A Review of Battery Electric Public Transport Timetabling and Scheduling: A 10 Year Retrospective and New Developments

Abstract

Battery electric vehicles (BEVs) have emerged as a cornerstone of sustainable transportation systems, driving a fundamental transformation in public transport (PT) operations over the past decade. The unique characteristics of BEVs, including range limitations and battery degradation dynamics, necessitate a multi-dimensional optimization framework that simultaneously considers energy supply management, operational efficiency, and battery lifecycle optimization in transit scheduling and timetabling. This paper presents a systematic review of BEV timetabling and scheduling research, structured around three main contributions. First, it comprehensively examines the evolution of electric vehicle timetabling problems, providing a detailed comparative analysis of methodological approaches in this domain. Second, it identifies and critically evaluates key developments in electric vehicle scheduling, including extended research directions (such as the integration with crew scheduling) and their practical implications. Third, it investigates the integration of BEV scheduling and timetabling, synthesizing the strengths and limitations of current methodologies while outlining promising avenues for future research. By offering a comprehensive analysis of the advancements in battery electric public transport scheduling over the past decade, this review serves as both a technical reference and a strategic guide for researchers and practitioners in the field of sustainable transportation systems.

1. Introduction

The increasing environmental threats from diesel vehicles’ emissions, such as particulate matter pollution and greenhouse gas emissions, have spurred a global shift towards low-carbon transportation models. BEVs, a key technology in sustainable mobility systems, hold great promise in balancing urban development and environmental protection. In Europe, BEV sales grew at a compound annual growth rate of 61% from 2016 to 2021, ahead of China (58%) and the US (32%). In China, many cities, such as Beijing, Shenzhen, and Shanghai, have fully transitioned their public transport fleets from fuel-powered vehicles to 100% electric buses. By 2021, over 71% of their public transit fleets were electric [1]. This large-scale transition highlights the crucial role of BEVs in achieving the United Nations Sustainable Development Goals.

The introduction of BEVs into the PT system has exerted certain influences on its planning process, bringing about some changes. Generally speaking, the planning process of PT is mainly divided into seven stages with three levels, as shown in Figure 1. Ideally, it would be better to consider all the relevant subproblems in a comprehensive manner. Due to the complexity of each subproblem, however, the sequential method is the normal way, or the integrated method combines two subproblems at most.

Notably, frequency setting sometimes serves as a pre-step of timetable construction [2]. It characterizes operation periods in line with the demand pattern, such as peak or off-peak hours, and decides the hourly number of trips to satisfy passenger demand during each period. On the other hand, timetabling further defines the arrival and departure times of vehicles at all stops within the PT network. In certain scenarios, the number of trips is pre-set, while in others, it is determined based on the trade-off between vehicle capacity and passenger demand. Moreover, the vehicle scheduling problem aims to allocate vehicles to meet the demand of all planned trips. The objectives are to reduce operational costs and minimize vehicle acquisition expenses. Crew assignment is used to determine the duty trip and driver duty assignment, i.e., crew scheduling and rostering [3].

Our study chiefly centers on the timetabling and vehicle scheduling problems, both vital aspects of PT planning. Given that BEVs still have certain limitations in battery life and charging technology, which are incompatible with the existing operation and scheduling management system, numerous issues and challenges arise during actual operation. These challenges undermine the operational efficiency of bus enterprises and the effectiveness of vehicle scheduling. Hence, a feasible and reasonable operation management and optimization of the BEV system has become a critical focus under the development of green and low-carbon PT.

2. Research Method

This paper aims to review the existing literature on the problem of BEV timetabling and scheduling to discuss the method and algorithm over the past decades. The paper provides a comprehensive overview of the state-of-the-art method of the electric bus timetabling and scheduling problem in terms of structural and procedural aspects. Firstly, the impact of different charging technologies on electric vehicle timetabling is analyzed, and the mainstream objectives and evolving trends of traditional PT timetabling are explored in depth. Then, the electric vehicle scheduling problem (EVSP) is defined and its solution methods, including exact, heuristic, machine learning, and other methods, are classified and reviewed in detail. The extended research on integrating electric vehicle scheduling with crew scheduling is also presented. Further, the methodologies for the integrated timetabling and vehicle scheduling of BEVs are discussed, with a comparison of exact and heuristic methods. Finally, the overall research is summarized, the limitations of the current methods are pointed out, and future research directions such as robust scheduling, multi-mode charging optimization, and big data and artificial intelligence applications are analyzed. Figure 2 illustrates the process of selecting related papers and the classification framework. We select different keywords (which can refer to specific section for more details) according to different themes to conduct article retrieval in the database, including Web of Science, Scopus, Google Scholar, etc., and screen out non-Open Access (OA) journal papers (including review papers) from 2015 to 2025. Based on the search results of databases, we further select and analyze the samples by statistical tools, such as Excel and Python 3.8.17.

Through the process of searching and selecting, we identified several recent reviews on electric vehicles in recent years. For instance, Behnia et al. [4] analyzed various solutions for EVSPs based on rigid objectives. Zhang et al. [1] examined 42 papers addressing EVSPs, with a focus on the impacts of charging modes and charging scheduling. Kalakanti and Rao [5] explored the development of electric vehicles and analyzed their impacts on power systems, fast-charging technology, vehicle-to-grid, vehicle-to-home, and vehicle-to-vehicle technologies, as well as cybersecurity and data privacy issues. Perumal et al. [6] evaluated the application of different charging infrastructures in related research from 1981 to 2020. However, the solution methods for BEVs in these reviews primarily focus on traditional mathematical approaches, such as heuristic or exact methods, while overlooking emerging technologies, like machine learning and modular bus systems, in the context of EVSPs.

