IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v64y2016i2p432-440.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2016.1485
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2016.1485?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Steven Nahmias, 1975. "Optimal Ordering Policies for Perishable Inventory—II," Operations Research, INFORMS, vol. 23(4), pages 735-749, August.
    2. Cong Shi & Huanan Zhang & Xiuli Chao & Retsef Levi, 2014. "Approximation algorithms for capacitated stochastic inventory systems with setup costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(4), pages 304-319, June.
    3. Z. Lian & L. Liu, 1999. "A discrete‐time model for perishable inventory systems," Annals of Operations Research, Springer, vol. 87(0), pages 103-116, April.
    4. Retsef Levi & Martin Pál & Robin O. Roundy & David B. Shmoys, 2007. "Approximation Algorithms for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 284-302, May.
    5. Guillermo Gallego & Özalp Özer, 2001. "Integrating Replenishment Decisions with Advance Demand Information," Management Science, INFORMS, vol. 47(10), pages 1344-1360, October.
    6. Retsef Levi & Cong Shi, 2013. "Approximation Algorithms for the Stochastic Lot-Sizing Problem with Order Lead Times," Operations Research, INFORMS, vol. 61(3), pages 593-602, June.
    7. Retsef Levi & Ganesh Janakiraman & Mahesh Nagarajan, 2008. "A 2-Approximation Algorithm for Stochastic Inventory Control Models with Lost Sales," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 351-374, May.
    8. Steven Nahmias, 1976. "Myopic Approximations for the Perishable Inventory Problem," Management Science, INFORMS, vol. 22(9), pages 1002-1008, May.
    9. Brant E. Fries, 1975. "Optimal Ordering Policy for a Perishable Commodity with Fixed Lifetime," Operations Research, INFORMS, vol. 23(1), pages 46-61, February.
    10. Zhaotong Lian & Liming Liu & Marcel F. Neuts, 2005. "A Discrete-Time Model for Common Lifetime Inventory Systems," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 718-732, August.
    11. Steven Nahmias, 1978. "The Fixed-Charge Perishable Inventory Problem," Operations Research, INFORMS, vol. 26(3), pages 464-481, June.
    12. Steven Nahmias, 1977. "Higher-Order Approximations for the Perishable-Inventory Problem," Operations Research, INFORMS, vol. 25(4), pages 630-640, August.
    13. Gregory P. Prastacos, 1984. "Blood Inventory Management: An Overview of Theory and Practice," Management Science, INFORMS, vol. 30(7), pages 777-800, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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).
    5. 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.
    6. 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).
    7. 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.
    8. 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.
    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. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. William L. Cooper, 2001. "Pathwise Properties and Performance Bounds for a Perishable Inventory System," Operations Research, INFORMS, vol. 49(3), pages 455-466, June.
    4. 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.
    5. 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.
    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. 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.
    8. 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.
    9. Elena Katok & Andrew Lathrop & William Tarantino & Susan H. Xu, 2001. "Jeppesen Uses a Dynamic-Programming-Based DSS to Manage Inventory," Interfaces, INFORMS, vol. 31(6), pages 54-65, December.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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).
    15. Van-Anh Truong, 2014. "Approximation Algorithm for the Stochastic Multiperiod Inventory Problem via a Look-Ahead Optimization Approach," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1039-1056, November.
    16. 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.
    17. Li‐Ming Chen & Amar Sapra, 2013. "Joint inventory and pricing decisions for perishable products with two‐period lifetime," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(5), pages 343-366, August.
    18. 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.
    19. 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.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:64:y:2016:i:2:p:432-440. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.