This study aims to determine the battery electric bus service and charging strategy to minimize the total operational cost of transit system, where the cost incurred by battery degradation and non-linear charging profile is taken into account. We formulate a set partitioning model for this problem, subject to predefined trip schedule and limited charging facilities. A tailored branch-and-price approach is then proposed to find the global optimal solution. In particular, we develop an effective multi-label correcting method to deal with the pricing problem (i.e., generating columns) in column generation procedure within the branch-and-price framework, coupled with a dual stabilization technique with an aim to accelerate the convergence rate. Meanwhile, a branch-and-bound solution approach is adopted to guarantee optimal integer solutions. Numerical experiments and a case study arising from real transit network are conducted to further assess the efficiency and applicability of the proposed method. Our experiments confirm that, despite the complexity of the considered problem, optimal solution can still be generated within reasonable computational time using the proposed algorithm. The results also show considerable cost saving (about 10.1–27.3% less) if this optimization model is implemented, mainly contributed by the substantial extension of battery life. A number of managerial insights stemmed from the numerical case study are outlined, which can help transit operators formulate more cost-efficient electric bus fleet scheduling plans.

本研究旨在确定电池电动巴士服务和充电策略，以最大限度地降低运输系统的总运营成本，其中考虑了电池退化和非线性充电曲线所产生的成本。我们为这个问题制定了一套分区模型，受预定义的行程安排和有限的充电设施的约束。然后提出了一种定制的分支和价格方法来找到全局最优解。特别是，我们开发了一种有效的多标签校正方法来处理分支和价格框架内列生成过程中的定价问题（即生成列），并结合双重稳定技术以加速收敛速度。同时，采用分支定界解法来保证最优整数解。进行了来自真实交通网络的数值实验和案例研究，以进一步评估所提出方法的效率和适用性。我们的实验证实，尽管所考虑问题的复杂性，仍然可以使用所提出的算法在合理的计算时间内生成最佳解决方案。结果还表明，如果实施此优化模型，可节省大量成本（减少约 10.1-27.3%），这主要归功于电池寿命的大幅延长。概述了源自数值案例研究的许多管理见解，可以帮助公交运营商制定更具成本效益的电动公交车队调度计划。