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A continuous‐review inventory system with lost sales and variable lead time

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  • Esmail Mohebbi
  • Morton J.M. Posner

Abstract

Using a system‐point (SP) method of level crossings, we derive the stationary distribution of the inventory level (stock on hand) in a continuous‐review inventory system with compound Poisson demand, Erlang as well as hyperexponentially distributed lead times, and lost sales. This distribution is then used to formulate long‐run average cost functions with/without a service level constraint. Some numerical results are also presented, and compared with the Hadley and Whitin heuristic. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 259–278, 1998

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  • Esmail Mohebbi & Morton J.M. Posner, 1998. "A continuous‐review inventory system with lost sales and variable lead time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(3), pages 259-278, April.
    • Handle: RePEc:wly:navres:v:45:y:1998:i:3:p:259-278
    DOI: 10.1002/(SICI)1520-6750(199804)45:33.0.CO;2-6
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    References listed on IDEAS

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    1. Johansen, Soren Glud & Thorstenson, Anders, 1993. "Optimal and approximate (Q, r) inventory policies with lost sales and gamma-distributed lead time," International Journal of Production Economics, Elsevier, vol. 30(1), pages 179-194, July.
    2. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    3. 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.
    4. P. H. Brill & M. J. M. Posner, 1977. "Level Crossings in Point Processes Applied to Queues: Single-Server Case," Operations Research, INFORMS, vol. 25(4), pages 662-674, August.
    5. P. H. Brill & M. J. M. Posner, 1981. "The System Point Method in Exponential Queues: A Level Crossing Approach," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 31-49, February.
    6. 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.
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