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Order‐statistic calculation, costs, and service in an (s, Q) inventory system

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  • Anne E. Lordahl
  • James H. Bookbinder

Abstract

A retailer or distributor of finished goods, or the manager of a spare‐parts inventory system, must generally forecast the major portion of demand. A specific customer‐service level p (fraction of replenishment intervals with no stockout) implies two challenges: achieve the service within a small interval plus or minus, and do so with a minimum‐cost investment in inventory. The pth fractile of lead‐time demand (LTD) is the reorder point (ROP) for this service measure, and is often approximated by that fractile of a normal distribution. With this procedure, it is easy to set safety stocks for an (s, Q) inventory system. However, Bookbinder and Lordahl [2] and others have identified cases where the normal approximation yields excessive costs and/or lower service than desired. This article employs an order‐statistic approach. Using available LTD data, the ROP is simply estimated from one or two of the larger values in the sample. This approach is sufficiently automatic and intuitive for routine implementation in industry, yet is distribution free. The order‐statistic method requires only a small amount of LTD data, and makes no assumptions on the form of the underlying LTD distribution, nor even its parameters μ and ρ. We compare the order‐statistic approach and the normal approximation, first in terms of customer service and then using a model of expected annual cost. Based upon characteristics of the available LTD data, we suggest a procedure to aid a practitioner in choosine between the normal and order‐statistic method. © 1994 John Wiley & Sons, Inc.

Suggested Citation

  • Anne E. Lordahl & James H. Bookbinder, 1994. "Order‐statistic calculation, costs, and service in an (s, Q) inventory system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 81-97, February.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:1:p:81-97
    DOI: 10.1002/1520-6750(199402)41:13.0.CO;2-9
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    References listed on IDEAS

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    1. Tadikamalla, Pandu R, 1984. "A comparison of several approximations to the lead time demand distribution," Omega, Elsevier, vol. 12(6), pages 575-581.
    2. Eliezer Naddor, 1978. "Note--Sensitivity to Distributions in Inventory Systems," Management Science, INFORMS, vol. 24(16), pages 1769-1772, December.
    3. Gary D. Eppen & R. Kipp Martin, 1988. "Determining Safety Stock in the Presence of Stochastic Lead Time and Demand," Management Science, INFORMS, vol. 34(11), pages 1380-1390, November.
    4. Helmut Schneider & Jeffrey L. Ringuest, 1990. "Power Approximation for Computing (s, S) Policies Using Service Level," Management Science, INFORMS, vol. 36(7), pages 822-834, July.
    5. Raymond A. Jacobs & Harvey M. Wagner, 1989. "Reducing Inventory System Costs by Using Robust Demand Estimators," Management Science, INFORMS, vol. 35(7), pages 771-787, July.
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    1. Janssen, E. & Strijbosch, L.W.G. & Brekelmans, R.C.M., 2006. "Assessing the Effects of using Demand Parameters Estimates in Inventory Control," Other publications TiSEM e61834bf-8202-4a25-9311-f, Tilburg University, School of Economics and Management.
    2. Hon‐Shiang Lau & Amy Hing‐Ling Lau, 2003. "Nonrobustness of the normal approximation of lead‐time demand in a (Q, R) system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(2), pages 149-166, March.

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