Investigation of inventory model of type (s,S) with certain subclasses of heavy tailed distributions

The aim of this study is to investigate an inventory model of type (s,S) with heavy tailed demands and to observe the impact of heavy tailed distributions on this model. It is important to investigate stock control models with heavy tailed demand quantities in order to analyze the effects of unexpected fluctuations of demands on these models. As a first step all subclasses of heavy-tailed distributions and their properties 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. Our goal is to observe the impacts of the different tail structure of heavy tailed distributions on inventory model of type (s,S). To achieve this goal an asymptotic expansion for ergodic distribution function and nth order moments of the ergodic distribution function will be obtained by using asymptotic methods. Then weak convergence theorem will be proved for the ergodic distribution function. Moreover by using Monte-Carlo simulation method, the accuracy between the moments obtained by using asymptotic formulas and exact formulas will be tested.