Robustness Measures for Stochastic Parallel Machine Scheduling and Train Unit Shunting

In this paper, we investigate measures that can give us information about the robustness for complex scheduling problems. We identify 14 robustness measures from the literature, as well as introduce 4 new ones. We then use simulation to investigate how well these robustness measures correlate with the stability of the objective function under disturbances (quality robustness), and with the stability of the schedule itself (solution robustness). We first do this in the context of Parallel Machine Scheduling, which is a very general setting that is comparable to many practical situations. We then take the results from that investigation and use the best performing measures as objectives in a local search for the Train Unit Shunting Problem with Service Scheduling. We investigate which of these measures give us a better quality robustness, and which measures give us a better solution robustness. We look at how these measures perform under different ways of inserting slacks into the schedule. We show how the performance of the measures can differ in these different cases, and conclude with what we believe to be a good set of robustness measures to consider for any scheduling problem.