Robust and stable scheduling of a single machine with random machine breakdowns

For single-machine scheduling with random machine breakdowns, a new method considering both robustness and stability is proposed in this paper. The stability of the predictive schedule is measured by the sum of the absolute deviations between the planned job completion times and the realized ones. A surrogate measure is developed to evaluate the stability, assuming that there is only one breakdown. Generating a robust and stable schedule becomes a bi-objective optimization problem. A two-stage multi-population genetic algorithm is proposed to solve the bi-objective optimization problem. The method is applied to minimizing the total weighted tardiness of all jobs. The computational results show that the schedule generated by the proposed method is insensitive to disturbances, along with providing better robustness and stability.