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Service levels in distribution systems with random customer order size

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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