Multi-mode resource-constrained project scheduling problem considering man-hour budget for automotive manufacturing in Industry 5.0.

Motivated by the Industry 5.0 paradigm, the introduction of human-robot collaboration (HRC) into automotive body-in-white (BIW) welding islands offers immense flexibility, yet it introduces a critical challenge: balancing production efficiency with strict non-renewable labor costs. To address this challenge, this study investigates a multi-mode resource-constrained project scheduling problem (MRCPSP) under rigid man-hour budgets. This paper proposes a tri-stage adaptive simulated annealing (TS-ASA) framework to resolve the structural budget deadlocks inherent in the optimization problem. The framework integrates three specialized mechanisms. Extensive validations on the standard dataset demonstrate the superior robustness of the framework compared to classic metaheuristics. Furthermore, an industrial case study based on real sedan welding data indicates that TS-ASA achieves a 13.54% reduction in cycle time compared to a rule-based baseline. This improvement will help build high-performance manufacturing systems and bring great benefits to actual production in the future.