Digital engineering.

Parameter study and industrial applicability of a quantum annealing approach for flexible job shop scheduling in manufacturing

Philipp Schworm, Xiangqian Wu, Marcel Wagner, Jan Christian Aurich

Published Jun 11, 2026• 0 citations

Abstract

The flexible job shop scheduling problem (FJSSP) is a challenging optimization problem arising in small-batch and single-unit manufacturing, where high product variety and short planning cycles impose strict demands on both schedule quality and computation time. Prior work has indicated the potential of an iterative hybrid quantum–classical solver (IHQPU) for multi-objective FJSSP, covering makespan, tardiness, priority, and workload objectives as well as reactive rescheduling. However, transferring this approach to industrial practice requires reliable parameter calibration and validation on real production data, both of which remain open. This paper targets both aspects. A time share analysis characterizes at which problem size the QPU branch loses time dominance to classical branches. A systematic parameter calibration using the Optuna framework evaluates 10,000 solver configurations per Brandimarte instance and objective function, yielding size-class-dependent recommendations for 21 bottleneck weighting coefficients and constraint-to-objective weight ratios. A reproducibility study across 96 parameter combinations identifies the operations-per-iteration count as the dominant source of solution variance and establishes that sub-problem sizes of at most 30 operations with at least three outer repetitions achieve a coefficient of variation below 2.5%. The calibrated configurations are transferred without modification to an industrial validation on six planning instances comprising 283 to 1386 operations and 30 to 67 machines, yielding makespan reductions of up to 1.7% and priority-weighted completion time improvements of up to 78% over existing industrial schedules, with all instances solved within 15 min. Reactive rescheduling completes in 227 to 242 s and reduces planning disruption by 93.7 to 96.0% compared to full plan revision.

DOI: 10.1016/j.dte.2026.100132

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