Abstract: Inevitable machine breakdowns always degrade the performance of the initial schedule in the practice. Considering the controllable processing time in unrelated parallel machines layout, how to generate a robust schedule to reduce the expectation value of the loss cost caused by the stochastic machine failures is studied. Therefore, a robust scheduling strategy of two nested layers is designed. In the inner layer, a nonlinear 0-1 mixed integer model is built to calculate the expectation of the loss cost. Because of the model's complexity, it is translated into second-order cone constrains for solving efficiency. In the outer layer, sorting algorithm is designed based on the job's flexibility and the probability of machine unavailability. Due to inherent complex and unstructured nature, genetic algorithm is used to optimize job's flexible parameters, and to further enhance the robustness of the initial schedule. Through randomly generated numerical experiments, It shows that the proposed scheduling strategy is robust against different disturbance cost per unit time and different mean time to repair of machine breakdown. The research has a certain reference for sorting robust schedule and optimizing job's flexible parameters.

Key words: robust scheduling, unrelated parallel machines, controllable processing time, stochastic breakdowns, match-up