IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i14p2520-d867111.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/14/2520/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/14/2520/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    3. Peter W. Glynn, 2022. "Queueing theory: past, present, and future," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 169-171, April.
    4. Neil Walton, 2022. "Queueing: a perennial theory," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 557-559, April.
    5. Foivos Psarommatis & Gökan May & Paul-Arthur Dreyfus & Dimitris Kiritsis, 2020. "Zero defect manufacturing: state-of-the-art review, shortcomings and future directions in research," International Journal of Production Research, Taylor & Francis Journals, vol. 58(1), pages 1-17, January.
    6. 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.
    7. Cosmika Goswami & N. Selvaraju, 2016. "Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations," Advances in Operations Research, Hindawi, vol. 2016, pages 1-17, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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 1-20, December.
    2. 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.
    3. 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.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Metzker Soares, Paula & Thevenin, Simon & Adulyasak, Yossiri & Dolgui, Alexandre, 2024. "Adaptive robust optimization for lot-sizing under yield uncertainty," European Journal of Operational Research, Elsevier, vol. 313(2), pages 513-526.
    2. Konstantinos S. Boulas & Georgios D. Dounias & Chrissoleon T. Papadopoulos, 2023. "A hybrid evolutionary algorithm approach for estimating the throughput of short reliable approximately balanced production lines," Journal of Intelligent Manufacturing, Springer, vol. 34(2), pages 823-852, February.
    3. Korporaal, R. & Ridder, A.A.N. & Kloprogge, P. & Dekker, R., 1999. "Capacity planning of prisons in the Netherlands," Econometric Institute Research Papers EI 9909-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Sumi Kim & Seongmoon Kim, 2015. "Differentiated waiting time management according to patient class in an emergency care center using an open Jackson network integrated with pooling and prioritizing," Annals of Operations Research, Springer, vol. 230(1), pages 35-55, July.
    5. Papadopoulos, H. T. & Vidalis, M. I., 2001. "Minimizing WIP inventory in reliable production lines," International Journal of Production Economics, Elsevier, vol. 70(2), pages 185-197, March.
    6. Rosmaini Ahmad & Rabiatul Fakhira Mohd Amin & Shaliza Azreen Mustafa, 2022. "Value stream mapping with lean thinking model for effective non-value added identification, evaluation and solution processes," Operations Management Research, Springer, vol. 15(3), pages 1490-1509, December.
    7. Chakravarthy, Srinivas R. & Shruti, & Kulshrestha, Rakhee, 2020. "A queueing model with server breakdowns, repairs, vacations, and backup server," Operations Research Perspectives, Elsevier, vol. 7(C).
    8. Osorio, Carolina & Bierlaire, Michel, 2009. "An analytic finite capacity queueing network model capturing the propagation of congestion and blocking," European Journal of Operational Research, Elsevier, vol. 196(3), pages 996-1007, August.
    9. Boysen, Nils & Fliedner, Malte & Scholl, Armin, 2009. "Sequencing mixed-model assembly lines: Survey, classification and model critique," European Journal of Operational Research, Elsevier, vol. 192(2), pages 349-373, January.
    10. Jeffrey M. Alden & Lawrence D. Burns & Theodore Costy & Richard D. Hutton & Craig A. Jackson & David S. Kim & Kevin A. Kohls & Jonathan H. Owen & Mark A. Turnquist & David J. Vander Veen, 2006. "General Motors Increases Its Production Throughput," Interfaces, INFORMS, vol. 36(1), pages 6-25, February.
    11. Gokan May & Foivos Psarommatis, 2023. "Maximizing Energy Efficiency in Additive Manufacturing: A Review and Framework for Future Research," Energies, MDPI, vol. 16(10), pages 1-28, May.
    12. Tan, Baris, 1998. "Effects of variability on the due-time performance of a continuous materials flow production system in series," International Journal of Production Economics, Elsevier, vol. 54(1), pages 87-100, January.
    13. Stefan Helber & Carolin Kellenbrink & Insa Südbeck, 2024. "Evaluation of stochastic flow lines with provisioning of auxiliary material," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 669-708, September.
    14. Nan Chen & Yuan Yuan & Shiyu Zhou, 2011. "Performance analysis of queue length monitoring of M/G/1 systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 782-794, December.
    15. Foivos Psarommatis & Gokan May, 2025. "A Cost–Benefit Model for Sustainable Product Reuse and Repurposing in Circular Remanufacturing," Sustainability, MDPI, vol. 17(1), pages 1-16, January.
    16. Carlos Chaves & Abhijit Gosavi, 2022. "On general multi-server queues with non-poisson arrivals and medium traffic: a new approximation and a COVID-19 ventilator case study," Operational Research, Springer, vol. 22(5), pages 5205-5229, November.
    17. Tang Tang & Lijuan Jia & Jin Hu & Yue Wang & Cheng Ma, 2022. "Reliability analysis and selective maintenance for multistate queueing system," Journal of Risk and Reliability, , vol. 236(1), pages 3-17, February.
    18. Jean-Sébastien Tancrez & Philippe Chevalier & Pierre Semal, 2011. "Probability masses fitting in the analysis of manufacturing flow lines," Annals of Operations Research, Springer, vol. 182(1), pages 163-191, January.
    19. Kiesmüller, G.P. & Sachs, F.E., 2020. "Spare parts or buffer? How to design a transfer line with unreliable machines," European Journal of Operational Research, Elsevier, vol. 284(1), pages 121-134.
    20. Sachs, F.E. & Helber, S. & Kiesmüller, G.P., 2022. "Evaluation of Unreliable Flow Lines with Limited Buffer Capacities and Spare Part Provisioning," European Journal of Operational Research, Elsevier, vol. 302(2), pages 544-559.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2520-:d:867111. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.