IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v72y2010i2p217-247.html
   My bibliography  Save this article

Continuous review inventory models for perishable items ordered in batches

Author

Listed:
  • Opher Baron
  • Oded Berman
  • David Perry

Abstract

This paper is an in-depth treatment of an inventory control problem with perishable items. We focus on two prototypes of perishability for items that have a common shelflife and that arrive in batches with zero lead time: (i) sudden deaths due to disasters (e.g., spoilage because of extreme weather conditions or a malfunction of the storage place) and (ii) outdating due to expirations (e.g., medicine or food items that have an expiry date). By using known mathematical tools we generalize the stochastic analysis of continuous review (s, S) policies to our problems. This is achieved by integrating with each inventory cycle stopping times that are independent of the inventory level. We introduce special cases of compound Poisson demand processes with negative jumps and consider demands (jumps) that are exponentially distributed or of a unit (i.e., Poisson) demand. For these special cases we derive a closed form expression of the total cost, including that of perishable items, given any order up to level. Since the stochastic analysis leads to tractable expressions only under specific assumptions, as an added benefit we use a fluid approximation of the inventory level to develop efficient heuristics that can be used in general settings. Numerical results comparing the solution of the heuristics with exact or simulated optimal solutions show that the approximation is accurate. Copyright Springer-Verlag 2010

Suggested Citation

  • Opher Baron & Oded Berman & David Perry, 2010. "Continuous review inventory models for perishable items ordered in batches," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 217-247, October.
    • Handle: RePEc:spr:mathme:v:72:y:2010:i:2:p:217-247
    DOI: 10.1007/s00186-010-0318-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-010-0318-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-010-0318-1?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Arvind Rajan & Richard Rakesh, 1992. "Dynamic Pricing and Ordering Decisions by a Monopolist," Management Science, INFORMS, vol. 38(2), pages 240-262, February.
    2. Stephen C. Graves, 1982. "The Application of Queueing Theory to Continuous Perishable Inventory Systems," Management Science, INFORMS, vol. 28(4), pages 400-406, April.
    3. Steven Nahmias, 1982. "Perishable Inventory Theory: A Review," Operations Research, INFORMS, vol. 30(4), pages 680-708, August.
    4. 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.
    5. Jing-Sheng Song & Paul H. Zipkin, 1996. "Managing Inventory with the Prospect of Obsolescence," Operations Research, INFORMS, vol. 44(1), pages 215-222, February.
    6. Howard J. Weiss, 1980. "Optimal Ordering Policies for Continuous Review Perishable Inventory Models," Operations Research, INFORMS, vol. 28(2), pages 365-374, April.
    7. Song, Yuyue & Lau, Hoong Chuin, 2004. "A periodic-review inventory model with application to the continuous-review obsolescence problem," European Journal of Operational Research, Elsevier, vol. 159(1), pages 110-120, November.
    8. Israel David & Avraham Mehrez, 1995. "An Inventory Model with Exogenous Failures," Operations Research, INFORMS, vol. 43(5), pages 902-903, October.
    9. 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.
    10. Cobbaert, Koen & Van Oudheusden, Dirk, 1996. "Inventory models for fast moving spare parts subject to "sudden death" obsolescence," International Journal of Production Economics, Elsevier, vol. 44(3), pages 239-248, 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. P., Vijaya Laxmi & M.L., Soujanya, 2015. "Perishable inventory system with service interruptions, retrial demands and negative customers," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 102-110.
    2. Barron, Yonit, 2022. "The continuous (S,s,Se) inventory model with dual sourcing and emergency orders," European Journal of Operational Research, Elsevier, vol. 301(1), pages 18-38.
    3. V. Yadavalli & Diatha Sundar & Swaminathan Udayabaskaran, 2015. "Two substitutable perishable product disaster inventory systems," Annals of Operations Research, Springer, vol. 233(1), pages 517-534, October.
    4. Mohammad Shokouhifar & Alireza Goli, 2023. "Designing a Resilient–Sustainable Supply Chain Network of Age-Differentiated Blood Platelets Using Vertical–Horizontal Transshipment and Grey Wolf Optimizer," IJERPH, MDPI, vol. 20(5), pages 1-20, February.
    5. Y. Barron, 2019. "A state-dependent perishability (s, S) inventory model with random batch demands," Annals of Operations Research, Springer, vol. 280(1), pages 65-98, September.
    6. Najla Alemsan & Guilherme Luz Tortorella & Alejandro Francisco Mac Cawley Vergara & Carlos Manuel Taboada Rodriguez & Alberto Portioli Staudacher, 2022. "Implementing a material planning and control method for special nutrition in a Brazilian public hospital," International Journal of Health Planning and Management, Wiley Blackwell, vol. 37(1), pages 202-213, January.
    7. Onno Boxma & David Perry & Wolfgang Stadje & Shelley Zacks, 2022. "A compound Poisson EOQ model for perishable items with intermittent high and low demand periods," Annals of Operations Research, Springer, vol. 317(2), pages 439-459, October.
    8. S. R. Chakravarthy & Arunava Maity & U. C. Gupta, 2017. "An ‘(s, S)’ inventory in a queueing system with batch service facility," Annals of Operations Research, Springer, vol. 258(2), pages 263-283, November.
    9. Onno Boxma & David Perry & Shelley Zacks, 2015. "A Fluid EOQ Model of Perishable Items with Intermittent High and Low Demand Rates," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 390-402, February.
    10. Lamay Bin Sabir & Jamal A. Farooquie, 2018. "Effect of Different Dimensions of Inventory Management of Fruits and Vegetables on Profitability of Retail Stores: An Empirical Study," Global Business Review, International Management Institute, vol. 19(1), pages 99-110, February.

