Motivated by the need for uninterrupted service provision in the telecommunications industry, this paper presents a novel problem concerning the transportation of diesel generators during an unplanned power outage. Given a set of base stations, each equipped with a capacitated back-up battery pack, the problem consists in finding an optimal delivery and pick-up schedule that minimises corresponding costs. The problem is significantly complicated by the fact that the delivery quantity is a decision variable, and the pick-up times depend on the delivery time, delivery quantity and constraints related to battery-charging requirements. To address the issue, we develop problem-specific pick-up time functions that can be effectively incorporated into the proposed algorithm. The problem is formulated as an arc-based model and a set-packing model. To solve it to optimality, we design a tailored branch-and-price-and-cut algorithm, including novel customised dominance criteria in the labelling algorithm and adopting heuristics that exploit the problem features and effectively improve the algorithmic performance. The efficacy of the proposed algorithm is validated based on the extensive computational study and compared with a commercial solver. The proposed acceleration techniques are found to be potent with regard to computational times, and useful managerial insights are provided as part of sensitivity analyses.

中文翻译：

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紧急停电时基站的发电机分配问题：分枝降价法


出于电信行业不间断服务提供的需求，本文提出了一个关于意外停电期间柴油发电机运输的新问题。给定一组基站，每个基站都配备有容量的备用电池组，问题在于找到最佳的交付和提货时间表，以最大限度地减少相应的成本。由于交货数量是一个决策变量，而提货时间取决于交货时间、交货数量以及与电池充电要求相关的约束，因此问题变得非常复杂。为了解决这个问题，我们开发了针对特定问题的拾取时间函数，可以有效地将其合并到所提出的算法中。该问题被表述为基于弧的模型和集合填充模型。为了解决这个问题，我们设计了一种定制的分支和价格和切割算法，包括在标记算法中新颖的定制优势标准，并采用利用问题特征并有效提高算法性能的启发式方法。基于广泛的计算研究并与商业求解器进行比较，验证了所提出算法的有效性。发现所提出的加速技术在计算时间方面非常有效，并且作为敏感性分析的一部分提供了有用的管理见解。