An integrated scheduling model for single-machine systems considering fatigue dynamics, speed control, maintenance, and learning-based performance

This paper presents an integrated mixed-integer nonlinear programming (MINLP) model for the sustainable scheduling of jobs on a single-machine system that explicitly incorporates operator fatigue, preventive maintenance (PM), minimal repair (MR), environmental constraints, and learning-based performance improvements. The primary objective is to minimize the makespan while simultaneously controlling operator fatigue, reducing machine downtime, and satisfying a global carbon footprint limit. Operator fatigue is dynamically modeled, accounting for fatigue accumulation and recovery during job processing and scheduled rest periods. Furthermore, the model incorporates a learning effect to reflect the operator’s performance improvement over time, capturing the gradual reduction in processing time as experience accumulates across the job sequence. Machine reliability is managed through proactive PM and Weibull-driven MR, while speed-scaling decisions link energy use to emissions. Based on the properties of the optimal solution, a tailored genetic algorithm (GA) is developed for medium- and large-scale instances. Taguchi parameter tuning further improves convergence. For validation, reduced instances are solved to global optimality using the Solving Constraint Integer Programs (SCIP) solver and serve as references to quantify GA gaps and stability; additional benchmarking against simulated annealing (SA) and particle swarm optimization (PSO) is conducted under the same decoding procedure. Numerical experiments on a 21-job instance confirm the model’s effectiveness. Ablation tests confirm that removing fatigue accelerates the schedule but increases emissions, whereas omitting rests or PM lengthens the makespan and doubles the repair workload. Sensitivity analysis demonstrates robustness across operational and environmental settings.