In addition, to the best of our knowledge, there have been no reviews on the integrated optimization of BEV timetabling and scheduling in recent years. Figure 3 illustrates the number of papers reviewed in this paper, categorized by research topic and publication year. It is shown that over 60 relevant papers have been published in SCI-indexed journals in the past decade (2020–2025), with a notable peak in 2023. Notably, research on electric vehicle scheduling problems (EVSPs) and its extensions—such as integrated timetabling (TT) and crew scheduling (CSP)—has grown significantly in recent years (2022–2025). Thus, a systematic review of current and advanced methodologies is essential to identify feasible technologies and guide future research directions.

The remainder of this paper is structured as follows. Section 3 provides a comprehensive analysis of how different charging technologies influence electric vehicle timetabling, accompanied by a systematic review of the evolution from traditional to emerging timetabling objectives and methodologies. Section 4 presents a classification framework for EV scheduling solution methods, with particular emphasis on the critical role of charge scheduling in operational optimization. This section further explores extended research domains, including the integration of EV scheduling with crew assignment problems. Section 5 introduces advanced solution methods for the integrated optimization of electric vehicle timetabling and scheduling. The paper concludes with Section 6, which summarizes key findings, discusses practical implications, and identifies promising directions for future research.

3. EV Timetabling

With the introduction of EVs, the question of whether their operating characteristics will bring changes to timetabling has been raised [2]. Häll et al. [2] comprehensively discussed the impact of different charging technologies on timetabling. They argued that neither overnight charging nor continuous charging will cause a change in timetable, except for fast charging.

Table 1. Impact or no impact between different charging technologies and timetabling and vehicle scheduling.

Charging Modes	Timetabling	Vehicle Scheduling
Quick charging	√	√
Overnight charging	×	√
Continuous charging (i.e., charging during driving)	×	×

Note: ‘×’ indicates no impact, while ‘√’ signifies the presence of an impact.

provides a tabulated summary of their viewpoints. It is worth noting that fast charging requires particular attention in TT, as its charging duration must be carefully coordinated with trip sets. For EVSPs under fast charging, it is necessary to consider the location of the charging station, energy consumption, charging time, and other parameters. Night charging has no impact on daytime trip scheduling, but battery capacity constraints are included in EVSPs to meet all-day operation needs. In addition, continuous charging presents unique characteristics where the charging process occurs simultaneously with vehicle operation, thereby eliminating impacts on both TT and EVSPs, as no dedicated charging stops or timetable adjustments are required.

We use keyword retrieval, including electric vehicle(s) or bus(es), timetabling or timetable, departure (time), synchronized stops, synchronized departure, and headways, which also confirm this point above. It is found that there is no separate study on BEV timetable optimization, and studies related to fast charging are almost all combined with vehicle scheduling and charging planning. We will discuss these articles in detail in Section 4.

Generally speaking, the core goal of traditional PT timetabling optimization is to deal with the trade-off between passenger service efficiency and operational economy. The former objectives usually include minimizing waiting time or passengers’ travel and transfer time, while the latter refers to vehicle utilization or operational cost control so as to cope with dynamic passenger demand and resource constraints.

Divided from the perspective of problem purpose, the mainstream objectives of timetabling can be summarized into four categories. For a more detailed description, Ibarra-Rojas et al. [3] defined them as follows:

• Timetabling to meet specific demand patterns;
• Timetabling to minimize waiting times;
• Timetabling to maximize synchronous events;
• Timetabling with multi-objective optimization.

Therein, timetabling to meet specific demand patterns refers to constructing a timetable based on passenger demand. It can better adapt to the needs of passengers and improve the service efficiency. Given the uncertainty of demand, which may result in a non-demand-driven timetable, determining the appropriate headway becomes challenging. Obviously, minimizing the waiting time is used to reduce the waiting time for passengers at the transfer station, which can directly improve the travel satisfaction of passengers. However, other factors, such as vehicle operating costs, may not be fully considered. Traditional PT timetabling also focuses on maximizing synchronous events. By optimizing the arrival times of vehicles, the number of simultaneous arrivals at the transfer station for different lines is increased, thus facilitating passenger transfers and reducing congestion. Typically, this problem is usually complex, difficult to solve, and may be affected by the uncertainty of actual traffic conditions. In order to consider more factors when constructing a timetable, multi-objective optimization is proposed. However, these objectives are usually conflicting; thus, the trade-off between them is more complex, making it difficult to find the optimal solution.

Nowadays, the current research trend is shifting from static single-objective optimization to multi-factor collaboration, such as combining timetabling with multi-type vehicles [7,8,9,10] or charging scheduling [11,12]. All of these make the research more comprehensive but complex; for a more detailed introduction and methods of extended research, we refer to Liu et al. [13].

Considering the uncertainty derived from passenger demand and travel time in actual operational situations, Gkiotsalitis and Alesiani [14] designed a genetic algorithm (GA) combined with sequential quadratic programming to solve the minimax problem and optimize a robust timetable. In addition, real-time adjustment strategies, such as holding, speed changing, and skip-stop strategies, have been proposed [15,16], which work as a supplementary means to optimize system performance. Zhang et al. [17] discussed the time dependency of travel time in timetabling and proposed a nonlinear programming model solved by a compass search algorithm. Its essence was to slightly shift vehicle departure times at the departure terminal with a holding strategy.

The holding strategy of traditional PT mainly considers the regularity of vehicle operation, such as maintaining the target headway and reducing the passengers’ waiting time. In contrast, the holding strategy of EBVs needs to consider factors such as charging demand and battery status in addition to these. Gkiotsalitis [18] considered the scheduled charging times to avoid charging delays and proposed a mathematical model with convex, quadratic objective functions and linear inequality constraints. Considering the uncertainty of travel time, the original problem was transformed into a stochastic optimization problem, which could be solved by iterative approximation methods, such as sample average approximation. The analytic solution could be used to solve the stochastic optimization problem in real time.

