精确字典排序与近似重排序
Exact Lexicographic Scheduling and Approximate Rescheduling
摘要：
在工业资源分配问题中，初始规划阶段可以解决名义问题实例，并且随后的恢复阶段可以干预以修复由于不确定性而导致的低效率和不可行性，例如机器故障和作业处理时间变化。在这种情况下，我们研究的最小完工时间调度问题，a.k.a. $P||C_{\max}$，在不确定性下。我们提出了一个两阶段的鲁棒调度方法，第一阶段的决定计算与精确的字典调度和第二阶段的决定，使用近似重新调度。我们探索的恢复策略占规划决策和限制从原来的时间表有限的允许偏差。我们的方法是证实分析，与价格的鲁棒性表征参数化的不确定性程度，和数值。这种分析是基于字典最优性的最优子结构。因此，字典优化能够更有效地重新调度。此外，我们重新审视国家的最先进的精确的词典最优化方法，并提出了一个词典分支定界算法，其性能进行了验证计算。
英文摘要：
In industrial resource allocation problems, an initial planning stage may solve a nominal problem instance and a subsequent recovery stage may intervene to repair inefficiencies and infeasibilities due to uncertainty, e.g.\ machine failures and job processing time variations. In this context, we investigate the minimum makespan scheduling problem, a.k.a.\ $P||C_{\max}$, under uncertainty. We propose a two-stage robust scheduling approach where first-stage decisions are computed with exact lexicographic scheduling and second-stage decisions are derived using approximate rescheduling. We explore recovery strategies accounting for planning decisions and constrained by limited permitted deviations from the original schedule. Our approach is substantiated analytically, with a price of robustness characterization parameterized by the degree of uncertainty, and numerically. This analysis is based on optimal substructure imposed by lexicographic optimality. Thus, lexicographic optimization enables more efficient rescheduling. Further, we revisit state-of-the-art exact lexicographic optimization methods and propose a lexicographic branch-and-bound algorithm whose performance is validated computationally.
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