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

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  • 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
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    References listed on IDEAS

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    1. Paul Zipkin, 1986. "Stochastic leadtimes in continuous‐time inventory models," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 763-774, November.
    2. 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.
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