4. Electric Vehicle Scheduling

The EVSP is an important research direction in the field of urban PT, aiming to optimize the operation plan of EVs, taking into account their limited driving range, charging requirements, and the layout of charging infrastructure. Compared to traditional vehicle scheduling, the EVSP requires coordinating the charging schedule while taking into account factors such as the time-of-use (TOU) electricity price, the start time of charging events, and other constraints, as emphasized by Behnia et al. [4]. Abdelwahed et al. [19] designed two mixed-integer linear programming (MILP) models, i.e., discrete time optimization and discrete event optimization, to solve the problem of opportunistic fast charging scheduling in the BEV network by CPLEX. Abdelwahed et al. [20] then extended the above method to the overall optimization of the electric bus network, studied the real-time scheduling problem under uncertainty, and developed a dynamic threshold-based algorithm to solve it. Raman et al. [21] constructed an electric vehicle charging behavior simulation model to simulate individual BEV travel and charging processes in Greater London based on actual data. An event-triggered algorithm was used to simulate charging behavior. The study mainly solved the resilience of urban public electric vehicle charging infrastructure under flood impact, assessed the impact of the flood on the charging network, and proposed countermeasures.

In addition, external factors such as uncertainty in traffic flow, fluctuations in passenger demand, and instability in charging times further increase the complexity of scheduling issues. Zhang et al. [1] pointed out the shortcomings of robust scheduling and dynamic adjustment strategies in current research. Therefore, how to optimize the charging strategy and reduce the operating cost while meeting the needs of bus operation has become the core issue of current research. Behnia et al. [4] reviewed from the perspective of objectives, discussed the relevant research of the problem and the corresponding methods proposed and also listed the application frequency of the corresponding algorithms in recent years.

Table 2. Comparison of relevant studies on EVSPs.

Publication	Objective(s)	Model	Solution Type				Solution Method
			Ex	Hu	ML	Others
Zhu and Chen (2013) [22]	to minimize the capital investment for the electric fleet and the total charging demand in stations	A multi-objective model		√			NSGA-II
Li (2014) [23]	to minimize total operational costs	ILP	√	√			BP+a truncated CG heuristic algorithm
Wen et al. (2016) [24]	to minimize the number of vehicles and the total traveling distance	MIP		√			ALNS
Yao et al. (2020) [25]	to minimize annual total scheduling costs	MILP		√			A heuristic procedure based on the GA
Alwesabi et al. (2020) [26]	to find the minimum total cost	MIQCP	√				Julia–Gurobi solver
Wang et al. (2020) [27]	to minimize battery replacement costs	An optimal scheduling method based on dynamic programming				√	Dynamic programming with a reverse-order matching strategy
Wang et al. (2021) [28]	to minimize the total cost	A connection network model		√			GA + CG
Zhang et al. (2021) [29]	to minimize the total operational cost of the transit system	A set partitioning model	√				BP
Lee and Boomsma (2022) [30]	to minimize the total cost	An MDP using DP				√	ADP, the LSMC method
Guo et al. (2023) [31]	to minimize the operating costs	MIP based on space–time–state framework		√			A Lagrangian relaxation algorithm and a dedicated dynamic dispatching procedure
Shen et al. (2023) [32]	to minimize the fleet size and operating cost and maximize on-time performance	A probabilistic model for EVSPs based on the probability density function of trip time		√			ALNS
Vendé et al. (2023) [33]	to minimize the total charging costs	MIP		√			AtS and D-AtS heuristic algorithm
Cao et al. (2023) [34]	to minimize the fleet size, idle mileage, and charging cost	MINLP		√			A preprocessing-based GA
Xie et al. (2023) [35]	to minimize the total cost for bus companies	MINLP				√	A two-stage solution algorithm based on ‘Generation and Selection’
Zhang et al. (2024) [36]	to maximize the profit	——			√		M-SAC
Li and Li (2024) [37]	——	A distributionally robust real-time flexibility evaluation model	√				CPLEX or Gurobi
De Vos et al. (2024) [38]	to minimize the total costs	Path-based binary programming model based on a connected network		√			Two heuristic algorithms based on CG (price and branch and diving heuristic)
Lu et al. (2025) [39]	to minimize the total cost	MIP model	√				DLS-BP

Note: ‘√’ signifies the solution type to which the research method belongs. Acronyms used in Table 2 include Ex—exact method; Hu—heuristic method; ML—machine learning method; ILP—integer linear programming; MIP—mixed-integer programming; MINLP—mixed-integer nonlinear programming model; MIQCP—mixed-integer quadratically constrained programming; CG—column generation; GA—genetic algorithm; MDP—Markov decision process; DP—dynamic programming; ADP—approximate dynamic programming; LSMC—least squares Monte Carlo; AtS—assign then schedule; D-AtS—daily assign then schedule; ALNS—an adaptive large neighborhood search algorithm; M-SAC—Munchausen reinforcement learning with the soft actor-critic method; BP—branch and price algorithm; DLS-BP—dynamic label setting-based branch and price algorithm; NSGA-II—non-dominated sorting genetic algorithm.

summarizes the EVSP research, including methods and solutions in recent years, which we generally divide into the following four categories: exact method, heuristic method, machine learning method, and other methods, such as the dynamic programming method.

Figure 4 offers a comprehensive visualization of methodological trends in EVSP research. The temporal distribution analysis reveals a significant concentration of studies, with approximately 90% of the reviewed literature published from 2015 to 2025.

Figure 5 further illustrates the evolving trends in solution methodologies. The longitudinal analysis reveals a predominant reliance on heuristic and exact methods during the 2020–2022 period, followed by the emergence of machine learning approaches in recent years (2023–2024). This trajectory suggests an ongoing methodological shift in the research field.

