Because of zero emissions and other social and economic benefits, electric vehicles (EVs) are currently being introduced in more and more transit agencies around the world. One of the most challenging tasks involves efficiently scheduling a set of EVs considering the limited driving range and charging requirement constraints. This study examines the battery-electric transit vehicle scheduling problem (BET-VSP) with stationary battery chargers installed at transit terminal stations. Two equivalent versions of mathematical formulations of the problem are provided. The first formulation is based on the deficit function theory, and the second formulation is an equivalent bi-objective integer programming model. The first objective of the math-programming optimization is to minimize the total number of EVs required, while the second objective is to minimize the total number of battery chargers required. To solve this bi-objective BET-VSP, two solution methods are developed. First, a lexicographic method-based two-stage construction-and-optimization solution procedure is proposed. Second, an adjusted max-flow solution method is developed. Three numerical examples are used as an expository device to illustrate the solution methods, together with a real-life case study in Singapore. The results demonstrate that the proposed math-programming models and solution methods are effective and have the potential to be applied in solving large-scale real-world BET-VSPs.

由于零排放以及其他社会和经济利益，电动汽车（EV）当前正被全球越来越多的公交机构采用。最具挑战性的任务之一是考虑到有限的行驶里程和充电要求约束条件，有效地调度一组电动汽车。本研究研究了在公交终端站安装固定式电池充电器的电池电动运输车辆调度问题（BET-VSP）。提供了该问题的数学公式的两个等效版本。第一个公式是基于赤字函数理论的，第二个公式是等效的双目标整数规划模型。数学编程优化的首要目标是最大程度地减少所需的电动汽车总数，第二个目标是最大程度地减少所需的电池充电器总数。为了解决这个双目标BET-VSP，开发了两种解决方法。首先，提出了一种基于词典方法的两阶段构建与优化的求解方法。其次，开发了一种调整后的最大流量解法。使用三个数值示例作为说明性工具来说明解决方法，并在新加坡进行了实际案例研究。结果表明，所提出的数学编程模型和求解方法是有效的，并且有可能用于解决大规模的现实世界中的BET-VSP。提出了一种基于词典方法的两阶段构造与优化的求解方法。其次，开发了一种调整后的最大流量解法。使用三个数值示例作为说明性工具来说明解决方法，并在新加坡进行了实际案例研究。结果表明，所提出的数学编程模型和求解方法是有效的，并且有可能用于解决大规模的现实世界中的BET-VSP。提出了一种基于词典方法的两阶段构造与优化的求解方法。其次，开发了一种调整后的最大流量解法。使用三个数值示例作为说明性工具来说明解决方法，并在新加坡进行了实际案例研究。结果表明，所提出的数学编程模型和求解方法是有效的，并且有可能用于解决大规模的现实世界中的BET-VSP。