Investigation the ergodic distribution of a semi-Markovian inventory model of type (s,S) with intuitive approximation approach

Authors : Aslı BEKTAŞ KAMIŞLIK, Büşra ALAKOÇ, Tulay KESEMEN, Tahir KHANIYEV

Pages : 1483-1492

Doi:10.56554/jtom.1226349

View : 27 | Download : 45

Publication Date : 2023-06-30

Article Type : Research Paper

Abstract :This paper concerns a stochastic process expressing insert ignore into journalissuearticles values(s,S); type inventory system with intuitive approximation approach. The stock level in the system is modeled as a semi-Markovian renewal reward process Xinsert ignore into journalissuearticles values(t);. Therefore, the ergodic distributions of this process can be analyzed with the help of the renewal function. Obtaining explicit formula for renewal function Uinsert ignore into journalissuearticles values(x); is difficult from a practical standpoint. Mitov and Omey recently present some intuitive approximations in literature for renewal function which cover a large number of existing results. Using their approach we were able to establish asymptotic approximations for ergodic distribution of a stochastic process Xinsert ignore into journalissuearticles values(t);. Obtained results can be used in many situations where demand random variables have different distributions from different classes such as Γinsert ignore into journalissuearticles values(g); class.
Keywords : Intuitive approximation, Inventory model of type s, S, Renewal reward process, Ergodic distribution, Γ g, class of distributions