Recoverable robust single machine scheduling with polyhedral uncertainty

Matthew Bold () and Marc Goerigk ()
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Matthew Bold: Lancaster University
Marc Goerigk: University of Passau

Journal of Scheduling, 2025, vol. 28, issue 3, No 1, 269-287

Abstract: Abstract 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 $$\Delta $$ Δ 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.

Keywords: Scheduling; Robust optimization; Recoverable robustness; Polyhedral uncertainty; Budgeted uncertainty (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10951-024-00828-7

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