Investigation of inventory model of type (s,S) with asymptotic metdods when demand distributions are in heavy tailed Gamma-g class

The aim of this study is to examine inventory model of type (s, S), one of the stock control models in the literature, with demand quantities distributed from Gamma-g class belonging to heavy tailed distributions. In this way, it is aimed to complete the lack in the literature by using approximate methods for mathematical analysis of inventory model of type (s, S) with heavy tailed distributions. In order to analyze the effects of unexpected fluctuations in demand on these models, it is important to investigate stock control models with heavy-tail demand quantities in the gamma class by approximate methods. In this study, firstly, a detailed literature review about Gamma-g class of heavy-tailed distributions will be discussed. Then, an inventory model of type (s,S) will be represented with a semi-Markovian model called a renewal reward process. A stochastic process which expresses this model will be constructed mathematically. When the random variables that make up the renewal function in the renewal process have the Gamma-g class of heavy-tailed distributions, approximate expansions for the ergodic distribution function of the constructed process will be achieved using approximate expansions proposed by Mitov and Omey (2014). Then, an asymptotic expansion for nth order finite moments of the ergodic distribution function will be obtained. Finally, weak convergence theorem will be expressed and proved for the ergodic distribution function.