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A make-to-stock mountain-type inventory model

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  • Onno Boxma
  • Mahmut Parlar
  • David Perry

Abstract

We consider the buffer content of a fluid queue or storage process. The buffer content varies in a way that depends on the state of an underlying three-state Markov process. In state 0 the buffer content increases at a rate α(x) that is a function of the current buffer level x; in states 1 and 2 it decreases linearly, with different speeds. We study the steady-state buffer content, by using level crossing theory and by exploiting relations between the fluid queue and queues with instantaneous input and/or output. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Onno Boxma & Mahmut Parlar & David Perry, 2015. "A make-to-stock mountain-type inventory model," Annals of Operations Research, Springer, vol. 231(1), pages 65-77, August.
    • Handle: RePEc:spr:annopr:v:231:y:2015:i:1:p:65-77:10.1007/s10479-013-1370-z
    DOI: 10.1007/s10479-013-1370-z
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    References listed on IDEAS

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    1. Offer Kella & Ward Whitt, 1992. "A Storage Model with a Two-State Random Environment," Operations Research, INFORMS, vol. 40(3-supplem), pages 257-262, June.
    2. Rubinovitch, Micheal, 1973. "The output of a buffered data communication system," Stochastic Processes and their Applications, Elsevier, vol. 1(4), pages 375-382, October.
    3. Cohen, J. W., 1974. "Superimposed renewal processes and storage with gradual input," Stochastic Processes and their Applications, Elsevier, vol. 2(1), pages 31-57, January.
    4. J. Michael Harrison & Sidney I. Resnick, 1976. "The Stationary Distribution and First Exit Probabilities of a Storage Process with General Release Rule," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 347-358, November.
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