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

Khaniyev Tahir | Zendy; Kokangul Ali | Zendy; Aliyev Rovshan | Zendy

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

Author(s) -

Khaniyev Tahir,

Kokangul Ali,

Aliyev Rovshan

Publication year - 2012

Publication title -

applied stochastic models in business and industry

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.413

H-Index - 40

eISSN - 1526-4025

pISSN - 1524-1904

DOI - 10.1002/asmb.1918

Subject(s) - ergodic theory , type (biology) , mathematics , markov process , distribution (mathematics) , order (exchange) , statistical physics , stochastic process , pure mathematics , mathematical economics , combinatorics , mathematical analysis , physics , statistics , economics , ecology , finance , biology

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 n th 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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