Algorithmic Strategies for Minimizing Makespan and Analysis of Retrial Queueing System with Various Techniques

Abstract

This research explores advanced models and algorithms in scheduling and queueing newlinetheory to enhance efficiency and performance across diverse operational settings. It examines newlinesingle machine, parallel machine, and unrelated parallel machine scheduling models with newlinebackup machines, focusing on optimizing metrics such as makespan, tardiness, rejection newlinecosts, preventive maintenance, and machine utilization. Queueing models incorporate features newlinelike retrial processes, breakdowns and repairs, balking, working vacations, disgruntled newlinejobs, heterogeneous servers, and reneging. Employing analytical frameworks and solving newlinetechniques such as Mixed Integer Programming techniques, Simulated Annealing, Genetic newlineAlgorithm, Supplementary Variable Technique, and recursive methods, the study uncovers newlinecritical efficiency indicators, including objective functions, CPU time, queue sizes, system newlinesizes, and server state probabilities. Findings are validated numerically and graphically, newlineoffering actionable insights for scheduling and queueing applications in industries such as metal newlinecutting, car steel manufacturing, steel manufacturing, email systems, semiconductor processes, newlineand weaving machines. This comprehensive investigation provides a strong foundation for newlineoptimizing performance in complex operational environments newline