IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v42y1995i1p39-56.html
   My bibliography  Save this article

Service levels in distribution systems with random customer order size

Author

Listed:
  • E. P. Chew
  • L. A. Johnson

Abstract

An approximate method for measuring the service levels of the warehouse‐retailer system operating under (s, S) policy is presented. All the retailers are identical and the demand process at each retailer follows a stationary stuttering Poisson process. This type of demand process allows customer orders to be for a random number of units, which gives rise to the undershoot quantity at both the warehouse and retailer levels. Exact analyses of the distribution of the undershoot quantity and the number of orders place by a retailer during the warehouse reordering lead time are derived. By using this distribution together with probability approximation and other heuristic approaches, we model the behavior of the warehouse level. Based on the results of the warehouse level and on an existing framework from previous work, the service level at the retailer level is estimated. Results of the approximate method are then compared with those of simulation. © 1995 John Wiley & Sons, Inc.

Suggested Citation

  • E. P. Chew & L. A. Johnson, 1995. "Service levels in distribution systems with random customer order size," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 39-56, February.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:1:p:39-56
    DOI: 10.1002/1520-6750(199502)42:13.0.CO;2-9
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199502)42:13.0.CO;2-9
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199502)42:13.0.CO;2-9?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. Martin Beckmann, 1961. "An Inventory Model for Arbitrary Interval and Quantity Distributions of Demand," Management Science, INFORMS, vol. 8(1), pages 35-57, October.
    2. Ralph D. Badinelli, 1992. "A Model for Continuous-Review Pull Policies in Serial Inventory Systems," Operations Research, INFORMS, vol. 40(1), pages 142-156, February.
    3. Sven Axsäter, 1990. "Simple Solution Procedures for a Class of Two-Echelon Inventory Problems," Operations Research, INFORMS, vol. 38(1), pages 64-69, February.
    4. Kamran Moinzadeh & Hau L. Lee, 1986. "Batch Size and Stocking Levels in Multi-Echelon Repairable Systems," Management Science, INFORMS, vol. 32(12), pages 1567-1581, December.
    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. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    2. Diks, E. B. & de Kok, A. G. & Lagodimos, A. G., 1996. "Multi-echelon systems: A service measure perspective," European Journal of Operational Research, Elsevier, vol. 95(2), pages 241-263, December.

    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. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.
    2. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    3. Hill, R.M. & Seifbarghy, M. & Smith, D.K., 2007. "A two-echelon inventory model with lost sales," European Journal of Operational Research, Elsevier, vol. 181(2), pages 753-766, September.
    4. Sven Axsäter, 1998. "Evaluation of Installation Stock Based (R, Q)-Policies for Two-Level Inventory Systems with Poisson Demand," Operations Research, INFORMS, vol. 46(3-supplem), pages 135-145, June.
    5. Ganesh Janakiraman & John A. Muckstadt, 2009. "A Decomposition Approach for a Class of Capacitated Serial Systems," Operations Research, INFORMS, vol. 57(6), pages 1384-1393, December.
    6. Chen, Frank Y. & Feng, Youyi & Simchi-Levi, David, 2002. "Uniform distribution of inventory positions in two-echelon periodic review systems with batch-ordering policies and interdependent demands," European Journal of Operational Research, Elsevier, vol. 140(3), pages 648-654, August.
    7. Fangruo Chen & Yu-Sheng Zheng, 1998. "Near-Optimal Echelon-Stock (R, nQ) Policies in Multistage Serial Systems," Operations Research, INFORMS, vol. 46(4), pages 592-602, August.
    8. Kim, Ilhyung & Tang, Christopher S., 1997. "Lead time and response time in a pull production control system," European Journal of Operational Research, Elsevier, vol. 101(3), pages 474-485, September.
    9. Chew, E. P. & Johnson, L. A., 1996. "Service level approximations for multiechelon inventory systems," European Journal of Operational Research, Elsevier, vol. 91(3), pages 440-455, June.
    10. Badinelli, Ralph D., 1996. "Approximating probability density functions and their convolutions using orthogonal polynomials," European Journal of Operational Research, Elsevier, vol. 95(1), pages 211-230, November.
    11. Joseph B. Mazzola & William F. McCoy & Harvey M. Wagner, 1987. "Algorithms and heuristics for variable‐yield lot sizing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(1), pages 67-86, February.
    12. 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).
    13. Axsater, Sven & Zhang, Wen-Fa, 1999. "A joint replenishment policy for multi-echelon inventory control," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 243-250, March.
    14. Guide, V. Daniel R. & Srivastava, Rajesh, 1997. "Repairable inventory theory: Models and applications," European Journal of Operational Research, Elsevier, vol. 102(1), pages 1-20, October.
    15. Gérard P. Cachon & Marshall Fisher, 2000. "Supply Chain Inventory Management and the Value of Shared Information," Management Science, INFORMS, vol. 46(8), pages 1032-1048, August.
    16. Hossein Abouee‐Mehrizi & Oded Berman & Hassan Shavandi & Ata G. Zare, 2011. "An exact analysis of a joint production‐inventory problem in two‐echelon inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 713-730, December.
    17. Thangam, A. & Uthayakumar, R., 2008. "A two-level supply chain with partial backordering and approximated Poisson demand," European Journal of Operational Research, Elsevier, vol. 187(1), pages 228-242, May.
    18. Gérard P. Cachon, 2001. "Stock Wars: Inventory Competition in a Two-Echelon Supply Chain with Multiple Retailers," Operations Research, INFORMS, vol. 49(5), pages 658-674, October.
    19. Johansen, Soren Glud & Thorstenson, Anders, 1996. "Optimal (r, Q) inventory policies with Poisson demands and lost sales: discounted and undiscounted cases," International Journal of Production Economics, Elsevier, vol. 46(1), pages 359-371, December.
    20. Berling, Peter & Marklund, Johan, 2013. "A model for heuristic coordination of real life distribution inventory systems with lumpy demand," European Journal of Operational Research, Elsevier, vol. 230(3), pages 515-526.

    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:42:y:1995:i:1:p:39-56. 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.