  This paper considers a recoverable robust single-machine scheduling problem
under polyhedral 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. Then following the realisation
of these processing times, they have the option to 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 on budgeted uncertainty sets compare the relative
strengths of the three compact models we propose.
