A compact reformulation of the two-stage robust resource-constrained project scheduling problem

Bold, Matthew; Goerigk, Marc

doi:10.48550/arxiv.2004.06547

Cited by 1 publication

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“…This problem is shown to be NP-hard even for budgeted uncertainty. In a series of papers Bruni et al (2017Bruni et al ( , 2018; Bold and Goerigk (2020), a two-stage resource-constrained project scheduling problem with budgeted uncertainty is introduced and solved.…”

Section: Introductionmentioning

confidence: 99%

Recoverable Robust Single Machine Scheduling with Polyhedral Uncertainty

Bold¹,

Goerigk²

2020

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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 ∆ 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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Section: Introductionmentioning

confidence: 99%