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On the Stationary Distribution for a Fuzzy Inventory Model of Type (s,S) with Inverse Gaussian Distributed Demands

Iranian Journal of Science and Technology, Transactions A: Science volume 42, pages 2035–2043 (2018)Cite this article

Abstract

In this study, we consider a fuzzy inventory model of type (s,S) with random demands having an inverse Gaussian distribution. We first show the monotonicity of the renewal function with respect to mean parameter. Thus we obtain the membership function of the fuzzy renewal function when the amount of demands is a random variable having an inverse Gaussian distribution with a fuzzy mean parameter by using the monotonicity property of renewal function. Making use of the membership function of the renewal function, we obtain the membership function of the fuzzy ergodic distribution of this process. We also present some numerical results obtained by using this membership function.

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Authors and Affiliations

  1. Department of Industrial Engineering, TOBB University of Economics and Technology, Sogutozu, 06560, Ankara, Turkey

    Tahir Khaniyev & I. Burhan Turksen

  2. Institute of Cybernetics, National Academy of Sciences of Azerbaijan, AZ 1141, Baku, Azerbaijan

    Tahir Khaniyev

  3. Department of Statistics, Gazi University, Teknikokullar, 06500, Ankara, Turkey

    Fikri Gökpınar

  4. Department of Industrial Engineering, Boğaziçi University, Istanbul, Turkey

    Tagi Hanalioglu

  5. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3 G8, Canada

    I. Burhan Turksen

Authors
  1. Tahir Khaniyev
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  2. Fikri Gökpınar
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  3. Tagi Hanalioglu
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  4. I. Burhan Turksen
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Correspondence to Fikri Gökpınar.

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Khaniyev, T., Gökpınar, F., Hanalioglu, T. et al. On the Stationary Distribution for a Fuzzy Inventory Model of Type (s,S) with Inverse Gaussian Distributed Demands. Iran J Sci Technol Trans Sci 42, 2035–2043 (2018). https://doi.org/10.1007/s40995-017-0363-1

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  • DOI: https://doi.org/10.1007/s40995-017-0363-1

Keywords

  • Inverse Gaussian distribution
  • Ergodic distribution
  • Fuzzy inventory model
  • Renewal function