batch demand: computational approaches

Author

Listed:
  • Walid W. Nasr

    (American University of Beirut(AUB))

Abstract

Modeling the behavior of customer demand is a key challenge in inventory control, where an accurate characterization of the demand process often involves accounting for a wide range of statistical descriptors. This motivates the use of Markovian processes, due to their proven versatility in matching key components of point processes, to capture the behavior of customer demand. Accordingly, this work presents computational frameworks for continuous inventory models with a batch Markovian demand. A Markovian formulation of the system state-space is presented along with computational approaches to obtain key inventory performance measures. Compact matrix representations are considered for the steady-state solution of the system performance measures. The transient and non-stationary behavior of the inventory system is calculated by numerically integrating the corresponding set of Kolmogorov forward equations. A byproduct of this work is explicitly expressing the solution of the moments of the batch Markovian counting process by a compact matrix exponential equation. Numerical examples illustrate the computational efficiency of the mathematical frameworks when evaluating and comparing the performance of different re-ordering policies.

Suggested Citation

  • Walid W. Nasr, 2022. "Inventory systems with stochastic and batch demand: computational approaches," Annals of Operations Research, Springer, vol. 309(1), pages 163-187, February.
    • Handle: RePEc:spr:annopr:v:309:y:2022:i:1:d:10.1007_s10479-021-04186-x
    DOI: 10.1007/s10479-021-04186-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-021-04186-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-021-04186-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Suresh P. Sethi & Feng Cheng, 1997. "Optimality of ( s , S ) Policies in Inventory Models with Markovian Demand," Operations Research, INFORMS, vol. 45(6), pages 931-939, December.
    2. Nasr, Walid W. & Maddah, Bacel, 2015. "Continuous (s, S) policy with MMPP correlated demand," European Journal of Operational Research, Elsevier, vol. 246(3), pages 874-885.
    3. Feng, Lin & Chan, Ya-Lan, 2019. "Joint pricing and production decisions for new products with learning curve effects under upstream and downstream trade credits," European Journal of Operational Research, Elsevier, vol. 272(3), pages 905-913.
    4. Li Chen & Jing-Sheng Song & Yue Zhang, 2017. "Serial Inventory Systems with Markov-Modulated Demand: Derivative Bounds, Asymptotic Analysis, and Insights," Operations Research, INFORMS, vol. 65(5), pages 1231-1249, October.
    5. Yingdong Lu, 2007. "Estimation of average backorders for an assemble‐to‐order system with random batch demands through extreme statistics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 33-45, February.
    6. Yingdong Lu & Jing-Sheng Song & David D. Yao, 2003. "Order Fill Rate, Leadtime Variability, and Advance Demand Information in an Assemble-to-Order System," Operations Research, INFORMS, vol. 51(2), pages 292-308, April.
    7. Özkan, Can & Karaesmen, Fikri & Özekici, Süleyman, 2013. "Structural properties of Markov modulated revenue management problems," European Journal of Operational Research, Elsevier, vol. 225(2), pages 324-331.
    8. Y. Barron, 2019. "A state-dependent perishability (s, S) inventory model with random batch demands," Annals of Operations Research, Springer, vol. 280(1), pages 65-98, September.
    9. Fangruo Chen & Jing-Sheng Song, 2001. "Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand," Operations Research, INFORMS, vol. 49(2), pages 226-234, April.
    10. Stephen C. Graves & Sean P. Willems, 2008. "Strategic Inventory Placement in Supply Chains: Nonstationary Demand," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 278-287, March.
