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Pathwise Properties and Performance Bounds for a Perishable Inventory System

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  • William L. Cooper

    (Department of Mechanical Engineering, University of Minnesota, 111 Church Street S.E., Minneapolis, MN 55455)

Abstract

We study a perishable inventory system under a fixed-critical number order policy. By using an appropriate transformation of the state vector, we derive several key sample-path relations. We obtain bounds on the limiting distribution of the number of outdates in a period, and we derive families of upper and lower bounds for the long-run number of outdates per unit time. Analysis of the bounds on the expected number of outdates shows that at least one of the new lower bounds is always greater than or equal to previously published lower bounds, whereas the new upper bounds are sometimes lower than and sometimes higher than the existing upper bounds. In addition, using an expected cost criterion, we compare optimal policies and different choices of critical-number policies.

Suggested Citation

  • William L. Cooper, 2001. "Pathwise Properties and Performance Bounds for a Perishable Inventory System," Operations Research, INFORMS, vol. 49(3), pages 455-466, June.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:3:p:455-466
    DOI: 10.1287/opre.49.3.455.11216
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Borga Deniz & Itir Karaesmen & Alan Scheller-Wolf, 2010. "Managing Perishables with Substitution: Inventory Issuance and Replenishment Heuristics," Manufacturing & Service Operations Management, INFORMS, vol. 12(2), pages 319-329, July.
    2. Ding, Jingying & Peng, Zhenkang, 2024. "Heuristics for perishable inventory systems under mixture issuance policies," Omega, Elsevier, vol. 126(C).
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    4. Xiuli Chao & Xiting Gong & Cong Shi & Huanan Zhang, 2015. "Approximation Algorithms for Perishable Inventory Systems," Operations Research, INFORMS, vol. 63(3), pages 585-601, June.
    5. Gorria, Carlos & Lezaun, Mikel & López, F. Javier, 2022. "Performance measures of nonstationary inventory models for perishable products under the EWA policy," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1137-1150.
    6. Hossein Abouee‐Mehrizi & Mahdi Mirjalili & Vahid Sarhangian, 2022. "Data‐driven platelet inventory management under uncertainty in the remaining shelf life of units," Production and Operations Management, Production and Operations Management Society, vol. 31(10), pages 3914-3932, October.
    7. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2019. "Performance improvement of a service system via stocking perishable preliminary services," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1000-1011.
    8. Hossein Abouee-Mehrizi & Mahdi Mirjalili & Vahid Sarhangian, 2026. "Platelet Inventory Management with Approximate Dynamic Programming," INFORMS Journal on Computing, INFORMS, vol. 38(1), pages 207-231, January.
    9. Xiuli Chao & Xiting Gong & Cong Shi & Chaolin Yang & Huanan Zhang & Sean X. Zhou, 2018. "Approximation Algorithms for Capacitated Perishable Inventory Systems with Positive Lead Times," Management Science, INFORMS, vol. 64(11), pages 5038-5061, November.
    10. Can Zhang & Turgay Ayer & Chelsea C. White & Joy N. Bodeker & John D. Roback, 2023. "Inventory Sharing for Perishable Products: Application to Platelet Inventory Management in Hospital Blood Banks," Operations Research, INFORMS, vol. 71(5), pages 1756-1776, September.
    11. Deming Zhou & Lawrence C. Leung & William P. Pierskalla, 2011. "Inventory Management of Platelets in Hospitals: Optimal Inventory Policy for Perishable Products with Regular and Optional Expedited Replenishments," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 420-438, October.
    12. Jinzhi Bu & Xiting Gong & Xiuli Chao, 2024. "Asymptotic Scaling of Optimal Cost and Asymptotic Optimality of Base-Stock Policy in Several Multidimensional Inventory Systems," Operations Research, INFORMS, vol. 72(5), pages 1765-1774, September.
    13. Bakker, Monique & Riezebos, Jan & Teunter, Ruud H., 2012. "Review of inventory systems with deterioration since 2001," European Journal of Operational Research, Elsevier, vol. 221(2), pages 275-284.
    14. Yves Crama & Mahmood Rezaei & Martin Savelsbergh & Tom Van Woensel, 2018. "Stochastic Inventory Routing for Perishable Products," Transportation Science, INFORMS, vol. 52(3), pages 526-546, June.
    15. Motamedi, Maryam & Li, Na & Down, Douglas G., 2026. "Optimal ordering policy for perishable products by incorporating demand forecasts," European Journal of Operational Research, Elsevier, vol. 329(1), pages 124-137.
    16. Jinzhi Bu & Xiting Gong & Xiuli Chao, 2023. "Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems," Management Science, INFORMS, vol. 69(2), pages 846-864, February.
    17. Haijema, René & Minner, Stefan, 2016. "Stock-level dependent ordering of perishables: A comparison of hybrid base-stock and constant order policies," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 215-225.
    18. Can Zhang & Turgay Ayer & Chelsea C. White, 2023. "Truncated Balancing Policy for Perishable Inventory Management: Combating High Shortage Penalties," Manufacturing & Service Operations Management, INFORMS, vol. 25(6), pages 2352-2370, November.
    19. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2020. "A service system with perishable products where customers are either fastidious or strategic," International Journal of Production Economics, Elsevier, vol. 228(C).

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