Quantum annealing heuristics for the job shop scheduling problem with availability constraints
Résumé
We study the Job Shop Scheduling Problem with machine Availability Constraints (JSSP-AC) within a quantum-annealing framework. Using a dummy-job transformation, both fixed and variable machine unavailability periods are incorporated into a standard time-indexed quadratic unconstrained binary optimization (QUBO) model. We then introduce a constructive heuristic H, its preemptive variant H∗, and three annealing-based methods: M1, based on a naive time horizon; M2, using the tighter bound returned by H; and M3, which additionally uses the heuristic solution as a warm start in a reverse-annealing setting. A proof-of-concept experiment on D-Wave hardware confirms that the proposed formulation can be embedded and solved on small instances. On a broader benchmark, H outperforms repaired dispatching heuristics, while the tighter horizon reduces QUBO size by 29.9%, quadratic terms by 46.4%, physical qubit usage by about 50%, and embedding time by 64%. The average optimality gap decreases from 18.3% for M1 to 5.0% for M2 and 3.3% for M3, highlighting the value of classical bounds and warm starts in quantum annealing for scheduling under machine unavailability.
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