Single machine scheduling with uncertain release times

This paper establishes a robust optimization model and proposes constraint generation algorithm to solve a robust single machine scheduling problem with random release times. The performance criterion of interest is the maximum waiting time (MWT) over all jobs. Unlike the traditional stochastic programming model which requires exact distributions, our robust optimization model needs only the information of release time intervals. We formulate this uncertain optimization problem as a 0-1 linear programming model with a large number of constraints. To solve the model efficiently, a constraint generation algorithm (CGA) is proposed which generate constraint iteratively to obtain the optimal solution. The robustness of the optimal sequence under various probability distributions of release times is verified by simulation. Extensive computational experiments are implemented to demonstrate the effectiveness and efficiency of the proposed solution method.