4.1. Exact Methods for Solving EVSPs

An exact method refers to obtaining globally optimal solutions through commercial solvers and exact algorithms. A notable application is presented by Alwesabi et al. [26], who developed a mixed-integer quadratically constrained programming model for optimizing electric bus scheduling under dynamic wireless charging infrastructure in single-depot systems. Their implementation utilizing the Julia programming language and Gurobi solver achieved a 0.000% relative optimality gap. Julia’s dynamic type system and multiple dispatch capabilities enabled adaptive function implementation based on parameter types, particularly advantageous for handling large-scale optimization problems with computationally intensive constraints and objective functions. Considering the uncertainty of the state of charge and the random early departure behavior of EVs, Ref. [37] proposed a distributionally robust real-time flexibility evaluation model. This model constructed uncertainty and ambiguity sets in a data-driven and online updating manner and was then transformed into a MILP problem for a solution through the duality theorem, which could be solved efficiently using a general-purpose solver, such as CPLEX or Gurobi.

The mixed-integer programming (MIP) framework has emerged as an effective framework for joint optimization of vehicle scheduling and charging operations. For example, Zhang et al. [29] formulated a MIP model incorporating battery degradation and nonlinear charging characteristics to minimize operational costs in electric bus fleets. Lu et al. [39] proposed a similar framework to provide an effective solution for the scheduling and charging strategy optimization of BEVs under the TOU pricing policy.

Mixed-integer programming (MIP) frequently faces computational complexity challenges when applied to large-scale cases. To address this issue, the branch-and-price (B&P) algorithm has been widely adopted for solving multi-depot vehicle scheduling problems. By decomposing the main problem and pricing subproblem, an effective vehicle scheduling scheme is gradually generated. In the pricing problem, Zhang et al. [29] used the electrochemical characteristics of lithium batteries to build a pseudo-network and designed a multi-label correction algorithm. The case verified that the algorithm could solve medium-sized problems (60–120 trips) in a reasonable time, such as less than 2.4 h. However, the computing efficiency was greatly affected by the number of trips, and the proportion of CPU time to solve pricing problems increased with the increase in the problem scale, which proved that the efficiency of the B&P algorithm largely depended on the computational efficiency of column generation, that is, the pricing problem of the label algorithm. Lu et al. [39] designed a dynamic label setting (DLS) algorithm in the B&P algorithm framework to generate feasible paths and improve computing efficiency through dominance rules. Compared with the GA [25] and the large neighborhood search algorithm [24], the DLS-B&P algorithm took longer computation time but could obtain a better solution; it demonstrated superior cost optimization capabilities that became particularly pronounced in large-scale implementations.

These findings align with Li’s [23] critical assessment of B&P algorithms. While demonstrating high efficiency for medium-scale problems (117–484 trips), its application to large-scale (947 trips with more than 1100 time nodes) systems remains constrained by computational resource requirements and algorithmic complexity. This limitation highlights the need for the continued development of hybrid algorithms that combine exact methods with heuristic approaches for practical large-scale implementations.

4.2. Heuristic Methods for Handling EVSPs

Given the computational limitations of exact methods in large-scale problems, heuristic methods have garnered significant attention due to their superior efficiency. Notably, GAs have demonstrated promising results as global search mechanisms. Zhu and Chen [22] successfully implemented GAs for electric bus scheduling optimization, achieving substantial reductions in both fleet size and charging costs. Cao et al. [34] developed a preprocessing-based GA to address the computational challenges of a mixed-integer nonlinear programming model in multi-type electric vehicle scheduling. Upon offering stronger local search capability, adaptive large neighborhood search (ALNS) emerged as another potent heuristic, particularly effective in handling complex constraints through dynamic strategy adaptation. Wen et al. [24] systematically compared ALNS with the CPLEX solver, revealing critical efficiency differentials. For small-scale instances, e.g., 10–30 trips, ALNS obtained solutions within seconds compared to CPLEX’s prolonged computation times, while in large-scale scenarios, e.g., 100–500 trips, ALNS delivered competitive solutions within hundreds of seconds. Importantly, parameter calibration proved essential for ALNS effectiveness, with post-optimization refinements improving target values by 3.1% on average.

Complementing these heuristic approaches, Vendé et al. [33] developed a hybrid framework combining MILP with multi-phase heuristics for multi-day scheduling challenges. Their experimental validation confirmed that while exact methods excelled in small- to medium-scale problems, heuristic variants demonstrated superior scalability for complex, large-scale instances.

Meanwhile, advancements in automation technology introduce novel scheduling complexities through modular autonomous electric-connected buses. Guo et al. [31] addressed this through a two-phase optimization system with initial static planning via space–time–state MILP followed by dynamic dispatching using Lagrange relaxation heuristics. The experimental results verified the framework’s effectiveness in balancing pre-scheduled operations with real-time demand responsiveness, particularly in data-intensive environments.

Regarding operational uncertainties, Shen et al. [32] enhanced scheduling robustness through probabilistic modeling, integrating trip duration probability density functions. Their ALNS-based implementation outperformed conventional LNS in EVSPs, maintaining fleet capacity while improving solution reliability—an advancement aligning with the findings of Wen et al. [24] on ALNS adaptability.

Finally, hybrid algorithmic integration shows particular promise for multi-depot challenges. Wang et al. [28] innovatively combined GAs with column generation, utilizing GAs within Ribeiro et al.’s [40] connection network framework to accelerate column generation convergence. This synthesis effectively mitigated the computational bottlenecks observed in traditional B&P algorithms for large-scale instances (510 trips in the real world), demonstrating the growing importance of methodological cross-pollination in scheduling optimization. De Vos et al. [38] designed a path-based binary programming model under the framework of a connected network to solve the scheduling problem of electric buses with limited capacity charging stations and partial charging. The B&P and diving algorithms were proposed. For small instances (including 100–185 trips), the diving algorithm performed well, with a gap of less than 1.5%. On large instances, combined with the node removal strategy, the algorithm could solve the instance with 816 trips within 7 h, achieving an optimality gap of less than 3%.

