Tractable Risk Measures for the Selective Scheduling Problem with Sequence-Dependent Setup Times

Quantifying and minimizing the risk is a basic problem faced in a wide range of applications. Once the risk is explicitly quantified by a risk measure, the crucial and ambitious goal is to obtain risk-averse solutions, given the computational hurdle typically associated with optimization problems under risk. This is especially true for many difficult combinatorial problems, and notably for scheduling problems. This paper aims to present a few tractable risk measures for the selective scheduling problem with parallel identical machines and sequence-dependent setup times. We indicate how deterministic reformulations can be obtained when the distributional information is limited to first and second-order moment information for a broad class of risk measures. We propose an efficient heuristic for addressing the computational difficulty of the resulting models and we showcase the practical applicability of the proposed approach providing computational evidence on a set of benchmark instances.