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

Bektaş Kamışlık A., Alakoç B., Kesemen T., Khaniyev T.

Journal of the Turkish Operations Management (JTOM), cilt.7, sa.1, ss.1483-1492, 2023 (Hakemli Dergi) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.56554/jtom.1226349
  • Dergi Adı: Journal of the Turkish Operations Management (JTOM)
  • Derginin Tarandığı İndeksler: Central & Eastern European Academic Source (CEEAS), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1483-1492
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

This paper concerns a stochastic process expressing (s,S) type inventory system with intuitive approximation approach. The stock level in the system is modeled as a semi-Markovian renewal reward process X(t). Therefore, the ergodic distributions of this process can be analyzed with the help of the renewal function. Obtaining explicit formula for renewal function U(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 X(t). Obtained results can be used in many situations where demand random variables have different distributions from different classes such as Γ(g) class.