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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 5

Steady-state analysis and optimization of a queueing-inventory system under joint impact of imperfect production and inspection processes

Şerife Özkar(BALIKESİR ÜNİVERSİTESİ)0000-0003-3475-5666
Umay Uzunoğlu Koçer(DOKUZ EYLUL UNIVERSITY)0000-0001-5044-6236
Pages
—
Publication Date
2026-10-28
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AI Summary & Key Takeaways

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

The results indicate that production, inspection, and service rates must be adjusted jointly according to the probability of defect and the capacity of the depot to achieve the minimum cost.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:During the production process, defective production rates as well as inspection processes become essential, as customers have become increasingly attentive to the quality of the products they receive.
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Key Findings & Data:The stability condition is derived, and several key performance measures are obtained.
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Conclusion & Impact:The results indicate that production, inspection, and service rates must be adjusted jointly according to the probability of defect and the capacity of the depot to achieve the minimum cost.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Imperfect inspection · imperfect production · finite capacity depots

Abstract

During the production process, defective production rates as well as inspection processes become essential, as customers have become increasingly attentive to the quality of the products they receive. This paper aims to analyze a queueing-inventory system in which both the production and inspection processes are imperfect. The novelty of this study lies in the combination of these two imperfections in a single inventory-queueing system. The inspection process involves two kinds of misclassification errors: Type-I occurs when a non-defective item is identified as defective, while Type-II occurs when a defective item is incorrectly labeled as non-defective. Two storage facilities of limited capacity are considered, one allocated for all produced items and the other reserved for items deemed non-defective after inspection, and a production process controlled by an $(s, S)$-policy. The proposed model is formulated as a continuous-time Markov chain and analyzed by the Matrix Geometric Method. The stability condition is derived, and several key performance measures are obtained. The cost function is then constructed and minimized with respect to production, inspection, and service rates using the Particle Swarm Optimization algorithm. The numerical study shows that the probability of defective production has a considerable impact on all performance measures and that the capacity of the second depot affects both the mean number of customers in the system and the total cost. The results indicate that production, inspection, and service rates must be adjusted jointly according to the probability of defect and the capacity of the depot to achieve the minimum cost.

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Cite This Article

Özkar, Ş., Koçer, U. U. (2026). Steady-state analysis and optimization of a queueing-inventory system under joint impact of imperfect production and inspection processes. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 5. https://doi.org/10.15672/hujms.1896092

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