具有多面体不确定性的可恢复鲁棒单机调度
Recoverable Robust Single Machine Scheduling with Polyhedral Uncertainty
摘要：
本文研究了多面体不确定条件下的可恢复鲁棒单机排序问题，目标是最小化总的流水时间。在这种情况下，决策者必须确定一个第一阶段的时间表不确定的工件加工时间。然后，在实现这些处理时间之后，他们可以选择交换多达Delta不相交的工件对的位置，以获得第二阶段的时间表。我们首先制定这个调度问题使用一个通用的可恢复的强大的框架，在此之前，我们进一步详细研究的增量子问题。我们证明了最大权重匹配问题的一般结果，表明对于特定形式的边权重，匹配多面体可以完全由多项式的许多约束。我们使用这个结果，以获得一个基于匹配的紧凑制定的完整的问题。增量问题的进一步分析导致一个额外的基于分配的紧凑型配方。预算的不确定性集的计算结果比较我们提出的三个紧凑的模型的相对优势。
英文摘要：
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.
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