4.3. Machine Learning Methods Applied to EVSPs

Machine learning, as a cutting-edge technology, has found applications in PT. Fescioglu-Unver and Yıldız Aktaş [41] reviewed the application of machine learning in routing, charging scheduling, pricing strategy adjustments, and charging facility planning during 2014–2023. As noted by Fescioglu-Unver and Yıldız Aktaş [41], machine learning facilitates rapid decision making in uncertain environments and can effectively address complex problems, such as predicting charging demand, optimizing charging schedules, and adjusting pricing strategies. Based on a systematic review of 111 studies, Zhao et al. [42] demonstrated that the Markov decision process framework could effectively address charging scheduling problems by incorporating the state space, action space, and reward function under operational uncertainties. Since the EVSP similarly encounters various uncertainties, including fluctuations of dynamic passenger demand and unpredictable BEV running times during actual operations, the reinforcement learning method can build a similar decision-making model, allowing the agent to continuously learn and optimize strategies in the face of these uncertain factors to adapt to the dynamically changing scheduling environment. For large-scale problems, it can also accelerate problem solving, as demonstrated by its exceptional performance in electric vehicle routing problems. However, the real-time responses generated by machine learning methods are not always optimal. Additionally, some algorithms require high-quality, large-scale data, and poor data quality can significantly degrade model performance. Moreover, model interpretability is often limited, posing challenges in scenarios that demand high levels of decision transparency.

Currently, most machine learning methods are applied to charging scheduling and facility management; for more details, refer to corresponding reviews [41,42]. Given that EVs can serve as flexible energy storage and transportation devices, these methods hold potential for extension to EVSPs. Lu et al. [43] reviewed energy transport scheduling for EVs and fuel cell vehicles in seaport areas, analyzing 1025 relevant publications. The problem explored in this paper extended EVSPs, typically represented as a nonlinear, non-convex model with a vast solution space. Machine learning methods are data driven, which can learn hidden patterns and patterns from large amounts of data. In EVSPs, a large amount of data about bus operation has been accumulated, such as historical driving track, passenger flow, charging time, and so on. Through the analysis and learning of these data, the machine learning model can mine the change rule behind passenger demand, the energy consumption through different time periods and sections of road, and other information so as to accurately predict future demand and make more reasonable scheduling schemes. Compared to traditional optimization methods, machine learning techniques offer significant advantages for three main reasons. Firstly, they leveraged neural networks’ powerful learning capabilities to uncover nonlinear relationships in data and effectively manage complex variable associations. Secondly, in complex and dynamic environments, they optimized strategies through iterative learning, enabling effective adaptation to uncertainties. Thirdly, they employed function approximation and other techniques to address large-scale state and action spaces, bypassed direct nonlinear constraint resolution during strategy training, and enhanced computational efficiency and real-time decision making. Notably, the number of decision variables reaches 2.2 × 10⁷ when coordinating 100 vehicles for 200 tasks.

The real-time aggregate flexibility scheduling problem for EV charging, a multi-period optimization challenge, can be formulated as multi-stage stochastic dynamic programming. However, due to the complexity of randomness, Zhang et al. [36] adopted a model-free deep reinforcement learning algorithm. This approach incorporated Munchausen reinforcement learning into the soft actor-critic method, making it suitable for EV aggregation scheduling under uncertainties. When compared to multiple baseline algorithms, it demonstrated advantages such as enhanced training stability, rapid convergence, a high charging completion rate, and reduced total costs. It effectively balanced economic efficiency and user satisfaction, performing well in both small-scale and large-scale systems.

4.4. Other Methods to Cope with EVSPs

Dynamic programming accurately solves problems with defined phases and state transitions; however, its computational complexity is high, making it challenging to scale to large problems. To overcome this limitation, Wang et al. [27] extended dynamic programming by incorporating a reverse-order matching strategy to mitigate the impact of battery capacity degradation on EVSPs. The experimental results indicated that the proposed method reduced battery replacement investment for the electric bus fleet system by 20% compared to scenarios where buses operated on fixed routes without accounting for such factors. Overall, dynamic programming combined with a reverse-order matching strategy has proven to be an efficient and effective approach for addressing large-scale electric bus scheduling problems.

In a market environment, an approximate dynamic programming algorithm, based on least squares and optimized Monte Carlo, was developed by Lee and Boomsma [30] to optimize the short-term operation of plug-in hybrid electric vehicle fleets. Experiments demonstrated that the algorithm converged as the sample size increased. While training time grew with fleet size, the growth rate remained relatively low, indicating the algorithm’s capability to address large-scale vehicle scheduling problems.

In the two-stage method, vehicle scheduling and charging scheduling are optimized sequentially, where the initial solution is generated in the first stage and then optimized in the second. Xie et al. [35] achieved collaborative optimization of electric buses through a two-stage algorithm based on ‘Generation and Selection’, although global optimization was not guaranteed. Compared to traditional GAs and CPLEX, the ‘Generation and Selection’ algorithm significantly improved solving accuracy, with a smaller performance gap compared to CPLEX. Regarding computational time, while the algorithm was less efficient than the GA, it outperformed CPLEX and demonstrated more balanced performance across various problem scales, including successful application to a real-world case study with 56 bus lines in the center of Beijing.

