The distributionally robust machine scheduling problem with job selection and sequence-dependent setup times

This paper proposes an interesting variant of the parallel machine scheduling problem with sequence-dependent setup times, where a subset of jobs has to be selected to guarantee a minimum profit level while the total completion time is minimized. The problem is addressed under uncertainty, considering both the setup and the processing times as random parameters. To deal with the uncertainty and to hedge against the worst-case performance, a risk-averse distributionally robust approach, based on the conditional value-at-risk measure, is adopted. The computational complexity of the problem is tackled by a hybrid large neighborhood search metaheuristic. The efficiency of the proposed method is tested via computational experiments, performed on a set of benchmark instances.