Identical parallel machine scheduling with tool changes under the peak power consumption constraint

In practical CNC machining for aerospace and automotive components, machine availability is constrained by tool changes due to tool wear, while each machine's continuous processing time is limited by tool life. Furthermore, total real-time power consumption must not exceed the predetermined peak power threshold at any time within the planning horizon. This study investigates an identical parallel machine scheduling problem with tool changes under the peak power consumption constraint, aiming to minimise the makespan. We propose two Mixed Integer Linear Programming (MILP) models: one based on the traditional scheduling procedure and the other inspired by the two-dimensional Strip Packing (SP) problem, and develop a Greedy heuristic to efficiently solve large-scale instances. Experimental results show that both models yield optimal solutions only for small-scale instances. The proposed Greedy heuristic is capable of obtaining near-optimal solutions for small-scale instances and outperforms three adapted benchmark algorithms (LJM-LMM, MSA and HGA) in both efficiency and solution quality for large-scale problems. Finally, we derive managerial insights to support industrial decision-making, offering a systematic approach to simultaneously meet peak power requirements, optimise tool utilisation, and enhance production effectiveness in real-world manufacturing settings.