4.5. Extended Research Directions to Optimize EVSPs

In the last decade, studies on EVSPs have expanded to include charging scheduling and charging facility planning, as comprehensively reviewed by Zhou et al. [44]. This review focuses primarily on the integration of EVSPs and crew scheduling in recent years. Crew scheduling, when considered independently, may remain unaffected by the introduction of BEVs; however, its integration with EVSPs introduces complexities due to deadhead trips and charging requirements. The limited driving range and recharging time of BEVs complicate the integrated optimization of vehicle and crew scheduling. Few studies, to our knowledge, have focused on synchronizing electric vehicles and crew scheduling. The adoption of the BEV influences the availability time of vehicles and generates additional deadhead trips due to charging scheduling, which subsequently affects crew scheduling schemes. Comprehensive approaches to integrating vehicle and crew scheduling are typically classified into three categories: (1) network flow-based models, (2) constraint-based models, and (3) maximum covering models [45].

Recent advancements in vehicle and crew scheduling optimization have demonstrated significant progress through various modeling approaches and solution algorithms. However, there are still few studies on EVSPs and crew scheduling. We entered electric vehicle scheduling and crew scheduling and integrated them as keywords into the Web of Science, and the following articles were retrieved. Jiang and He [46] pioneered a discrete mixed-integer linear programming framework specifically designed for crew scheduling on single bidirectional routes, incorporating lunch breaks as a critical operational constraint. Building on this foundation and addressing the emerging challenge of mixed fleets Wang et al. [47] proposed a novel bi-level multi-objective programming model that optimized vehicle and crew scheduling concurrently. Their methodological contribution was further enhanced by an advanced ε-constraint-based multi-objective particle swarm optimization algorithm.

From a network optimization perspective, Perumal et al. [48] developed dual network flow models validated through real-world case studies, employing an ALNS algorithm integrated with branch-and-price heuristics. Extending this network-based approach, Sistig and Sauer [49] incorporated practical charging considerations by modeling both depot and opportunity charging scenarios while accounting for crew labor regulations. Their methodological framework employed an adaptive variable neighborhood search algorithm, demonstrating the evolution of solution techniques in this domain. Xie et al. [35] formulated an integer nonlinear programming model to co-optimize vehicle scheduling, charging plans, and crew scheduling for pure electric bus lines under three modes: fast charging, slow charging, and battery swapping. The two-stage algorithm based on ‘Generation and Selection’ was applied to solve the problem. Cong et al. [50] studied vehicle scheduling and driver scheduling on a hybrid electric and fuel bus network and proposed an improved simulated annealing algorithm to solve the model. A more detailed approach to the integration of vehicle scheduling and crew scheduling was provided by Perumal et al. [51].

5. The Integration of Electric Vehicle Scheduling and Timetabling

Improving PT systems involves tackling complex planning problems. Traditionally, these issues were solved step by step. However, stepwise optimization may result in sub-optimal solutions [52] and global coordination of complex systems is still a key challenge, requiring the development of more efficient integration models and algorithms. Nowadays, integrating multiple planning stages has proven to enhance both service quality and cost efficiency [53].

In what follows, the methodologies addressing the integrated EVSPs and timetabling problem will be discussed. To the best of our knowledge, no reviews have been conducted on this integrated problem in recent years. Electric vehicle scheduling, timetables, and timetabling were selected as the keywords to conduct searches in Web of Science and Google Scholar. It was found that corresponding research on this topic is limited. Based on the methodologies discussed in existing research, they are categorized into two types: exact methods and heuristic methods.

5.1. Exact Methods

Currently, exact methods are predominantly applied through simplified models solved with commercial solvers; however, their efficiency in handling large-scale and complex problems remains limited. Quttineh et al. [11] formulated a mixed-integer programming model that integrates timetabling, vehicle scheduling, and charging facility locations for EVs, with the objective of minimizing their overall number. The model was solvable using the CPLEX solver to determine optimal solutions for small-scale problems. However, the actual operational planning of EVs was often highly complex. As the problem’s scale expanded, the number of associated variables and constraints grew, thereby highlighting the limitations of exact methods. For large-scale problems, certain instances cannot achieve optimality within one hour, with significant duality gaps, underscoring the need for enhanced solving efficiency. To address this, Gkiotsalitis et al. [54] introduced valid inequalities to tighten the solution space, thereby reducing computation time. Additionally, they linearized the original mixed-integer nonlinear programming model into a MILP model to obtain the global optimal solution via a commercial solver. The findings demonstrated that the model performed effectively under base-case conditions. Although valid inequalities increased the number of constraints, they substantially improved computational efficiency, enabling the resolution of up to 30 travel cases and providing an effective solution for the EVSPs.

5.2. Heuristic Methods

Heuristic methods have emerged as an effective alternative to address the limitations of exact methods in solving large-scale, complex problems. These methods demonstrate their practical value by trading off some accuracy to achieve approximate optimal solutions within a reasonable timeframe.

Moreover, focusing on the operational planning of multi-type electric buses under time and space imbalance, Tang et al. [10] developed a nonlinear integer programming model to minimize the total costs for users and operators. Given the nonlinear and non-convex complexity of the model, a heuristic algorithm based on the GA and a right-shift departure time strategy was designed to address the problem.

Xu et al. [55] proposed a multi-commodity flow model based on a space–time network and applied a Lagrange relaxation heuristic algorithm to solve the problem. The experimental results demonstrated that the algorithm provided tighter upper and lower bounds within significantly shorter CPU times and exhibited a smaller average gap compared to the CPLEX solver in small-scale cases. However, for complex line topologies, the CPU time increased along with a larger optimality gap.

Particle swarm optimization (PSO) has proven to be highly effective in dynamic scheduling applications, particularly for addressing multi-objective optimization challenges. Teng et al. [56] implemented a multi-objective PSO algorithm to optimize electric bus charging schedules, achieving approximately a 19% improvement in the average vehicle kilometers compared to the existing schedule. However, their experimental results indicated a computational duration of approximately four hours, potentially limiting its applicability in time-sensitive scenarios requiring sub-hourly decision cycles. Nonetheless, the study empirically validated PSO’s capability to effectively balance conflicting objectives—minimizing energy costs and maximizing charging completeness—with Pareto optimal solutions showing deviations of ≤5% from theoretical optima. This highlighted PSO’s potential as a robust framework for operational decision support systems when appropriately calibrated.

