The paper examines the complexity of assigning multiple breaks to shifts in the context of large-scale tour scheduling. A mixed-integer programming (MIP) model is presented that includes shift and days-off scheduling along with break assignments for a multi-skilled workforce. To achieve tractability, a two-stage decomposition procedure is proposed that separates the tour scheduling problem (TShP) from the break assignment problem (BAP). The former MIP is first solved to determine the shifts and days off for the workforce that minimize labor and shortages costs over the planning horizon. The results are used as input to a second MIP that optimally places the breaks to minimize the costs of working hours and uncovered periods. Three implicit BAP formulations are investigated. To better understand the literature and the models previously developed, a 3-field break classification scheme is introduced. The first field characterizes the number of breaks permitted per shift, the second specifies whether the length of the breaks is fixed or variable, and the third limits their position in a shift. A complexity analysis of the resulting 12 BAPs along with a few special cases is also included. Most problems are shown to be strongly NP-hard. Computations are presented for a wide variety of scenarios for both the TShP and the BAP using data provided by a European airport ground handler company. In all, over 500 instances were investigated using high and low demand fluctuation curves and the various break and shift flexibility options. The results indicate that increasing flexibility in break regulations can make a significant difference in coverage, but the degree depends on the underlying structure of the demand curve as well as on the types of shifts permitted. Formulations with the most flexible shift and break regulations reduced undercoverage by up to 16.68% compared to the most common scenarios in which shifts are limited to a single lunch break.

中文翻译：

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应用于机场地勤人员的大型旅游调度问题的灵活休息分配问题

本文研究了在大规模旅游调度的背景下为轮班分配多个休息时间的复杂性。提出了一种混合整数编程 (MIP) 模型，其中包括轮班和休息日计划以及多技能劳动力的休息分配。为了实现易处理性，提出了一个两阶段分解过程，将旅游调度问题 (TShP) 与休息分配问题 (BAP) 分开。首先解决前 MIP 以确定劳动力的轮班和休假天数，以最大限度地减少计划范围内的劳动力和短缺成本。结果将用作第二个 MIP 的输入，该 MIP 可以最佳地放置休息时间，以最大限度地减少工作时间和未覆盖时间的成本。研究了三种隐式 BAP 公式。为了更好地理解先前开发的文献和模型，引入了 3 场中断分类方案。第一个字段表征每个班次允许的休息次数，第二个字段指定休息的长度是固定的还是可变的，第三个字段限制它们在班次中的位置。还包括对生成的 12 个 BAP 以及一些特殊情况的复杂性分析。大多数问题都被证明是强 NP 难的。使用欧洲机场地勤公司提供的数据，对 TShP 和 BAP 的各种场景进行了计算。总共使用高低需求波动曲线以及各种休息和换班灵活性选项对 500 多个实例进行了调查。结果表明，增加违反法规的灵活性可以显着影响覆盖范围，但程度取决于需求曲线的基本结构以及允许的移动类型。与轮班仅限于一次午休的最常见情况相比，具有最灵活轮班和休息规定的配方将覆盖不足减少了多达 16.68%。