    11. Joachim Arts & Rob Basten & Geert-Jan Van Houtum, 2016. "Repairable Stocking and Expediting in a Fluctuating Demand Environment: Optimal Policy and Heuristics," Operations Research, INFORMS, vol. 64(6), pages 1285-1301, December.
    12. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    13. Maddah, Bacel & Nasr, Walid W. & Charanek, Ali, 2017. "A multi-station system for reducing congestion in high-variability queues," European Journal of Operational Research, Elsevier, vol. 262(2), pages 602-619.
    14. John J. Neale & Sean P. Willems, 2009. "Managing Inventory in Supply Chains with Nonstationary Demand," Interfaces, INFORMS, vol. 39(5), pages 388-399, October.
    15. Arts, Joachim, 2017. "A multi-item approach to repairable stocking and expediting in a fluctuating demand environment," European Journal of Operational Research, Elsevier, vol. 256(1), pages 102-115.
    16. Yonit Barron & David Perry & Wolfgang Stadje, 2016. "A make-to-stock production/inventory model with MAP arrivals and phase-type demands," Annals of Operations Research, Springer, vol. 241(1), pages 373-409, June.
    17. Lee, Loo Hay & Chew, Ek Peng, 2005. "A dynamic joint replenishment policy with auto-correlated demand," European Journal of Operational Research, Elsevier, vol. 165(3), pages 729-747, September.
    18. Michael Katehakis & Laurens Smit, 2012. "On computing optimal (Q,r) replenishment policies under quantity discounts," Annals of Operations Research, Springer, vol. 200(1), pages 279-298, November.
    19. Junmin Shi & Michael Katehakis & Benjamin Melamed, 2013. "Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands," Annals of Operations Research, Springer, vol. 208(1), pages 593-612, September.
    20. Frank Youhua Chen & Candace Arai Yano, 2010. "Improving Supply Chain Performance and Managing Risk Under Weather-Related Demand Uncertainty," Management Science, INFORMS, vol. 56(8), pages 1380-1397, August.
    21. Nasr, Walid W. & Elshar, Ibrahim J., 2018. "Continuous inventory control with stochastic and non-stationary Markovian demand," European Journal of Operational Research, Elsevier, vol. 270(1), pages 198-217.
    22. Dirk Beyer & Feng Cheng & Suresh P. Sethi & Michael Taksar, 2010. "Markovian Demand Inventory Models," International Series in Operations Research and Management Science, Springer, number 978-0-387-71604-6, April.
    23. Zhao, Yao, 2009. "Analysis and evaluation of an Assemble-to-Order system with batch ordering policy and compound Poisson demand," European Journal of Operational Research, Elsevier, vol. 198(3), pages 800-809, November.
    24. Emre Nadar & Mustafa Akan & Alan Scheller-Wolf, 2014. "Technical Note---Optimal Structural Results for Assemble-to-Order Generalized M -Systems," Operations Research, INFORMS, vol. 62(3), pages 571-579, June.
    25. Savas Dayanik & Jing-Sheng Song & Susan H. Xu, 2003. "The Effectiveness of Several Performance Bounds for Capacitated Production, Partial-Order-Service, Assemble-to-Order Systems," Manufacturing & Service Operations Management, INFORMS, vol. 5(3), pages 230-251, December.
    26. Yao Zhao & David Simchi-Levi, 2006. "Performance Analysis and Evaluation of Assemble-to-Order Systems with Stochastic Sequential Lead Times," Operations Research, INFORMS, vol. 54(4), pages 706-724, August.
    27. Sanket Bhat & Ananth Krishnamurthy, 2015. "Value of capacity flexibility in manufacturing systems with seasonal demands," IISE Transactions, Taylor & Francis Journals, vol. 47(7), pages 693-714, July.
    28. Walid W. Nasr & Michael R. Taaffe, 2013. "Fitting the Ph t / M t / s / c Time-Dependent Departure Process for Use in Tandem Queueing Networks," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 758-773, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nasr, Walid W. & Elshar, Ibrahim J., 2018. "Continuous inventory control with stochastic and non-stationary Markovian demand," European Journal of Operational Research, Elsevier, vol. 270(1), pages 198-217.
