Robust optimization for identical parallel machine scheduling with uncertain processing time

In this paper, we propose to apply robust optimization approaches to the problem of identical parallel machine scheduling with processing time uncertainty. Box uncertainty and cardinality-constrained uncertainty are considered, and robust counterpart is reformulated as deterministic MILP problems. We explore the impact of the protection level, and show the trade-off between robustness and conservativeness. The results of numerical experiments demonstrate that the robust counterpart with cardinality-constrained uncertainty outperforms that with box uncertainty with respect to the mean and standard deviation of realized objective values. However, the robust counterpart with box uncertainty has an advantage in that it requires less computational efforts to solve the problem.