Given the increasing heterogeneity of the types of aircraft operated, many airlines have switched from the traditional team scheduling approach to the individual scheduling approach for cabin crew planning. The individual approach not only allows for greater scheduling flexibility, but also helps achieve better utilization of available manpower through cross-class substitution (i.e., assigning a high-class crew member to substitute a low-class crew member), which is especially important in view of the recent industry-wide manpower shortage led by the post-pandemic traffic recovery. In this study, we present a new crew pairing approach with accurate characterization of cross-class substitution. This approach is novel as it can distinguish the substitutions among different pairs of crew classes with precise characterization of work time and costs. We develop a branch-and-price solution approach. A new specialized flight network that characterizes each crew class for each flight is constructed to realize the recognition of substitution heterogeneity. Although the size of the new flight network increases dramatically, it can be simplified to consider only one crew class for each flight in each column generation iteration without affecting optimality. We also propose a new column-fixing branching strategy to identify integer solutions for the newly developed model with non-negative integer variables. Computational experiments based on real-world collected flight schedules are conducted to validate the performance of the proposed approach in obtaining high-quality solutions (e.g., achieving a 0.01% optimality gap). The cost saving of the new crew pairing approach is examined, which is shown to vary greatly across different manpower availability levels and part-time cost settings. Besides, rich managerial insights are derived. Among others, we find that if it is expensive for a high crew class to directly substitute a low class (e.g., one that is experiencing a shortage), indirect assistance can be provided through an intermediate class.

中文翻译：

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航空公司空乘人员配对与跨舱位替代的准确表征：一种分支和价格方法


鉴于所运营飞机类型的异质性日益增加，许多航空公司已经从传统的团队调度方法转向个人调度方法进行机组人员规划。个人化方法不仅允许更大的调度灵活性，还有助于通过跨等级替代（即分配一名高级船员来替代一名低等级船员）更好地利用可用人力，鉴于最近大流行后交通复苏导致整个行业的人力短缺，这一点尤为重要。在这项研究中，我们提出了一种新的船员配对方法，可以准确表征跨类替换。这种方法很新颖，因为它可以区分不同船员等级对之间的替换，并精确描述工作时间和成本。我们开发了一种分支和价格解决方案方法。构建了一个新的专用飞行网络，该网络描述了每个航班的每个机组人员类别的特征，以实现对替代异质性的识别。尽管新飞行网络的大小急剧增加，但可以简化为在每个列生成迭代中为每个飞行仅考虑一个机组组类别，而不会影响最优性。我们还提出了一种新的列固定分支策略，用于识别新开发的具有非负整数变量的模型的整数解。基于真实世界收集的航班时刻表进行计算实验，以验证所提出的方法在获得高质量解决方案（例如，实现 0.01% 最优性差距）方面的性能。 研究了新船员配对方法的成本节省，结果表明，在不同的人力可用性水平和兼职成本设置中，成本节省差异很大。此外，还得出了丰富的管理见解。其中，我们发现，如果高船员等级直接替代低等级（例如，正在经历短缺的等级）的成本很高，那么可以通过中间等级提供间接援助。