IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v101y2025i2d10.1007_s00186-025-00888-1.html
   My bibliography  Save this article

On non-negative auto-correlated integer demand processes

Author

Listed:
  • Lotte Hezewijk

    (Eindhoven University of Technology
    ORTEC B.V.)

  • Nico P. Dellaert

    (Eindhoven University of Technology)

  • Willem L. Jaarsveld

    (Eindhoven University of Technology)

Abstract

Methods to generate realistic non-stationary demand scenarios are a key component for analyzing and optimizing decision policies in supply chains. Typical forecasting techniques recommended in standard inventory control textbooks consist of some form of simple exponential smoothing (SES) for both the estimates for the mean and standard deviation. We study demand generating processes (DGPs) that yield non-stationary demand scenarios, and that are consistent with SES, meaning that SES yields unbiased estimates when applied to the generated demand scenarios. As demand in typical practical settings is discrete and non-negative, we study consistent DGPs on the non-negative integers. We derive conditions under which the existence of such DGPs can be guaranteed, and propose a specific DGP that yields autocorrelated, discrete demands when these conditions are satisfied. Our subsequent simulation study gains further insights into the proposed DGP. It demonstrates that from a given initial forecast, our DGP yields a diverse set of demand scenarios with a wide range of properties. To show the applicability of the DGP, we apply it to generate demand in a standard inventory problem with full backlogging and a positive lead time. We find that appropriate dynamic base-stock levels can be obtained using a new and relatively simple algorithm, and we demonstrate that this algorithm outperforms relevant benchmarks.

Suggested Citation

  • Lotte Hezewijk & Nico P. Dellaert & Willem L. Jaarsveld, 2025. "On non-negative auto-correlated integer demand processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(2), pages 135-161, April.
  • Handle: RePEc:spr:mathme:v:101:y:2025:i:2:d:10.1007_s00186-025-00888-1
    DOI: 10.1007/s00186-025-00888-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-025-00888-1
    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/s00186-025-00888-1?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Onur Kaya & Sajjad Rahimi Ghahroodi, 2018. "Inventory control and pricing for perishable products under age and price dependent stochastic demand," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(1), pages 1-35, August.
    2. de Kok, Ton, 2018. "Inventory Management: Modeling Real-life Supply Chains and Empirical Validity," Foundations and Trends(R) in Technology, Information and Operations Management, now publishers, vol. 11(2), pages 343-437, April.
    3. Kenneth Gilbert, 2005. "An ARIMA Supply Chain Model," Management Science, INFORMS, vol. 51(2), pages 305-310, February.
    4. Babai, M. Zied & Dai, Yong & Li, Qinyun & Syntetos, Aris & Wang, Xun, 2022. "Forecasting of lead-time demand variance: Implications for safety stock calculations," European Journal of Operational Research, Elsevier, vol. 296(3), pages 846-861.
    5. Ma, Xiyuan & Rossi, Roberto & Archibald, Thomas Welsh, 2022. "Approximations for non-stationary stochastic lot-sizing under (s,Q)-type policy," European Journal of Operational Research, Elsevier, vol. 298(2), pages 573-584.
    6. Prak, Dennis & Teunter, Ruud, 2019. "A general method for addressing forecasting uncertainty in inventory models," International Journal of Forecasting, Elsevier, vol. 35(1), pages 224-238.
    7. Boute, Robert N. & Gijsbrechts, Joren & van Jaarsveld, Willem & Vanvuchelen, Nathalie, 2022. "Deep reinforcement learning for inventory control: A roadmap," European Journal of Operational Research, Elsevier, vol. 298(2), pages 401-412.
    8. Snyder, Ralph D. & Koehler, Anne B. & Ord, J. Keith, 2002. "Forecasting for inventory control with exponential smoothing," International Journal of Forecasting, Elsevier, vol. 18(1), pages 5-18.
    9. Erhan Bayraktar & Michael Ludkovski, 2010. "Inventory management with partially observed nonstationary demand," Annals of Operations Research, Springer, vol. 176(1), pages 7-39, April.
    10. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    11. Klaus Altendorfer & Thomas Felberbauer & Herbert Jodlbauer, 2016. "Effects of forecast errors on optimal utilisation in aggregate production planning with stochastic customer demand," International Journal of Production Research, Taylor & Francis Journals, vol. 54(12), pages 3718-3735, June.
    12. Dimitris Bertsimas & Melvyn Sim & Meilin Zhang, 2019. "Adaptive Distributionally Robust Optimization," Management Science, INFORMS, vol. 65(2), pages 604-618, February.
    13. Amniattalab, Ayda & Frenk, J.B.G. & Hekimoğlu, Mustafa, 2023. "On spare parts demand and the installed base concept: A theoretical approach," International Journal of Production Economics, Elsevier, vol. 266(C).
    14. Goltsos, Thanos E. & Syntetos, Aris A. & Glock, Christoph H. & Ioannou, George, 2022. "Inventory – forecasting: Mind the gap," European Journal of Operational Research, Elsevier, vol. 299(2), pages 397-419.
    15. Stephen C. Graves, 1999. "A Single-Item Inventory Model for a Nonstationary Demand Process," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 50-61.
    16. Janssen, Elleke & Strijbosch, Leo & Brekelmans, Ruud, 2009. "Assessing the effects of using demand parameters estimates in inventory control and improving the performance using a correction function," International Journal of Production Economics, Elsevier, vol. 118(1), pages 34-42, March.
    17. Visentin, Andrea & Prestwich, Steven & Rossi, Roberto & Tarim, S. Armagan, 2021. "Computing optimal (R,s,S) policy parameters by a hybrid of branch-and-bound and stochastic dynamic programming," European Journal of Operational Research, Elsevier, vol. 294(1), pages 91-99.
    18. Rostami-Tabar, Bahman & Disney, Stephen M., 2023. "On the order-up-to policy with intermittent integer demand and logically consistent forecasts," International Journal of Production Economics, Elsevier, vol. 257(C).
    19. Kolassa, Stephan, 2016. "Evaluating predictive count data distributions in retail sales forecasting," International Journal of Forecasting, Elsevier, vol. 32(3), pages 788-803.
    20. Jianqiang Hu & Cheng Zhang & Chenbo Zhu, 2016. "( s , S ) Inventory Systems with Correlated Demands," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 603-611, November.
    21. Stephen C. Graves, 1999. "Addendum to "A Single-Item Inventory Model for a Nonstationary Demand Process"," Manufacturing & Service Operations Management, INFORMS, vol. 1(2), pages 174-174.
    22. Sarah Gelper & Roland Fried & Christophe Croux, 2010. "Robust forecasting with exponential and Holt-Winters smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(3), pages 285-300.
    23. Strijbosch, Leo W.G. & Syntetos, Aris A. & Boylan, John E. & Janssen, Elleke, 2011. "On the interaction between forecasting and stock control: The case of non-stationary demand," International Journal of Production Economics, Elsevier, vol. 133(1), pages 470-480, September.
    24. Xiang, Mengyuan & Rossi, Roberto & Martin-Barragan, Belen & Tarim, S. Armagan, 2018. "Computing non-stationary (s, S) policies using mixed integer linear programming," European Journal of Operational Research, Elsevier, vol. 271(2), pages 490-500.
    25. Goltsos, T. .E. & Syntetos, A & Glock, C. H. & Ioannou, G, 2022. "Inventory – forecasting: Mind the gap," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 131494, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    Full references (including those not matched with items on IDEAS)