    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. Onno Boxma & David Perry & Shelley Zacks, 2015. "A Fluid EOQ Model of Perishable Items with Intermittent High and Low Demand Rates," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 390-402, February.
    2. Onno Boxma & David Perry & Wolfgang Stadje & Shelley Zacks, 2022. "A compound Poisson EOQ model for perishable items with intermittent high and low demand periods," Annals of Operations Research, Springer, vol. 317(2), pages 439-459, October.
    3. 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.
    4. van Jaarsveld, Willem & Dekker, Rommert, 2011. "Estimating obsolescence risk from demand data to enhance inventory control--A case study," International Journal of Production Economics, Elsevier, vol. 133(1), pages 423-431, September.
    5. Goyal, S. K. & Giri, B. C., 2001. "Recent trends in modeling of deteriorating inventory," European Journal of Operational Research, Elsevier, vol. 134(1), pages 1-16, October.
    6. M. Amirthakodi & V. Radhamani & B. Sivakumar, 2015. "A perishable inventory system with service facility and feedback customers," Annals of Operations Research, Springer, vol. 233(1), pages 25-55, October.
    7. Kouki, Chaaben & Sahin, Evren & Jemaï, Zied & Dallery, Yves, 2013. "Assessing the impact of perishability and the use of time temperature technologies on inventory management," International Journal of Production Economics, Elsevier, vol. 143(1), pages 72-85.
    8. R. Suganya & Lewis Nkenyereye & N. Anbazhagan & S. Amutha & M. Kameswari & Srijana Acharya & Gyanendra Prasad Joshi, 2021. "Perishable Inventory System with N-Policy, MAP Arrivals, and Impatient Customers," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    9. Onur Kaya & Sajjad Rahimi Ghahroodi, 2018. "Inventory control and pricing for perishable products under age and price dependent stochastic demand," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(1), pages 1-35, August.
    10. Aswin Dhamodharan & Ruben Proano, 2012. "Determining the optimal vaccine vial size in developing countries: a Monte Carlo simulation approach," Health Care Management Science, Springer, vol. 15(3), pages 188-196, September.
    11. 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.
    12. Song, Yuyue & Lau, Hoong Chuin, 2004. "A periodic-review inventory model with application to the continuous-review obsolescence problem," European Journal of Operational Research, Elsevier, vol. 159(1), pages 110-120, November.
    13. Zahra Azadi & Harsha Gangammanavar & Sandra Eksioglu, 2020. "Developing childhood vaccine administration and inventory replenishment policies that minimize open vial wastage," Annals of Operations Research, Springer, vol. 292(1), pages 215-247, September.
    14. 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.
    15. 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.
    16. Ruibin Bai & Graham Kendall, 2008. "A Model for Fresh Produce Shelf-Space Allocation and Inventory Management with Freshness-Condition-Dependent Demand," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 78-85, February.
    17. Avi Herbon & Uriel Spiegel & Joseph Templeman, 2012. "Simulation study of the price differentiation effect in a stochastic deteriorating inventory with heterogeneous consumers -- freshness sensitivity," Applied Economics, Taylor & Francis Journals, vol. 44(24), pages 3101-3119, August.
    18. Ravichandran, N., 1995. "Stochastic analysis of a continuous review perishable inventory system with positive lead time and Poisson demand," European Journal of Operational Research, Elsevier, vol. 84(2), pages 444-457, July.
    19. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2016. "A coordinated multi-item inventory system for perishables with random lifetime," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 226-237.
    20. Tang, Kwei & Gong, Linguo & Chang, Dong-Shang, 2003. "Optimal process control policies under a time-varying cost structure," European Journal of Operational Research, Elsevier, vol. 149(1), pages 197-210, August.

    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:spr:mathme:v:72:y:2010:i:2:p:217-247. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.