Hybrid Classical-Quantum Optimization Techniques for Solving Mixed-Integer Programming Problems in Production Scheduling

Quantum computing (QC) holds great promise to open up a new era of computing and has been receiving significant attention recently. To overcome the performance limitations of near-term QC, utilizing the current quantum computers to complement classical techniques for solving real-world problems is of utmost importance. In this article, we develop QC-based solution strategies that exploit quantum annealing and classical optimization techniques for solving large-scale scheduling problems in manufacturing systems. The applications of the proposed algorithms are illustrated through two case studies in production scheduling. First, we present a hybrid QC-based solution approach for the job-shop scheduling problem. Second, we propose a hybrid QC-based parametric method for the multipurpose batch scheduling problem with a fractional objective. The proposed hybrid algorithms can tackle optimization problems formulated as mixed-integer linear and mixed-integer fractional programs, respectively, and provide feasibility guarantees. Performance comparison between state-of-the-art exact and heuristic solvers and the proposed QC-based hybrid solution techniques is presented for both job-shop and batch scheduling problems. Unlike conventional classical solution techniques, the proposed hybrid frameworks harness quantum annealing to supplement established deterministic optimization algorithms and demonstrate performance efficiency over standard off-the-shelf optimization solvers.