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Journals / Journal of Turkish Operations Management / 2023 / Cilt: 7 Sayı: 1

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

Aslı BEKTAŞ KAMIŞLIK
Büşra ALAKOÇ
Tulay KESEMEN
Tahir KHANIYEV
Pages
1483–1492
Publication Date
2023-06-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Obtained results can be used in many situations where demand random variables have different distributions from different classes such as Γ(g) class.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper concerns a stochastic process expressing (s,S) type inventory system with intuitive approximation approach.
📊
Key Findings & Data:The stock level in the system is modeled as a semi-Markovian renewal reward process X(t).
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Conclusion & Impact:Obtained results can be used in many situations where demand random variables have different distributions from different classes such as Γ(g) class.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Intuitive approximation · Inventory model of type (s · Renewal reward process

Abstract

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.

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Cite This Article

KAMIŞLIK, A. B., ALAKOÇ, B., KESEMEN, T., KHANIYEV, T. (2023). Investigation the ergodic distribution of a semi-Markovian inventory model of type (s,S) with intuitive approximation approach. Journal of Turkish Operations Management, Cilt: 7 Sayı: 1, 1483–1492. https://ajindex.com/articles/952522

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