IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01742197.html
   My bibliography  Save this paper

Solution procedures for lost sales base-stock inventory systems with compound Poisson demand

Author

Listed:
  • Zied Jemai

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

  • Chaaben Kouki

    (ESSCA Research Lab - ESSCA - Ecole Supérieure des Sciences Commerciales d'Angers)

  • Mohamed Zied Babai

    (Kedge Business School [Talence])

  • Stefan Minner

    (TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich)

Abstract

The continuous review base-stock policy under the lost sales assumption has been extensively studied in the inventory literature. However, most of the research that deals with the optimal policy parameter determination under compound Poisson demand focuses on the stuttering Poisson case. In this paper, we extend earlier research by providing a method that calculates the best cost-driven base-stock policy under more general compound Poisson demand processes and for both the complete and the partial rejection case. This is done by developing a simple recursive formula that computes the steady-state probabilities of the number of outstanding orders for general demand and lead-time distributions. Based on this, we are able to obtain the optimal base-stock level under the complete rejection case and an approximate base-stock level under the partial rejection policy. Through a numerical investigation, we show that our approach outperforms existing methods with regard to computational requirements.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Zied Jemai & Chaaben Kouki & Mohamed Zied Babai & Stefan Minner, 2019. "Solution procedures for lost sales base-stock inventory systems with compound Poisson demand," Post-Print hal-01742197, HAL.
    • Handle: RePEc:hal:journl:hal-01742197
    DOI: 10.1016/j.ijpe.2018.01.021
    Note: View the original document on HAL open archive server: https://hal.science/hal-01742197
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01742197/document
    Download Restriction: no
    File URL: https://libkey.io/10.1016/j.ijpe.2018.01.021?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Johansen, Søren Glud, 2013. "Modified base-stock policies for continuous-review, lost-sales inventory models with Poisson demand and a fixed lead time," International Journal of Production Economics, Elsevier, vol. 143(2), pages 379-384.
    2. Jie Chen & Peter L. Jackson & John A. Muckstadt, 2011. "TECHNICAL NOTE---Exact Analysis of a Lost Sales Model Under Stuttering Poisson Demand," Operations Research, INFORMS, vol. 59(1), pages 249-253, February.
    3. Ganesh Janakiraman & Robin O. Roundy, 2004. "Lost-Sales Problems with Stochastic Lead Times: Convexity Results for Base-Stock Policies," Operations Research, INFORMS, vol. 52(5), pages 795-803, October.
    4. F R Johnston & J E Boylan & E A Shale, 2003. "An examination of the size of orders from customers, their characterisation and the implications for inventory control of slow moving items," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 833-837, August.
    5. Paul Zipkin, 1991. "Evaluation of base‐stock policies in multiechelon inventory systems with compound‐poisson demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 397-412, June.
    6. Hill, Roger M., 1999. "On the suboptimality of (S-1, S) lost sales inventory policies," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 387-393, March.
    7. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    8. 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.
    9. Ward Whitt, 1980. "Continuity of Generalized Semi-Markov Processes," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 494-501, November.
    10. Marco Bijvank & Woonghee Tim Huh & Ganesh Janakiraman & Wanmo Kang, 2014. "Robustness of Order-Up-to Policies in Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 62(5), pages 1040-1047, October.
    11. G. J. Feeney & C. C. Sherbrooke, 1966. "The (S - 1, S) Inventory Policy Under Compound Poisson Demand," Management Science, INFORMS, vol. 12(5), pages 391-411, January.
    12. Disney, Stephen M. & Maltz, Arnold & Wang, Xun & Warburton, Roger D.H., 2016. "Inventory management for stochastic lead times with order crossovers," European Journal of Operational Research, Elsevier, vol. 248(2), pages 473-486.
    13. Johansen, Soren Glud, 2005. "Base-stock policies for the lost sales inventory system with Poisson demand and Erlangian lead times," International Journal of Production Economics, Elsevier, vol. 93(1), pages 429-437, January.
    14. Kamran Moinzadeh, 1989. "Operating Characteristics of the (S - 1, S) Inventory System with Partial Backorders and Constant Resupply Times," Management Science, INFORMS, vol. 35(4), pages 472-477, April.
    15. Jing-Sheng Song, 1994. "The Effect of Leadtime Uncertainty in a Simple Stochastic Inventory Model," Management Science, INFORMS, vol. 40(5), pages 603-613, May.
    16. Riezebos, Jan, 2006. "Inventory order crossovers," International Journal of Production Economics, Elsevier, vol. 104(2), pages 666-675, December.
    17. van Donselaar, Karel & de Kok, Ton & Rutten, Werner, 1996. "Two replenishment strategies for the lost sales inventory model: A comparison," International Journal of Production Economics, Elsevier, vol. 46(1), pages 285-295, December.
    18. C Larsen & A Thorstenson, 2008. "A comparison between the order and the volume fill rate for a base-stock inventory control system under a compound renewal demand process," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(6), pages 798-804, June.
    19. Antony Svoronos & Paul Zipkin, 1991. "Evaluation of One-for-One Replenishment Policies for Multiechelon Inventory Systems," Management Science, INFORMS, vol. 37(1), pages 68-83, January.
    20. Bijvank, Marco & Johansen, Søren Glud, 2012. "Periodic review lost-sales inventory models with compound Poisson demand and constant lead times of any length," European Journal of Operational Research, Elsevier, vol. 220(1), pages 106-114.
