In this paper, a new full cover modeling framework is developed to design refueling station infrastructure, where the focus is on locating fast-charging stations for battery electric vehicles to enable long-distance transportation. A mathematical model is introduced to determine the optimal locations of these charging stations so that every origin-destination trip on a given transportation network is covered with respect to vehicle range. This full cover model allows deviations from the shortest paths and also determines an optimal route for each trip that requires the minimum total en route recharging. Two variants of this model are proposed: one that minimizes the total cost of locating charging stations and total en route recharging, and another that determines the locations of a predetermined number of stations to minimize the total en route recharging. Computational experiments performed on benchmark data sets validate that the proposed full cover models perform better than the maximum or set cover problem settings in the literature in terms of routing-related measures, such as total trip distance and maximum deviation from the shortest paths. A Benders decomposition algorithm is developed to optimally solve real-life instances of the problem. The Benders subproblem is identified as a many-to-many shortest path problem with an additional constraint that restricts the nodes that can be used to open facilities that are determined by the master problem. A new algorithmic methodology is developed to construct the dual solution for this subproblem and to generate non-dominated optimality cuts and strong valid inequalities for feasibility cuts. This novel algorithm accelerates the performance of the Benders algorithm up to 900 times over the tested large-size instances.

在本文中，开发了一个新的全覆盖建模框架来设计加油站基础设施，其重点是为电池电动车定位快速充电站以实现长途运输。引入数学模型来确定这些充电站的最佳位置，以便在给定的交通网络中，每次出发地到目的地的行程都涵盖车辆范围。这种全覆盖模型不仅允许偏离最短路径，还可以确定每次行程所需的最佳路线，而此行程需要最少的总路线充电。提出了此模型的两种变体：一种将定位充电站的总成本和整个途中充电的总成本降到最低，另一个确定预定数量的站点的位置，以使整个途中充电最小。在基准数据集上进行的计算实验证明，在路由相关度量（例如总行程距离和距最短路径的最大偏差）方面，建议的全覆盖模型的性能优于文献中的最大或覆盖问题设置。开发Benders分解算法以最佳地解决问题的实际情况。Benders子问题被标识为多对多最短路径问题，并带有附加约束，该约束约束可用于打开由主问题确定的设施的节点。开发了一种新的算法方法来构造该子问题的对偶解，并生成非支配的最优性削减和可行性削减的强有效不等式。在经过测试的大型实例上，这种新颖的算法将Benders算法的性能提高了900倍。