Electric utility companies perform numerous technical interventions every day. Since it is generally not possible to complete all planned interventions within a single day, companies face two objectives: maximizing the total duration of completed interventions (primary objective) and minimizing the associated operational cost (secondary objective). In this paper, we introduce a multi-objective variant of the technician routing and scheduling problem in which both objectives are optimized in lexicographic order. We propose a compact mixed-integer linear formulation and an extended set-packing-based formulation. To handle the objectives within a single-objective framework, we consider weighted-sum reformulations that preserve lexicographic priorities as well as sequential reformulations that individually optimize each objective while maintaining the optimal value of higher-priority ones. For the extended formulation, we develop an exact column-generation-based algorithm, in which the pricing subproblems are solved via a labeling algorithm based on dynamic programming. As technician schedules are typically generated on a daily basis, the algorithm is designed to deliver high-quality solutions within short computation times (e.g., 5 minutes). Computational experiments on real-life instances provided by the French electric utility company show that the CG-based algorithm proves optimality on a larger number of small instances than the compact formulation and consistently outperforms it on larger instances. In particular, the sequential CG-based variant finds the best-known solutions on more instances and achieves lower mean gaps relative to the best solution found in each instance category.

翻译：电力公司每天需执行大量技术干预任务。由于无法在单日内完成所有计划干预，企业面临双重目标：最大化已完成干预的总时长（首要目标）和最小化相关运营成本（次要目标）。本文引入一种多目标变体的技术人员路径规划与调度问题，其中两个目标按词典序优化。我们提出了一种紧凑的混合整数线性规划模型和一种基于集合覆盖的扩展模型。为在单目标框架下处理多目标，我们考虑了保留词典优先级的加权求和重构方法，以及依次优化各目标同时保持更高优先级目标最优值的序列化重构方法。针对扩展模型，我们开发了一种基于列生成的精确算法，其中定价子问题通过动态规划的标记算法求解。由于技术员日程通常按日生成，该算法设计为可在短计算时间（如5分钟）内输出高质量解。在法国电力公司提供的真实场景实例上的计算实验表明，基于列生成的算法在更多小规模实例上证明了最优性，且在大规模实例上始终优于紧凑模型。特别地，序列化列生成变体在更多实例上找到了已知最优解，并在每个实例类别中相对于最佳解实现了更低的平均差距。