Student:	Büşra Alakoç
Supervisor:	Prof. Dr. Tülay KESEMEN
Department:	Matematik
Institution:	Graduate School of Natural and Applied Sciences
University:	Karadeniz Technical University Turkey

Title of the Thesis:	INVESTIGATION OF INVENTORY MODEL OF TYPE (s, S) WITH ASYMPTOTIC METDODS WHEN DEMAND DISTRIBUTIONS ARE IN HEAVY TAILED GAMMA-𝑔 CLASS
Level:	M.Sc.
Acceptance Date:	10/1/2020
Number of Pages:	65
Registration Number:	i3717

Summary:

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 heavytailed

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.

Keywords: Inventory model of type (s, S), Renewal reward process, Renewal function,

Ergodic distribution function, Heavy tailed distributions, Gamma-𝑔 class,

Moments of ergodic distribution, Weak convergence.