IJMEMES logo

International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749 . Open Access


Cost Optimization using Genetic Algorithm in Customers Intolerance Markovian Model with Working Vacation and Multiple Working Breakdowns

Cost Optimization using Genetic Algorithm in Customers Intolerance Markovian Model with Working Vacation and Multiple Working Breakdowns

Anamika Jain
Department of Mathematics & Statistics, Manipal University Jaipur, Jaipur- 303 007, India.

Chandrima Raychaudhuri
Department of Mathematics & Statistics, Manipal University Jaipur, Jaipur- 303 007, India.

DOI https://doi.org/10.33889/IJMEMS.2022.7.5.043

Received on January 24, 2022
  ;
Accepted on June 26, 2022

Abstract

In this paper, we consider a single server queueing model with working vacation and multiple working breakdowns. When on vacation, the server works at a different pace. Disturbances occur in the server due to multiple breakdowns. In working breakdowns server works at a different rate. During the time of interruption caused by working vacation and working breakdowns, the main server can find many implementations in operation. Both the server's lifespan and the time it takes to repair it are considered to be exponentially dispersed. Also, we have considered balking and reneging behaviours of customers. The stationary queue length distribution is computed using a matrix-analytic technique. Using Genetic Algorithm (GA) we optimize the cost function. The predicted length of a busy period, the expected length of a working vacation period, the expected length of a working breakdown period, the mean waiting time, and the average delay are all established. We compute numerical results to verify the analytical point of view. The effect of individual parameters is investigated using sensitivity analysis.

Keywords- Working breakdowns; Matrix-analytic method; Working vacation; Balking; Reneging; Genetic algorithm.

Citation

Jain, A., & Raychaudhuri, C. (2022). Cost Optimization using Genetic Algorithm in Customers Intolerance Markovian Model with Working Vacation and Multiple Working Breakdowns. International Journal of Mathematical, Engineering and Management Sciences, 7(5), 656-669. https://doi.org/10.33889/IJMEMS.2022.7.5.043.