    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. van Hezewijk, Lotte & Dellaert, Nico P. & van Jaarsveld, Willem L., 2025. "Scalable deep reinforcement learning in the non-stationary capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 284(C).
    2. Saoud, Patrick & Kourentzes, Nikolaos & Boylan, John E., 2022. "Approximations for the Lead Time Variance: a Forecasting and Inventory Evaluation," Omega, Elsevier, vol. 110(C).
    3. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    4. 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.
    5. Xiang, Mengyuan & Rossi, Roberto & Martin-Barragan, Belen & Tarim, S. Armagan, 2018. "Computing non-stationary (s, S) policies using mixed integer linear programming," European Journal of Operational Research, Elsevier, vol. 271(2), pages 490-500.
    6. Layth C. Alwan & Christian H. Weiß, 2017. "INAR implementation of newsvendor model for serially dependent demand counts," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1085-1099, February.
    7. Ren, Ke & Bidkhori, Hoda & Shen, Zuo-Jun Max, 2024. "Data-driven inventory policy: Learning from sequentially observed non-stationary data," Omega, Elsevier, vol. 123(C).
    8. Dehaybe, Henri & Catanzaro, Daniele & Chevalier, Philippe, 2024. "Deep Reinforcement Learning for inventory optimization with non-stationary uncertain demand," European Journal of Operational Research, Elsevier, vol. 314(2), pages 433-445.
    9. Yee, Hannah & van Staden, Heletjé E. & Boute, Robert N., 2024. "Dual sourcing under non-stationary demand and partial observability," European Journal of Operational Research, Elsevier, vol. 314(1), pages 94-110.
    10. 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.
    11. Jianqiang Hu & Cheng Zhang & Chenbo Zhu, 2016. "( s , S ) Inventory Systems with Correlated Demands," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 603-611, November.
    12. Wang, Zhaodong & Wang, Xin & Ouyang, Yanfeng, 2015. "Bounded growth of the bullwhip effect under a class of nonlinear ordering policies," European Journal of Operational Research, Elsevier, vol. 247(1), pages 72-82.
    13. Ma, Yungao & Wang, Nengmin & He, Zhengwen & Lu, Jizhou & Liang, Huigang, 2015. "Analysis of the bullwhip effect in two parallel supply chains with interacting price-sensitive demands," European Journal of Operational Research, Elsevier, vol. 243(3), pages 815-825.
    14. Ouyang, Yanfeng & Daganzo, Carlos, 2008. "Robust tests for the bullwhip effect in supply chains with stochastic dynamics," European Journal of Operational Research, Elsevier, vol. 185(1), pages 340-353, February.
    15. 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.
    16. Babai, M.Z. & Ali, M.M. & Boylan, J.E. & Syntetos, A.A., 2013. "Forecasting and inventory performance in a two-stage supply chain with ARIMA(0,1,1) demand: Theory and empirical analysis," International Journal of Production Economics, Elsevier, vol. 143(2), pages 463-471.
    17. Ma, Xiyuan & Rossi, Roberto & Archibald, Thomas Welsh, 2022. "Approximations for non-stationary stochastic lot-sizing under (s,Q)-type policy," European Journal of Operational Research, Elsevier, vol. 298(2), pages 573-584.
    18. Li Chen & Wei Luo & Kevin Shang, 2017. "Measuring the Bullwhip Effect: Discrepancy and Alignment Between Information and Material Flows," Manufacturing & Service Operations Management, INFORMS, vol. 19(1), pages 36-51, February.
    19. Nagaraja, C.H. & Thavaneswaran, A. & Appadoo, S.S., 2015. "Measuring the bullwhip effect for supply chains with seasonal demand components," European Journal of Operational Research, Elsevier, vol. 242(2), pages 445-454.
    20. M M Ali & J E Boylan, 2011. "Feasibility principles for Downstream Demand Inference in supply chains," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(3), pages 474-482, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:mathme:v:101:y:2025:i:2:d:10.1007_s00186-025-00888-1. 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.