    2. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    3. Nasr, Walid W. & Maddah, Bacel, 2015. "Continuous (s, S) policy with MMPP correlated demand," European Journal of Operational Research, Elsevier, vol. 246(3), pages 874-885.
    4. Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.
    5. Atan, Zümbül & Ahmadi, Taher & Stegehuis, Clara & Kok, Ton de & Adan, Ivo, 2017. "Assemble-to-order systems: A review," European Journal of Operational Research, Elsevier, vol. 261(3), pages 866-879.
    6. Arnoud den Boer & Ohad Perry & Bert Zwart, 2018. "Dynamic pricing policies for an inventory model with random windows of opportunities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 660-675, December.
    7. Xiang, Mengyuan & Rossi, Roberto & Martin-Barragan, Belen & Tarim, S. Armagan, 2023. "A mathematical programming-based solution method for the nonstationary inventory problem under correlated demand," European Journal of Operational Research, Elsevier, vol. 304(2), pages 515-524.
    8. Manafzadeh Dizbin, Nima & Tan, Barış, 2020. "Optimal control of production-inventory systems with correlated demand inter-arrival and processing times," International Journal of Production Economics, Elsevier, vol. 228(C).
    9. Stößlein, Martin & Kanet, John Jack & Gorman, Mike & Minner, Stefan, 2014. "Time-phased safety stocks planning and its financial impacts: Empirical evidence based on European econometric data," International Journal of Production Economics, Elsevier, vol. 149(C), pages 47-55.
    10. Jinhui Han & Suresh P. Sethi & Chi Chung Siu & Sheung Chi Phillip Yam, 2023. "Co‐op advertising in randomly fluctuating markets," Production and Operations Management, Production and Operations Management Society, vol. 32(6), pages 1617-1635, June.
    11. Qi‐Ming He & James H. Bookbinder & Qishu Cai, 2020. "Optimal policies for stochastic clearing systems with time‐dependent delay penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 487-502, October.
    12. Boxiao Chen, 2021. "Data‐Driven Inventory Control with Shifting Demand," Production and Operations Management, Production and Operations Management Society, vol. 30(5), pages 1365-1385, May.
    13. Eugene A. Feinberg & Yan Liang, 2022. "On the optimality equation for average cost Markov decision processes and its validity for inventory control," Annals of Operations Research, Springer, vol. 317(2), pages 569-586, October.
    14. Rahimi-Ghahroodi, S. & Al Hanbali, A. & Vliegen, I.M.H. & Cohen, M.A., 2019. "Joint optimization of spare parts inventory and service engineers staffing with full backlogging," International Journal of Production Economics, Elsevier, vol. 212(C), pages 39-50.
    15. Benjamin Avanzi & Greg Taylor & Bernard Wong & Alan Xian, 2020. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," Papers 2003.13888, arXiv.org, revised May 2020.
    16. Li Chen & Jing-Sheng Song & Yue Zhang, 2017. "Serial Inventory Systems with Markov-Modulated Demand: Derivative Bounds, Asymptotic Analysis, and Insights," Operations Research, INFORMS, vol. 65(5), pages 1231-1249, October.
    17. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Xian, Alan, 2021. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," European Journal of Operational Research, Elsevier, vol. 290(1), pages 177-195.
    18. Tan, Tarkan & Gullu, Refik & Erkip, Nesim, 2007. "Modelling imperfect advance demand information and analysis of optimal inventory policies," European Journal of Operational Research, Elsevier, vol. 177(2), pages 897-923, March.
    19. van Jaarsveld, W.L. & Dollevoet, T.A.B., 2011. "Spare parts inventory control for an aircraft component repair shop," Econometric Institute Research Papers EI2011-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    20. Guillermo Gallego & Özalp Özer, 2003. "Optimal Replenishment Policies for Multiechelon Inventory Problems Under Advance Demand Information," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 157-175, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:309:y:2022:i:1:d:10.1007_s10479-021-04186-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.