Recoverable Robust Single Machine Scheduling with Budgeted Uncertainty
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This paper considers a recoverable robust single-machine scheduling problem under continuous budgeted uncertainty with the objective of minimising the total flow time. In this setting, a decision-maker must determine a first-stage schedule subject to the uncertain job processing times, and then following the realisation of these processing times, can swap the positions of up to Delta disjoint pairs of jobs to obtain a second-stage schedule. We first formulate this scheduling problem using a general recoverable robust framework, before we examine the incremental subproblem in further detail. We prove a general result for max-weight matching problems, showing that for edge weights of a specific form, the matching polytope can be fully characterised by polynomially many constraints. We use this result to derive a matching-based compact formulation for the full problem. Further analysis of the incremental problem leads to an additional assignment-based compact formulation. Computational results compare the relative strengths of the three compact models we propose.
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