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Modelling and analysis of production management system using vacation queueing theoretic approach

Author

Listed:
  • Ambika, K.
  • Vijayashree, K.V.
  • Janani, B.

Abstract

This paper explores a queueing model in a production management context, featuring periods of working vacations and Bernoulli vacation. When there are no pending orders, the manufacturing unit transits into a maintenance phase, also termed as working vacation, during which production continues, albeit at a slower rate. This diminished productivity could result in longer lead times and potential customer dissatisfaction. Depending on the influx of demand, the maintenance phase could be interrupted, propelling the unit back to full operational capacity. Conversely, if no orders are received during the maintenance phase, the unit has the choice of switching to standby mode in anticipation of incoming orders, or initiating an extended break. We utilize mathematical techniques such as continued fractions, Modified Bessel functions, and Laplace transforms to precisely compute the transient state probabilities of this model. To further illustrate the impact of these operational dynamics on production management, we present corroborative numerical examples.

Suggested Citation

  • Ambika, K. & Vijayashree, K.V. & Janani, B., 2024. "Modelling and analysis of production management system using vacation queueing theoretic approach," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    • Handle: RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003175
    DOI: 10.1016/j.amc.2024.128856
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    References listed on IDEAS

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    1. Janani, B., 2022. "Transient Analysis of Differentiated Breakdown Model," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    2. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    3. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, July-Dece.
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