Inventory model of type (8,8) with subexponential weibull distributed demand

Abstract

In this study we consider semi-Markovian inventory model of type (5, S) with Subexponential Weibull distributed demand and uniform distributed interference of chance. By using special asymptotic expansion proposed by Geluk and Frenk (2011) we derived an asymptotic expansion for the renewal function generated by the subexponential Weibull distributed demand random variables. Trough this renewal function we obtained two term asymptotic expansion for the ergodic distribution function of the process which represents the model that we consider here. Moreover we proved weak convergence theorem for the ergodic distribution function and derived the limit distribution.