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An asymptotic approach for a semi-Markovian inventory model of type (s, S)

Authors

  • Tahir Khaniyev,

    Corresponding author
    • Faculty of Engineering, Department of Industrial Engineering, TOBB University of Economics and Technology, Ankara, Turkey
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  • Ali Kokangul,

    1. Faculty of Engineering and Architecture, Department of Industrial Engineering, Cukurova University, Adana, Turkey
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  • Rovshan Aliyev

    1. Institute of Cybernetics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
    2. Department of Probability Theory and Mathematical Statistics, Baku State University, Baku, Azerbaijan
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Correspondence to: Tahir Khaniyev, Industrial Engineering, TOBB University of Economics and Technology, 06560 Ankara, Turkey.

E-mail: tahirkhaniyev@etu.edu.tr

Abstract

In this study, we constructed a stochastic process (X(t)) that expresses a semi-Markovian inventory model of type (s, S) and it is shown that this process is ergodic under some weak conditions. Moreover, we obtained exact and asymptotic expressions for the nth order moments (n = 1,2,3, … ) of ergodic distribution of the process X(t), as S − s → ∞ . Finally, we tested how close the obtained approximation formulas are to the exact expressions. Copyright © 2012 John Wiley & Sons, Ltd.

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