Although the PSO algorithm has been widely applied across various fields due to its inspiration from the predation behavior of birds, it faces certain limitations, including poor diversity, susceptibility to local optimization, and iteration stagnation. To address these challenges, researchers have proposed various improvement strategies, such as adjusting algorithm parameter distributions, modifying the particle swarm position update formula, altering population initialization processes, and integrating other intelligent algorithms. For instance, improved algorithms in some studies can establish stable ecological niches and identify multiple potential optimal solutions for multi-modal, multi-objective optimization problems. Moreover, these enhanced algorithms achieve more than 95% proximity to the real Pareto frontier when addressing related problems through specific structural designs. For additional details on the PSO algorithm, refer to Qiao et al. [57].

Considering the nonlinear energy consumption caused by vehicle dynamic load and multi-line interactions at charging stations, Fan et al. [58] developed a novel nonlinear energy consumption model that accounts for these factors. An improved particle swarm optimization (IPSO) algorithm was designed to solve the model. In terms of efficiency, the IPSO algorithm outperformed traditional PSO algorithms across various particle population sizes. As the problem scale increased, IPSO demonstrated higher improvement ratios and faster convergence. The study indicated that compared to existing scheduling schemes, the optimized IPSO approach reduced the number of vehicles, decreased charging costs, and lowered the proportion of peak charging times from 26.50% to 3.78%.

For the single-line timetabling integrated EVSP problem, Gao et al. [59] proposed a data-driven multi-objective optimization model, solved using an improved NSGA-II algorithm. The heuristic algorithm efficiently calculated Pareto optimal solutions within a reasonable timeframe.

Duan et al. [12] introduced an integrated arc-based model that incorporated practical considerations, such as battery degradation, nonlinear charging curves, and TOU pricing, alongside flexible charging and timetable-shifting strategies. The model was subsequently transformed into a two-stage framework. In the first stage, the total operating cost was minimized using column generation technology, while in the second stage, two timetable-shifting strategies were employed to minimize peak power demand.

Table 3. Comparison of relevant studies on integrated research on the EVSP and TT.

Publication (Chronologically)	Objective(s)	Model	Solution Type		Solution Method
			Ex	Hu
Teng et al. (2020) [56]	To minimize the number of vehicles and total charging costs	A multi-objective optimization model for a single bus line operated with electric buses		√	MOPSO algorithm
Gkiotsalitis et al. (2023) [54]	To minimize the total cost	MINLP	√		Commericial solver with linearization and valid inequalities
Duan et al. (2023) [12]	To minimize the total costs considering the power grid pressure cost	An integrated arc-based model		√	CG and two timetable-shifting algorithms
Quttineh et al. (2023) [11]	To minimize the number of buses (the number of arcs leaving the depot)	MIP	√		MIP solver complex
Tang et al. (2023) [10]	To minimize the total cost to users and operators	Nonlinear non-convex integer programming model		√	GA associated with the right shifting of departure time
Xu et al. (2023) [55]	To maximize the total profit	A multi-commodity network flow model based on a time–space network framework		√	A Lagrangian relaxation heuristic algorithm
Fan et al. (2023) [58]	To minimize the number of vehicles and total operation costs	Multi-objective MINLP		√	An improved PSO algorithm
Gao et al. (2025) [59]	To minimize the mixed cost, including passenger travel cost and bus enterprise operating cost	A data-driven multi-objective optimization model		√	An improved NSGA-II algorithm

Note: ‘√’ signifies the solution type to which the research method belongs. Acronyms used in Table 3 include Ex—exact approach; Hu—heuristic approach; MINLP—mixed-integer nonlinear programming model; MIP—mixed-integer programming; MOPSO—multi-objective particle swarm optimization; CG—column generation; GA—genetic algorithm; NSGA-II—non-dominated sorting genetic algorithms.

presents a comparative analysis of relevant studies on integrated research addressing the EVSP and TT, highlighting key aspects such as charging methods, multi-depot considerations, vehicle heterogeneity and optimization, model structures, and solution methods.

Generally speaking, the exact method and the heuristic method have their own advantages in algorithm research. Although the exact method can find the theoretical optimal solution, it has low efficiency in the face of large-scale complex problems. Although the heuristic method cannot guarantee finding the global optimal solution, in practice, it provides a feasible approach by quickly obtaining approximate optimal solutions. Different algorithms are applicable to different scenarios, and researchers and decision makers can choose the appropriate algorithm to optimize EVSPs and timetabling problems according to the scale, complexity, and accuracy requirements of the specific problem.

6. Conclusions and Future Research Directions

The integration of BEVs into PT represents a crucial stride towards sustainable urban mobility, echoing the global pursuit of environmental conservation and reduced carbon footprints. BEVs, as a cornerstone of this transition, promise to mitigate air pollution, optimize operational costs, and elevate the overall quality of public transit services. Nevertheless, their widespread implementation is hindered by inherent limitations, particularly the restricted driving range stemming from battery degradation and the energy demands of onboard systems, which pose formidable challenges to seamless PT operations.

This paper undertakes an in-depth exploration of BEV timetabling and scheduling, encompassing a comprehensive review of the existing literature on the method or algorithms proposed. We delve into the development of timetabling problems for electric vehicles, meticulously comparing diverse methods employed in this field. We further scrutinize the EV scheduling landscape, with a specific emphasis on four main categories of solution methods: exact methods, heuristic methods, machine learning methods, and other methods (such as dynamic programming). Each method exhibits distinct characteristics, advantages, and drawbacks. (i) Exact methods can yield globally optimal solutions but struggle with high computational complexity in large-scale scenarios; (ii) heuristic methods sacrifice some accuracy for enhanced efficiency, rendering them suitable for real-world complex problems; (iii) machine learning methods hold promise in handling uncertainties and complex relationships but face issues like limited interpretability and data dependency; and (iv) other methods, though effective in certain contexts, have their own limitations in terms of scalability and optimality.

