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A Markovian Model for a Perishable Product Inventory

Author

Listed:
  • Dan Chazan

    (IBM Israel Scientific Center)

  • Shmuel Gal

    (IBM Israel Scientific Center)

Abstract

The rate of outdating of a perishable product (such as blood) and the age distribution of the inventory are analyzed. It is assumed that after each period's demand, the inventory is replenished with fresh product, up to a constant level. The age distribution is treated as a finite Markov chain. Expected outdating is shown to be convex in the inventory level. Upper and lower bounds for the expected outdating are obtained for the case of general demand distribution. Better and easily computable bounds and approximate distribution are found for the Poisson demand case.

Suggested Citation

  • Dan Chazan & Shmuel Gal, 1977. "A Markovian Model for a Perishable Product Inventory," Management Science, INFORMS, vol. 23(5), pages 512-521, January.
    • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:5:p:512-521
    DOI: 10.1287/mnsc.23.5.512
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    Cited by:

    1. De Moor, Bram J. & Gijsbrechts, Joren & Boute, Robert N., 2022. "Reward shaping to improve the performance of deep reinforcement learning in perishable inventory management," European Journal of Operational Research, Elsevier, vol. 301(2), pages 535-545.
    2. Kopach, Renata & Balcioglu, Baris & Carter, Michael, 2008. "Tutorial on constructing a red blood cell inventory management system with two demand rates," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1051-1059, March.
    3. 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.
    4. Lian, Zhaotong & Liu, Xiaoming & Zhao, Ning, 2009. "A perishable inventory model with Markovian renewal demands," International Journal of Production Economics, Elsevier, vol. 121(1), pages 176-182, September.
    5. Wang, Ke-Ming & Ma, Zu-Jun, 2015. "Age-based policy for blood transshipment during blood shortage," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 80(C), pages 166-183.
    6. Chiu, Huan Neng, 1995. "A heuristic (R, T) periodic review perishable inventory model with lead times," International Journal of Production Economics, Elsevier, vol. 42(1), pages 1-15, November.
    7. van Donselaar, Karel H. & Broekmeulen, Rob A.C.M., 2012. "Approximations for the relative outdating of perishable products by combining stochastic modeling, simulation and regression modeling," International Journal of Production Economics, Elsevier, vol. 140(2), pages 660-669.
    8. Anna Nagurney & Pritha Dutta, 2019. "Supply chain network competition among blood service organizations: a Generalized Nash Equilibrium framework," Annals of Operations Research, Springer, vol. 275(2), pages 551-586, April.
    9. Yu, Yang & Jaenicke, Edward C., 2021. "The effect of sell-by dates on purchase volume and food waste," Food Policy, Elsevier, vol. 98(C).
    10. Liming Liu & Zhaotong Lian, 1999. "(s, S) Continuous Review Models for Products with Fixed Lifetimes," Operations Research, INFORMS, vol. 47(1), pages 150-158, February.
    11. Z Shen & M Dessouky & F Ordonez, 2011. "Perishable inventory management system with a minimum volume constraint," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(12), pages 2063-2082, December.
    12. Sasanuma, Katsunobu & Hibiki, Akira & Sexton, Thomas, 2022. "An opaque selling scheme to reduce shortage and wastage in perishable inventory systems," Operations Research Perspectives, Elsevier, vol. 9(C).
    13. Lowalekar, Harshal & Ravi, R. Raghavendra, 2017. "Revolutionizing blood bank inventory management using the TOC thinking process: An Indian case study," International Journal of Production Economics, Elsevier, vol. 186(C), pages 89-122.
    14. William L. Cooper, 2001. "Pathwise Properties and Performance Bounds for a Perishable Inventory System," Operations Research, INFORMS, vol. 49(3), pages 455-466, June.
    15. Duan, Qinglin & Liao, T. Warren, 2014. "Optimization of blood supply chain with shortened shelf lives and ABO compatibility," International Journal of Production Economics, Elsevier, vol. 153(C), pages 113-129.
    16. Chiu, Huan Neng, 1995. "An approximation to the continuous review inventory model with perishable items and lead times," European Journal of Operational Research, Elsevier, vol. 87(1), pages 93-108, November.
    17. K Katsaliaki & S C Brailsford, 2007. "Using simulation to improve the blood supply chain," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(2), pages 219-227, February.
    18. Minner, Stefan & Transchel, Sandra, 2017. "Order variability in perishable product supply chains," European Journal of Operational Research, Elsevier, vol. 260(1), pages 93-107.
    19. Duan, Qinglin & Liao, T. Warren, 2013. "A new age-based replenishment policy for supply chain inventory optimization of highly perishable products," International Journal of Production Economics, Elsevier, vol. 145(2), pages 658-671.
    20. 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.
    21. Osorio, Andres F. & Brailsford, Sally C. & Smith, Honora K., 2018. "Whole blood or apheresis donations? A multi-objective stochastic optimization approach," European Journal of Operational Research, Elsevier, vol. 266(1), pages 193-204.

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