Cost optimization for Computer Numerical Control machining workshop: A queueing modeling approach using the meta-heuristic techniques

Abstract

This research paper introduces an innovative approach to optimize repair of failed Computer Numerical Control (CNC) machines within CNC machining workshops by leveraging queueing theory. The proposed model addresses a spectrum of real-world scenarios encountered in manufacturing environments, including CNC machine failures, robotic server breakdowns, reneging behavior of failed CNC machines, and mechanisms to handle unsatisfactory repairs. In this system, failed CNC machines are attended by a single robotic server following a first come first served protocol, while also accounting for potential breakdowns of the robotic server during servicing. The arrival of failed CNC machines is regulated using the $F$-policy, and repairs to the robotic server are conducted following Bernoulli’s $p$-phases under a threshold recovery ($Q$) policy. Through the development of steady-state equations of a system and their solutions through matrix-analytic techniques, the distribution of queue sizes within the system is derived. Numerical results are presented graphically to illustrate the influence of various parameters on overall system performance. Additionally, sensitivity analysis on total expected costs are conducted to assess the impact of parameter variations. To optimize system costs, three meta-heuristic approaches are employed: Particle Swarm Optimization(PSO), Ant Colony Optimization(ACO), and Flower Pollination Algorithm(FPA). Comparative analysis of these techniques’ performances is conducted using data generated through their application. This novel combination of theoretical modeling, numerical analysis, and meta-heuristic optimization offers a comprehensive framework for enhancing efficiency and cost-effectiveness in CNC machining workshops.