IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v287y2020i3p901-915.html
   My bibliography  Save this article

Analysis of base-stock perishable inventory systems with general lifetime and lead-time

Author

Listed:
  • Kouki, Chaaben
  • Legros, Benjamin
  • Zied Babai, M.
  • Jouini, Oualid

Abstract

A base-stock inventory system for perishables with Markovian demand and general lead-time and lifetime distributions is investigated. Using a queueing network model, we derive explicit expressions of the stationary distribution of the inventory state together with the total expected cost in a base-stock system with lost-sales. Next, we show some monotonicity properties of the cost function and propose a procedure to derive the optimal base-stock. Extensions to the backorders case and to a dual-sourcing system with multiple warehouses are also provided. Our results generalize existing ones from the literature where the lifetime and the lead-time follow either deterministic or exponential distributions. Finally, we investigate the effect of the lifetime and lead-time variability on the system cost and the optimal base-stock level. In particular, we show the substantial errors made when assuming deterministic or exponential distributions for the lifetime. This further shows the need to have results beyond exponential or deterministic assumptions.

Suggested Citation

  • Kouki, Chaaben & Legros, Benjamin & Zied Babai, M. & Jouini, Oualid, 2020. "Analysis of base-stock perishable inventory systems with general lifetime and lead-time," European Journal of Operational Research, Elsevier, vol. 287(3), pages 901-915.
    • Handle: RePEc:eee:ejores:v:287:y:2020:i:3:p:901-915
    DOI: 10.1016/j.ejor.2020.05.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221720304549
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2020.05.024?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. Liu, Liming & Yang, Tao, 1999. "An (s,[punctuation space]S) random lifetime inventory model with a positive lead time," European Journal of Operational Research, Elsevier, vol. 113(1), pages 52-63, February.
    2. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Indifferent Clerks," Operations Research, INFORMS, vol. 5(5), pages 644-649, October.
    3. Fredrik Olsson, 2014. "Analysis of inventory policies for perishable items with fixed leadtimes and lifetimes," Annals of Operations Research, Springer, vol. 217(1), pages 399-423, June.
    4. Minner, Stefan & Transchel, Sandra, 2017. "Order variability in perishable product supply chains," European Journal of Operational Research, Elsevier, vol. 260(1), pages 93-107.
    5. Olsson, Fredrik & Tydesjö, Patrik, 2010. "Inventory problems with perishable items: Fixed lifetimes and backlogging," European Journal of Operational Research, Elsevier, vol. 202(1), pages 131-137, April.
    6. Kouki, Chaaben & Babai, M. Zied & Minner, Stefan, 2018. "On the benefit of dual-sourcing in managing perishable inventory," International Journal of Production Economics, Elsevier, vol. 204(C), pages 1-17.
    7. Emre Berk & Ülkü Gürler, 2008. "Analysis of the ( Q , r ) Inventory Model for Perishables with Positive Lead Times and Lost Sales," Operations Research, INFORMS, vol. 56(5), pages 1238-1246, October.
    8. Tekin, Eylem & Gurler, Ulku & Berk, Emre, 2001. "Age-based vs. stock level control policies for a perishable inventory system," European Journal of Operational Research, Elsevier, vol. 134(2), pages 309-329, October.
    9. 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.
    10. Fransoo, Jan C. & Sridharan, V. & Bertrand, J.Will M., 1995. "A hierarchical approach for capacity coordination in multiple products single-machine production systems with stationary stochastic demands," European Journal of Operational Research, Elsevier, vol. 86(1), pages 57-72, October.
    11. Song-Hee Kim & Ward Whitt, 2014. "Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 464-480, July.
    12. Jing-Sheng Song & Paul Zipkin, 2009. "Inventories with Multiple Supply Sources and Networks of Queues with Overflow Bypasses," Management Science, INFORMS, vol. 55(3), pages 362-372, March.
    13. M Bijvank & I F A Vis, 2012. "Inventory control for point-of-use locations in hospitals," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(4), pages 497-510, April.
