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Higher-Order Approximations for the Perishable-Inventory Problem

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  • Steven Nahmias

    (University of Pittsburgh, Pittsburgh, Pennsylvania)

Abstract

Computation of an optimal policy for ordering a perishable commodity with a fixed lifetime of m periods requires the solution of a dynamic program whose state variable has dimension m − 1. Unless m is small, the computations quickly become unreasonable. By bounding the expected outdating function and using an approximate transfer function, we obtain an approximation of the original problem that can be computed as if the lifetime were r m periods. When r = 2, it is demonstrated under reasonable assumptions that the appropriate function to be minimized each period is quasi-convex. We include computations that compare this approximation to both the optimal policy and a critical number approximation.

Suggested Citation

  • Steven Nahmias, 1977. "Higher-Order Approximations for the Perishable-Inventory Problem," Operations Research, INFORMS, vol. 25(4), pages 630-640, August.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:4:p:630-640
    DOI: 10.1287/opre.25.4.630
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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. 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.
    3. Huanan Zhang & Cong Shi & Xiuli Chao, 2016. "Technical Note—Approximation Algorithms for Perishable Inventory Systems with Setup Costs," Operations Research, INFORMS, vol. 64(2), pages 432-440, April.
    4. Kouki, Chaaben & Jemaï, Zied & Minner, Stefan, 2015. "A lost sales (r, Q) inventory control model for perishables with fixed lifetime and lead time," International Journal of Production Economics, Elsevier, vol. 168(C), pages 143-157.
    5. 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.
    6. Puranam, Kartikeya & Novak, David C. & Lucas, Marilyn T. & Fung, Mark, 2017. "Managing blood inventory with multiple independent sources of supply," European Journal of Operational Research, Elsevier, vol. 259(2), pages 500-511.
    7. 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.
    8. 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.
    9. Y-W Zhou & S-L Yang, 2003. "An optimal replenishment policy for items with inventory-level-dependent demand and fixed lifetime under the LIFO policy," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(6), pages 585-593, June.
    10. Hailun Zhang & Jiheng Zhang & Rachel Q. Zhang, 2020. "Simple Policies with Provable Bounds for Managing Perishable Inventory," Production and Operations Management, Production and Operations Management Society, vol. 29(11), pages 2637-2650, November.
    11. 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.
    12. Shouchang Chen & Yanzhi Li & Yi Yang & Weihua Zhou, 2021. "Managing Perishable Inventory Systems with Age‐differentiated Demand," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3784-3799, October.
    13. Hwang, Hark & Hahn, Kyu Hun, 2000. "An optimal procurement policy for items with an inventory level-dependent demand rate and fixed lifetime," European Journal of Operational Research, Elsevier, vol. 127(3), pages 537-545, December.
    14. 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.
    15. Williams, Craig L. & Patuwo, B. Eddy, 1999. "A perishable inventory model with positive order lead times," European Journal of Operational Research, Elsevier, vol. 116(2), pages 352-373, July.
    16. Kouki, Chaaben & Jouini, Oualid, 2015. "On the effect of lifetime variability on the performance of inventory systems," International Journal of Production Economics, Elsevier, vol. 167(C), pages 23-34.
    17. Janssen, Larissa & Diabat, Ali & Sauer, Jürgen & Herrmann, Frank, 2018. "A stochastic micro-periodic age-based inventory replenishment policy for perishable goods," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 445-465.

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