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Technical Note—Approximation Algorithms for Perishable Inventory Systems with Setup Costs

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  • Huanan Zhang

    (Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48105)

  • Cong Shi

    (Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48105)

  • Xiuli Chao

    (Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48105)

Abstract

We develop the first approximation algorithm for periodic-review perishable inventory systems with setup costs. The ordering lead time is zero. The model allows for correlated demand processes that generalize the well-known approaches to model dynamic demand forecast updates. The structure of optimal policies for this fundamental class of problems is not known in the literature. Thus, finding provably near-optimal control policies has been an open challenge. We develop a randomized proportional-balancing policy (RPB) that can be efficiently implemented in an online manner, and we show that it admits a worst-case performance guarantee between 3 and 4. The main challenge in our analysis is to compare the setup costs between RPB and the optimal policy in the presence of inventory perishability, which departs significantly from the previous works in the literature. The numerical results show that the average performance of RPB is good (within 1% of optimality under i.i.d. demands and within 7% under correlated demands).

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:2:p:432-440
    DOI: 10.1287/opre.2016.1485
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    References listed on IDEAS

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    Cited by:

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    2. 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).
    3. Kebing Chen & Jing‐Sheng Song & Jennifer Shang & Tiaojun Xiao, 2022. "Managing hospital platelet inventory with mid‐cycle expedited replenishments and returns," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2015-2037, May.
    4. Ding, Jingying & Peng, Zhenkang, 2024. "Heuristics for perishable inventory systems under mixture issuance policies," Omega, Elsevier, vol. 126(C).
    5. Sasanuma, Katsunobu & Delasay, Mohammad & Pitocco, Christine & Scheller-Wolf, Alan & Sexton, Thomas, 2022. "A marginal analysis framework to incorporate the externality effect of ordering perishables," Operations Research Perspectives, Elsevier, vol. 9(C).
    6. 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.
    7. 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.
    8. Huanan Zhang & Cong Shi & Chao Qin & Cheng Hua, 2016. "Stochastic regret minimization for revenue management problems with nonstationary demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(6), pages 433-448, September.
    9. Ketzenberg, Michael & Gaukler, Gary & Salin, Victoria, 2018. "Expiration dates and order quantities for perishables," European Journal of Operational Research, Elsevier, vol. 266(2), pages 569-584.
    10. 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.
    11. Alkaabneh, Faisal & Diabat, Ali & Gao, Huaizhu Oliver, 2021. "A unified framework for efficient, effective, and fair resource allocation by food banks using an Approximate Dynamic Programming approach," Omega, Elsevier, vol. 100(C).

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