Investigation the ergodic distribution of a semi-Markovian inventory model of type (s,S) with intuitive approximation approach

Abstract

This paper concerns a stochastic process X(t) expressing (s, S) type inventory system with intuitive approximation approach. The ergodic distributions of the process X(t) can be analyzed with the help of the renewal function. Obtaining an explicit formula for renewal function U(x) is difficult from a practical standpoint. Mitov and Omey recently present some intuitive approximations in literature for renewal function which cover a large number of existing results. Using their approach we were able to establish asymptotic approximations for ergodic distribution of a stochastic process X(t). Obtained results can be used in many situations where demand random variables have different distributions from different classes such as the r(g) class.