    14. Lengu, D. & Syntetos, A.A. & Babai, M.Z., 2014. "Spare parts management: Linking distributional assumptions to demand classification," European Journal of Operational Research, Elsevier, vol. 235(3), pages 624-635.
    15. Haijema, René & Minner, Stefan, 2019. "Improved ordering of perishables: The value of stock-age information," International Journal of Production Economics, Elsevier, vol. 209(C), pages 316-324.
    16. Janssen, Larissa & Claus, Thorsten & Sauer, Jürgen, 2016. "Literature review of deteriorating inventory models by key topics from 2012 to 2015," International Journal of Production Economics, Elsevier, vol. 182(C), pages 86-112.
    17. Legros, Benjamin, 2020. "Late-rejection, a strategy to perform an overflow policy," European Journal of Operational Research, Elsevier, vol. 281(1), pages 66-76.
    18. Kamran Moinzadeh & Charles P. Schmidt, 1991. "An (S − 1, S) Inventory System with Emergency Orders," Operations Research, INFORMS, vol. 39(2), pages 308-321, April.
    19. Haijema, René & Minner, Stefan, 2016. "Stock-level dependent ordering of perishables: A comparison of hybrid base-stock and constant order policies," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 215-225.
    20. Bakker, Monique & Riezebos, Jan & Teunter, Ruud H., 2012. "Review of inventory systems with deterioration since 2001," European Journal of Operational Research, Elsevier, vol. 221(2), pages 275-284.
    21. 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.
    22. Logachov, A. & Logachova, O. & Yambartsev, A., 2019. "Large deviations in a population dynamics with catastrophes," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 29-37.
    23. Haijema, Rene, 2014. "Optimal ordering, issuance and disposal policies for inventory management of perishable products," International Journal of Production Economics, Elsevier, vol. 157(C), pages 158-169.
    24. Steven Nahmias, 1977. "On Ordering Perishable Inventory when Both Demand and Lifetime are Random," Management Science, INFORMS, vol. 24(1), pages 82-90, September.
    25. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Ordered Service," Operations Research, INFORMS, vol. 5(5), pages 650-656, October.
    26. Charles P. Schmidt & Steven Nahmias, 1985. "(S - 1, S) Policies for Perishable Inventory," Management Science, INFORMS, vol. 31(6), pages 719-728, June.
    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. Gorria, Carlos & Lezaun, Mikel & López, F. Javier, 2022. "Performance measures of nonstationary inventory models for perishable products under the EWA policy," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1137-1150.
    2. Yan, Xiaoming & Chao, Xiuli & Lu, Ye, 2024. "Optimal control policies for dynamic inventory systems with service level dependent demand," European Journal of Operational Research, Elsevier, vol. 314(3), pages 935-949.
    3. Siawsolit, Chokdee & Gaukler, Gary M., 2021. "Offsetting omnichannel grocery fulfillment cost through advance ordering of perishables," International Journal of Production Economics, Elsevier, vol. 239(C).
    4. Zhou, Haijie & Chen, Kebing & Wang, Shengbin, 2023. "Two-period pricing and inventory decisions of perishable products with partial lost sales," European Journal of Operational Research, Elsevier, vol. 310(2), pages 611-626.
    5. Arunmozhi, Manimuthu & Venkatesh, V.G. & Arisian, Sobhan & Shi, Yangyan & Raja Sreedharan, V., 2022. "Application of blockchain and smart contracts in autonomous vehicle supply chains: An experimental design," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 165(C).
    6. Manik Debnath & Sanat Kr. Mazumder & Md Billal Hossain & Arindam Garai & Csaba Balint Illes, 2023. "Optimal Base-Stock Inventory-Management Policies of Cement Retailers under Supply-Side Disruptions," Mathematics, MDPI, vol. 11(18), pages 1-34, September.
    7. 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).
    8. Hanukov, Gabi, 2022. "Improving efficiency of service systems by performing a part of the service without the customer's presence," European Journal of Operational Research, Elsevier, vol. 302(2), pages 606-620.
    9. Yonit Barron, 2024. "Shortage Policies for a Jump Process with Positive and Negative Batch Arrivals in a Random Environment," Mathematics, MDPI, vol. 12(9), pages 1-30, April.

