An Asymptotic Approach for a Semi-Markovian Inventory Model of Type (s, S)

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 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 (c) 2012 John Wiley & Sons, Ltd.