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Queueing Theory-Based Mathematical Models Applied to Enterprise Organization and Industrial Production Optimization

Author

Listed:
  • Laurentiu Rece

    (Department of Mechanical Technology, Tehnical University of Civil Engineering of Bucharest, 020396 Bucharest, Romania)

  • Sorin Vlase

    (Department of Mechanical Engineering, Transilvania University of Brasov, B-dul Eroilor 20, 500036 Brasov, Romania
    Romanian Academy of Technical Sciences, B-dul Dacia 26, 030167 Bucharest, Romania)

  • Daniel Ciuiu

    (Department of Mechanical Technology, Tehnical University of Civil Engineering of Bucharest, 020396 Bucharest, Romania)

  • Giorgian Neculoiu

    (Department of Mechanical Technology, Tehnical University of Civil Engineering of Bucharest, 020396 Bucharest, Romania)

  • Stefan Mocanu

    (Department of Mechanical Technology, Tehnical University of Civil Engineering of Bucharest, 020396 Bucharest, Romania)

  • Arina Modrea

    (Faculty of Engineering, George Emil Palade University of Medicine, Pharmacy, Science, and Technology of Targu Mures, 540142 Targu Mures, Romania)

Abstract

In the paper, a new method was presented using queueing theory models in order to ensure an optimal production department size, optimized production costs and optimal provision. Queueing/waiting mathematical models represent the development matrix for an experimental algorithm and implicitly numerical approach, both successfully applied (and confirmed in practice) in a production section design for a real industrial engineering unit with discussed method technological flow and equipment schemes compatibility. The total costs for a queueing system with S servers depend on the number of servers. The problem of minimizing cost in terms of S was the main aim of the paper. In order to solve it, we estimated all the variables of the system that influence the cost using the Monte Carlo method. For a Jackson queueing network, the involved linear system has good properties such that it can be solved by iterative methods such as Jacobi and Gauss–Seidel.

Suggested Citation

  • Laurentiu Rece & Sorin Vlase & Daniel Ciuiu & Giorgian Neculoiu & Stefan Mocanu & Arina Modrea, 2022. "Queueing Theory-Based Mathematical Models Applied to Enterprise Organization and Industrial Production Optimization," Mathematics, MDPI, vol. 10(14), pages 1-32, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2520-:d:867111
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    References listed on IDEAS

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    1. Chen Chen & Lee Kong Tiong, 2019. "Using queuing theory and simulated annealing to design the facility layout in an AGV-based modular manufacturing system," International Journal of Production Research, Taylor & Francis Journals, vol. 57(17), pages 5538-5555, September.
    2. Laurentiu Rece & Virgil Florescu & Arina Modrea & Victor Jeflea & Marta Harničárová & Jan Valíček & Marian Borzan, 2020. "Optimization of the 2 ½ D Processing Method of Complex Parts, through a Predictive Algorithm for Controlling the Geometric Shape Deviations Resulting from Processing," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
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    Cited by:

    1. S. P. Niranjan & S. Devi Latha & Miroslav Mahdal & Krishnasamy Karthik, 2023. "Multiple Control Policy in Unreliable Two-Phase Bulk Queueing System with Active Bernoulli Feedback and Vacation," Mathematics, MDPI, vol. 12(1), pages 1-21, December.
    2. Anatoliy Alabugin & Sergei Aliukov & Tatyana Khudyakova, 2022. "Review of Models for and Socioeconomic Approaches to the Formation of Foresight Control Mechanisms: A Genesis," Sustainability, MDPI, vol. 14(19), pages 1-19, September.
    3. Konstantin Samouylov & Olga Dudina & Alexander Dudin, 2023. "Analysis of Multi-Server Queueing System with Flexible Priorities," Mathematics, MDPI, vol. 11(4), pages 1-22, February.
    4. Valeriya V. Tynchenko & Vadim S. Tynchenko & Vladimir A. Nelyub & Vladimir V. Bukhtoyarov & Aleksey S. Borodulin & Sergei O. Kurashkin & Andrei P. Gantimurov & Vladislav V. Kukartsev, 2024. "Mathematical Models for the Design of GRID Systems to Solve Resource-Intensive Problems," Mathematics, MDPI, vol. 12(2), pages 1-33, January.

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