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

K. Ambika, K.V. Vijayashree and B. Janani

Applied Mathematics and Computation, 2024, vol. 479, issue C

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.

Keywords: Continued fractions; Transient state probabilities; Vacation interruption; Confluent Hypergeometric Function; Production Management (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324003175
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003175

DOI: 10.1016/j.amc.2024.128856

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().