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Title: On The Moments For Ergodic Distribution Of An Inventory Model Of Type (S, S) With Regularly Varying Demands Having Infinite Variance
Authors: Kamışlık, Aslı Bektaş
Kesemen, Tülay
Khaniyev, Tahir
Keywords: Semi Markovian Inventory Model
Renewal Reward Process
Regular Variation
Asymptotic Expansion
Issue Date: 2018
Publisher: Turkic World Mathematical Soc
Source: Kesemen, T., & Khaniyev, T. (2018). On The Moments For Ergodic Distribution Of An Inventory Model Of Type (S; S) With Regularly Varying Demands Having Infinite Variance. TWMS Journal of Applied and Engineering Mathematics, 8(1a), 318.
Abstract: In this study a stochastic process X(t) which represents a semi Markovian inventory model of type (s,S) has been considered in the presence of regularly varying tailed demand quantities. The main purpose of the current study is to investigate the asymptotic behavior of the moments of ergodic distribution of the process X(t) when the demands have any arbitrary distribution function from the regularly varying subclass of heavy tailed distributions with in finite variance. In order to obtain renewal function generated by the regularly varying random variables, we used a special asymptotic expansion provided by Geluk [14]. As a first step we investigate the current problem with the whole class of regularly varying distributions with tail parameter 1 < alpha < 2 rather than a single distribution. We obtained a general formula for the asymptotic expressions of nth order moments (n = 1, 2, 3, ...) of ergodic distribution of the process X(t). Subsequently we consider this system with Pareto distributed demand random variables and apply obtained results in this special case.
[Kamislik, A. Bektas] Recep Tayyip Erdogan Univ, Fac Arts & Sci, Dept Math, Rize, Turkey; [Kesemen, T.] Karadeniz Tech Univ, Fac Sci, Dept Math, Trabzon, Turkey; [Khaniyev, T.] TOBB Univ Econ & Technol, Fac Engn, Dept Ind Engn, Ankara, Turkey
ISSN: 2146-1147
Appears in Collections:Endüstri Mühendisliği Bölümü / Department of Industrial Engineering
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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