IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v35y1988i2p247-257.html
   My bibliography  Save this article

The use of phase‐type distributions in inventory‐control models

Author

Listed:
  • Paul Zipkin

Abstract

This article investigates the use of phase‐type distributions to model the demand process and the replenishment leadtimes in the standard reorder‐point/order‐quantity model of inventory control. Our main result is that the marginal distribution of leadtime demand has a discrete phase‐type distribution with the same number of phases as the leadtime distribution, regardless of the complexity of the inter‐demand times. This result leads to relatively tractable formulas for several standard performance criteria.

Suggested Citation

  • Paul Zipkin, 1988. "The use of phase‐type distributions in inventory‐control models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(2), pages 247-257, April.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:2:p:247-257
    DOI: 10.1002/1520-6750(198804)35:23.0.CO;2-L
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198804)35:23.0.CO;2-L
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198804)35:23.0.CO;2-L?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. Neuts, M. F. & Chakravarthy, S., 1981. "A single server queue with platooned arrivals and phase type services," European Journal of Operational Research, Elsevier, vol. 8(4), pages 379-389, December.
    2. Paul Zipkin, 1986. "Stochastic leadtimes in continuous‐time inventory models," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 763-774, November.
    Full references (including those not matched with items on IDEAS)

    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. Ben-Ammar, Oussama & Bettayeb, Belgacem & Dolgui, Alexandre, 2019. "Optimization of multi-period supply planning under stochastic lead times and a dynamic demand," International Journal of Production Economics, Elsevier, vol. 218(C), pages 106-117.
    2. Marcus Ang & Karl Sigman & Jing-Sheng Song & Hanqin Zhang, 2017. "Closed-Form Approximations for Optimal ( r , q ) and ( S , T ) Policies in a Parallel Processing Environment," Operations Research, INFORMS, vol. 65(5), pages 1414-1428, October.
    3. Daniela Favaretto & Alessandro Marin & Marco Tolotti, 2023. "A theoretical validation of the DDMRP reorder policy," Computational Management Science, Springer, vol. 20(1), pages 1-28, December.
    4. Riezebos, Jan & Zhu, Stuart X., 2020. "Inventory control with seasonality of lead times," Omega, Elsevier, vol. 92(C).
    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. 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.
    7. Tamer Boyacı & Guillermo Gallego, 2002. "Managing waiting times of backordered demands in single‐stage (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 557-573, September.
    8. Vipul Agrawal & Sridhar Seshadri, 2000. "Distribution free bounds for service constrained (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 635-656, December.
    9. Jing‐Sheng Song & Paul H. Zipkin, 1992. "Evaluation of base‐stock policies in multiechelon inventory systems with state‐dependent demands part I: State‐independent policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 715-728, August.
    10. Alain Bensoussan & Lama Moussawi-Haidar & Metin Çakanyıldırım, 2010. "Inventory control with an order-time constraint: optimality, uniqueness and significance," Annals of Operations Research, Springer, vol. 181(1), pages 603-640, December.
    11. Michna, Zbigniew & Disney, Stephen M. & Nielsen, Peter, 2020. "The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts," Omega, Elsevier, vol. 93(C).
    12. Awi Federgruen & Linda Green, 1988. "Queueing systems with service interruptions II," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(3), pages 345-358, June.
    13. Tao Lu & Jan C. Fransoo & Chung-Yee Lee, 2017. "Carrier Portfolio Management for Shipping Seasonal Products," Operations Research, INFORMS, vol. 65(5), pages 1250-1266, October.
    14. Yu‐Sheng Zheng & Fangruo Chen, 1992. "Inventory policies with quantized ordering," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 285-305, April.
    15. Ruud Heuts & Jan de Klein, 1995. "An (s, q) inventory model with stochastic and interrelated lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(5), pages 839-859, August.
    16. Yonit Barron & Opher Baron, 2020. "The residual time approach for (Q, r) model under perishability, general lead times, and lost sales," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 601-648, December.
    17. Neda Mirzaeian & Soo-Haeng Cho & Alan Scheller-Wolf, 2021. "A Queueing Model and Analysis for Autonomous Vehicles on Highways," Management Science, INFORMS, vol. 67(5), pages 2904-2923, May.
    18. 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.
    19. F. G. Badía & C. Sangüesa, 2015. "Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(5), pages 345-356, August.
    20. 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.

    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:wly:navres:v:35:y:1988:i:2:p:247-257. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.