    21. Zied Jemai & M. Zied Babai & Y. Dallery, 2011. "Analysis of order-up-to-level inventory systems with compound Poisson demand," Post-Print hal-01672399, HAL.
    22. Johansen, Soren Glud, 2001. "Pure and modified base-stock policies for the lost sales inventory system with negligible set-up costs and constant lead times," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 391-399, May.
    23. Eric Smeitink, 1990. "A Note on "Operating Characteristics of the (S-1, S) Inventory System with Partial Backorders and Constant Resupply Times"," Management Science, INFORMS, vol. 36(11), pages 1413-1414, November.
    24. Babai, M.Z. & Jemai, Z. & Dallery, Y., 2011. "Analysis of order-up-to-level inventory systems with compound Poisson demand," European Journal of Operational Research, Elsevier, vol. 210(3), pages 552-558, May.
    25. Stephen A. Smith, 1977. "Optimal Inventories for an (S - 1, S) System with No Backorders," Management Science, INFORMS, vol. 23(5), pages 522-528, January.
    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. Kouki, Chaaben & Arts, Joachim & Babai, M. Zied, 2024. "Performance evaluation of a two-echelon inventory system with network lost sales," European Journal of Operational Research, Elsevier, vol. 314(2), pages 647-664.
    2. Johansen, Søren Glud, 2021. "The Markov model for base-stock control of an inventory system with Poisson demand, non-crossing lead times and lost sales," International Journal of Production Economics, Elsevier, vol. 231(C).
    3. 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.
    4. Cheng, Lihong & Guo, Xiaolong & Li, Xiaoxiao & Yu, Yugang, 2022. "Data-driven ordering and transshipment decisions for online retailers and logistics service providers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 161(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. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    2. Bijvank, Marco & Vis, Iris F.A., 2012. "Lost-sales inventory systems with a service level criterion," European Journal of Operational Research, Elsevier, vol. 220(3), pages 610-618.
    3. Hill, R.M., 2007. "Continuous-review, lost-sales inventory models with Poisson demand, a fixed lead time and no fixed order cost," European Journal of Operational Research, Elsevier, vol. 176(2), pages 956-963, January.
    4. Prak, Derk & Teunter, Rudolf & Babai, M. Z. & Syntetos, A. A. & Boylan, D, 2018. "Forecasting and Inventory Control with Compound Poisson Demand Using Periodic Demand Data," Research Report 2018010, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    5. Johansen, Søren Glud, 2021. "The Markov model for base-stock control of an inventory system with Poisson demand, non-crossing lead times and lost sales," International Journal of Production Economics, Elsevier, vol. 231(C).
    6. Cai, Gangshu (George) & Chiang, Wen-Chyuan & Chen, Xiangfeng, 2011. "Game theoretic pricing and ordering decisions with partial lost sales in two-stage supply chains," International Journal of Production Economics, Elsevier, vol. 130(2), pages 175-185, April.
    7. Babai, M.Z. & Jemai, Z. & Dallery, Y., 2011. "Analysis of order-up-to-level inventory systems with compound Poisson demand," European Journal of Operational Research, Elsevier, vol. 210(3), pages 552-558, May.
    8. Erica L. Plambeck & Amy R. Ward, 2007. "Note: A Separation Principle for a Class of Assemble-to-Order Systems with Expediting," Operations Research, INFORMS, vol. 55(3), pages 603-609, June.
    9. Kouki, Chaaben & Arts, Joachim & Babai, M. Zied, 2024. "Performance evaluation of a two-echelon inventory system with network lost sales," European Journal of Operational Research, Elsevier, vol. 314(2), pages 647-664.
    10. Johansen, Soren Glud, 2005. "Base-stock policies for the lost sales inventory system with Poisson demand and Erlangian lead times," International Journal of Production Economics, Elsevier, vol. 93(1), pages 429-437, January.
    11. Hayya, Jack C. & Bagchi, Uttarayan & Ramasesh, Ranga, 2011. "Cost relationships in stochastic inventory systems: A simulation study of the (S, S-1, t=1) model," International Journal of Production Economics, Elsevier, vol. 130(2), pages 196-202, April.
    12. Prak, Dennis & Teunter, Ruud & Babai, Mohamed Zied & Boylan, John E. & Syntetos, Aris, 2021. "Robust compound Poisson parameter estimation for inventory control," Omega, Elsevier, vol. 104(C).
    13. Hill, Roger M. & Johansen, Soren Glud, 2006. "Optimal and near-optimal policies for lost sales inventory models with at most one replenishment order outstanding," European Journal of Operational Research, Elsevier, vol. 169(1), pages 111-132, February.
    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. Tan, Ken Seng & Wei, Pengyu & Wei, Wei & Zhuang, Sheng Chao, 2020. "Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle," European Journal of Operational Research, Elsevier, vol. 282(1), pages 345-362.
    16. Lin, X. & Basten, R.J.I. & Kranenburg, A.A. & van Houtum, G.J., 2017. "Condition based spare parts supply," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 240-248.
    17. Ganesh Janakiraman & Robin O. Roundy, 2004. "Lost-Sales Problems with Stochastic Lead Times: Convexity Results for Base-Stock Policies," Operations Research, INFORMS, vol. 52(5), pages 795-803, October.
    18. Emre Tokgöz & Hillel Kumin, 2012. "Mixed convexity and optimization results for an (S − 1, S) inventory model under a time limit on backorders," Computational Management Science, Springer, vol. 9(4), pages 417-440, November.
    19. Achin Srivastav & Sunil Agrawal, 2020. "On a single item single stage mixture inventory models with independent stochastic lead times," Operational Research, Springer, vol. 20(4), pages 2189-2227, December.
    20. Johansen, Søren Glud, 2013. "Modified base-stock policies for continuous-review, lost-sales inventory models with Poisson demand and a fixed lead time," International Journal of Production Economics, Elsevier, vol. 143(2), pages 379-384.

    More about this item

    Statistics

    Access and download statistics

    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:hal:journl:hal-01742197. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.