    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. Kouki, Chaaben & Babai, M. Zied & Minner, Stefan, 2018. "On the benefit of dual-sourcing in managing perishable inventory," International Journal of Production Economics, Elsevier, vol. 204(C), pages 1-17.
    2. Dehghani, Maryam & Abbasi, Babak, 2018. "An age-based lateral-transshipment policy for perishable items," International Journal of Production Economics, Elsevier, vol. 198(C), pages 93-103.
    3. Hansen, Ole & Transchel, Sandra & Friedrich, Hanno, 2023. "Replenishment strategies for lost sales inventory systems of perishables under demand and lead time uncertainty," European Journal of Operational Research, Elsevier, vol. 308(2), pages 661-675.
    4. Avinadav, Tal, 2020. "The effect of decision rights allocation on a supply chain of perishable products under a revenue-sharing contract," International Journal of Production Economics, Elsevier, vol. 225(C).
    5. Jake Clarkson & Michael A. Voelkel & Anna‐Lena Sachs & Ulrich W. Thonemann, 2023. "The periodic review model with independent age‐dependent lifetimes," Production and Operations Management, Production and Operations Management Society, vol. 32(3), pages 813-828, March.
    6. Siawsolit, Chokdee & Gaukler, Gary M., 2021. "Offsetting omnichannel grocery fulfillment cost through advance ordering of perishables," International Journal of Production Economics, Elsevier, vol. 239(C).
    7. Ehsan Ahmadi & Dale T. Masel & Seth Hostetler & Reza Maihami & Iman Ghalehkhondabi, 2020. "A centralized stochastic inventory control model for perishable products considering age-dependent purchase price and lead time," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 231-269, April.
    8. Janssen, Larissa & Claus, Thorsten & Sauer, Jürgen, 2016. "Literature review of deteriorating inventory models by key topics from 2012 to 2015," International Journal of Production Economics, Elsevier, vol. 182(C), pages 86-112.
    9. 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.
    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. 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.
    12. Emre Berk & Ülkü Gürler & Saeed Poormoaied, 2020. "On the $$\varvec{(Q,r)}$$(Q,r) policy for perishables with positive lead times and multiple outstanding orders," Annals of Operations Research, Springer, vol. 284(1), pages 81-98, January.
    13. Haijema, René & Minner, Stefan, 2019. "Improved ordering of perishables: The value of stock-age information," International Journal of Production Economics, Elsevier, vol. 209(C), pages 316-324.
    14. Gorria, Carlos & Lezaun, Mikel & López, F. Javier, 2022. "Performance measures of nonstationary inventory models for perishable products under the EWA policy," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1137-1150.
    15. Chernonog, Tatyana, 2020. "Inventory and marketing policy in a supply chain of a perishable product," International Journal of Production Economics, Elsevier, vol. 219(C), pages 259-274.
    16. Fredrik Olsson, 2019. "Simple modeling techniques for base-stock inventory systems with state dependent demand rates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 61-76, August.
    17. Gioia, Daniele Giovanni & Minner, Stefan, 2023. "On the value of multi-echelon inventory management strategies for perishable items with on-/off-line channels," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 180(C).
    18. Poormoaied, Saeed & Atan, Zümbül, 2020. "A multi-attribute utility theory approach to ordering policy for perishable items," International Journal of Production Economics, Elsevier, vol. 225(C).
    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. 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.

    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:eee:ejores:v:287:y:2020:i:3:p:901-915. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.