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Inventory model with incomplete information: sales and zero-balance signals

Author

Listed:
  • Alain Bensoussan

    (University of Texas at Dallas)

  • Metin Çakanyıldırım

    (University of Texas at Dallas)

  • Meng Li

    (University of Houston)

  • Suresh Sethi

    (University of Texas at Dallas)

Abstract

Inventory problems with incomplete inventory information arise frequently in practice because demand or invisible demand is not observed directly but both reduce the inventory level. In this paper, we develop a periodic-review lost-sales inventory model, where the sales is always observed while the inventory level is observed only when it reaches zero. Our objective is to minimize the expected discounted cost over an infinite horizon, and we use dynamic programming along with the concept of unnormalized probability to solve the problem. The interaction between the sales and zero-balance walk signal simplifies the updating process of the inventory level distribution. Interestingly, the evolution of inventory distribution is independent of the demand. We also find a mean-based approximation has the customary dynamic program of the completely observed problem giving rise to a lower bound on the optimal cost of the original problem. Furthermore, incorporating the variance of inventory level improves the bound.

Suggested Citation

  • Alain Bensoussan & Metin Çakanyıldırım & Meng Li & Suresh Sethi, 2025. "Inventory model with incomplete information: sales and zero-balance signals," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 33(2), pages 571-584, June.
    • Handle: RePEc:spr:cejnor:v:33:y:2025:i:2:d:10.1007_s10100-025-00979-8
    DOI: 10.1007/s10100-025-00979-8
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    References listed on IDEAS

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    1. William S. Lovejoy, 1991. "Computationally Feasible Bounds for Partially Observed Markov Decision Processes," Operations Research, INFORMS, vol. 39(1), pages 162-175, February.
    2. Li Chen, 2021. "Fixing Phantom Stockouts: Optimal Data‐Driven Shelf Inspection Policies," Production and Operations Management, Production and Operations Management Society, vol. 30(3), pages 689-702, March.
    3. Li Chen & Adam J. Mersereau, 2015. "Analytics for Operational Visibility in the Retail Store: The Cases of Censored Demand and Inventory Record Inaccuracy," International Series in Operations Research & Management Science, in: Narendra Agrawal & Stephen A. Smith (ed.), Retail Supply Chain Management, edition 2, chapter 0, pages 79-112, Springer.
    4. A. Gürhan Kök & Kevin H. Shang, 2007. "Inspection and Replenishment Policies for Systems with Inventory Record Inaccuracy," Manufacturing & Service Operations Management, INFORMS, vol. 9(2), pages 185-205, February.
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    7. Alain Bensoussan & Metin Çakanyildirim & Meng Li & Suresh P. Sethi, 2016. "Managing Inventory with Cash Register Information: Sales Recorded but Not Demands," Production and Operations Management, Production and Operations Management Society, vol. 25(1), pages 9-21, January.
    8. Adam J. Mersereau, 2015. "Demand Estimation from Censored Observations with Inventory Record Inaccuracy," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 335-349, July.
    9. Achal Bassamboo & Antonio Moreno & Ioannis Stamatopoulos, 2020. "Inventory Auditing and Replenishment Using Point‐of‐Sales Data," Production and Operations Management, Production and Operations Management Society, vol. 29(5), pages 1219-1231, May.
    10. Nicole DeHoratius & Adam J. Mersereau & Linus Schrage, 2008. "Retail Inventory Management When Records Are Inaccurate," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 257-277, November.
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    Cited by:

    1. Gustav Feichtinger & Christophe Deissenberg & Ulrike Leopold-Wildburger, 2025. "George Leitmann’s 100th birthday," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 33(2), pages 333-344, June.

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