Investigation of inventory model of type (s,S) with asymptotic and approximate methods when demand distribution are heavy tailed with finite variance

In this thesis study a semi-Markovian inventory model of type (s,S) is modelled with the help of a stochastic process known as the renewal reward process. In this process, it is assumed that the demand random variables have a heavy tail distribution from the D∩L class first and then the R_α class. Thus, the effect of the heavy-tail distributions from these classes is investigated on the characteristics of inventory model of type (s,S). In the renewal process, the asymptotic expansion proposed by Emrechts and Omey (1984) for the renewal function which is generated by the D∩L class of random variables was used and the asymptotic expansions for ergodic distribution function of the process were reached by applying this asymptotic expansion. Subsequently, approximate results proposed by Mitov and Omey (2014) for the renewal function generated by random variables from the R_α class have been applied to the system and approximate solutions have been obtained for the ergodic distribution function.