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This study investigates the effectiveness of quantum and quantum-inspired methods for solving an industrial variant of the Job-Shop Scheduling Problem, comparing them against classical approaches on IBM Quantum, D-Wave, and Fujitsu platforms. By implementing hardware-specific formulations, the research highlights the critical role of hardware-software co-design in enhancing solution quality and scalability. The findings reveal that quantum optimization can significantly inform industrial solver selection and integration, paving the way for improved approximations in scheduling tasks.
Quantum optimization methods can outperform classical solvers in industrial scheduling tasks when tailored to specific hardware constraints.
Quantum Processing Units promise speed-ups for selected computational problems, including combinatorial optimisation, but their industrial utility remains an open challenge. We study an industrial variant of the Job-Shop Scheduling Problem using quantum, quantum-inspired, and classical methods across three platforms: IBM Quantum, the D-Wave Quantum Annealer, and the Fujitsu Digital Annealer. By tailoring formulations to hardware-specific constraints, we show that hardware-software co-design is essential for solution quality and scalability. We benchmark all approaches against an exact classical solver and a MILP formulation, evaluating runtime, solution quality, and scalability. Our results indicate that quantum and quantum-inspired optimisation can support industrial solver selection, integration in classical workflows, modelling decisions, and early proof-of-concept development, while suggesting a potential path towards improved approximations for industrial scheduling.