At present, most of the studies are mainly based on heuristic and exact algorithms, but with the continuous development of machine learning technology and the influence of realistic uncertainties, it is an inevitable trend to apply machine learning methods to the field of EVSPs.

Subsequently, the paper delves into the integrated timetabling and scheduling of BEVs, analyzing the state-of-the-art approaches and highlighting the strengths and weaknesses of current methods. By synthesizing these insights, the paper distills the key findings from the past decade of research in this domain and showcases the emerging trends in battery electric PT timetabling and scheduling. Based on the comprehensive analysis in this paper, several future research directions, as shown in Figure 4, have been identified as follows.

6.1. Robust Scheduling and Dynamic Adjustment

Robust scheduling and dynamic adjustment mechanisms are essential for enhancing the operational reliability of electric bus systems. A robust scheduling framework should be developed to address uncertainties in traffic flow, passenger demand variability, and charging time fluctuations. This framework must be complemented by real-time dynamic adjustment capabilities to maintain service reliability under unpredictable conditions. Empirical studies have demonstrated that traffic congestion patterns and passenger demand volatility significantly impact electric bus scheduling efficiency. The implementation of robust optimization techniques, combined with adaptive adjustment protocols, can lead to measurable improvements in both service punctuality and operational cost efficiency, as evidenced by multiple case studies in urban transit systems.

6.2. Integration of Multiple Planning Processes

The integration of multiple planning processes remains a critical challenge in EVSPs. While traditional PT systems have established relatively mature frameworks for integrated planning, the coordination of EVSPs with other PT optimization problems—such as timetabling and crew scheduling—has received limited research attention. This gap is particularly significant given the potential of integrated planning to optimize resource utilization across operational levels, thereby enhancing both systemic efficiency and economic performance. The development of comprehensive EVSP integration frameworks represents a necessary evolution in PT optimization, as it addresses the unique constraints of electric bus systems, including charging infrastructure limitations and energy consumption variability. Future research directions should focus on developing unified optimization models that simultaneously consider vehicle scheduling, crew assignment, and timetable synchronization while accounting for the distinctive characteristics of electric bus operations.

6.3. Application of Intelligent Algorithms and Techniques

The application of intelligent algorithms and advanced technologies has emerged as a transformative approach in EVSPs. Enabled by the Internet of Vehicles and intelligent transportation systems, big data analytics and artificial intelligence techniques—particularly machine learning and deep learning—are being leveraged to extract actionable insights from operational data. These technologies facilitate accurate prediction of critical parameters, including traffic flow patterns, passenger demand fluctuations, and charging demand, thereby providing real-time decision support for dynamic scheduling.

Especially, inverse optimization (IO), a supervised learning technique, has recently gained significant attention in transportation research. The core premise of IO lies in reconstructing decision-makers’ implicit cost functions by analyzing their observed behaviors. A notable application was demonstrated by Scroccaro et al. [60], who successfully implemented an IO framework to decode behavioral preferences in vehicle routing problems, achieving superior performance in real-world routing scenarios.

The potential extension of IO methods to EVSPs warrants careful consideration. While the EVSP introduces additional complexity through battery capacity constraints, charging infrastructure limitations, and temporal charging requirements, the inherent flexibility of IO suggests promising adaptation possibilities. Specifically, IO could be modified to incorporate EV-specific parameters as exogenous signals, potentially learning optimal strategies from expert decisions or historical operational data.

However, several methodological adaptations would be required for successful EVSP implementation, such as (1) the development of advanced hypothesis functions capable of accurately modeling battery degradation and energy consumption patterns and (2) the redesign of loss functions and optimization algorithms to accommodate EV-specific constraints, including range limitations and charging time windows. Despite these challenges, the adaptability of IO methods positions them as a viable approach for addressing complex transportation optimization problems, particularly in the evolving landscape of electric mobility systems.

6.4. Combined with New Traffic Modes

The integration of emerging transportation modes presents new opportunities and challenges for urban transit scheduling research. As cities evolve, novel mobility solutions—characterized by distinct operational patterns and service models—are reshaping traditional approaches to scheduling optimization. These include shared mobility platforms, demand-responsive transit systems, and autonomous PT vehicles, each offering unique perspectives for addressing complex scheduling problems.

The convergence of conventional timetabling methods with these innovative service models enables transit systems to better accommodate diverse travel demands. Based on dial-a-ride problems on a fixed circuit problem for introducing service variants with flexible stopping patterns and schedules, Molenbruch et al. [61] designed a MILP model with a dynamic programming algorithm and LNS algorithm. Another notable example was the coupling–decoupling strategy proposed by Cao et al. [62] for autonomous PT vehicle scheduling, which optimized system performance through dynamic vehicle resizing and adaptive station configuration. This approach demonstrated significant improvements in key performance indicators, including reduced passenger waiting times and lower operational costs, while maintaining service flexibility. With the development of modular vehicle technology, a Modular Autonomous Electric Vehicle (MAEV) unit is created. Yuan et al. [63] focused on the application of MAEVs in demand-responsive bus services, aiming to optimize their routing and charging scheduling. A MILP is proposed to minimize the total cost of the system by considering factors such as passenger transfer and vehicle charging time. To solve this model, an ALNS algorithm is developed. Building upon the foundational work on MAEV in Reference [63] and incorporating the latest literature identified through systematic searches in Web of Science and Google Scholar, we chronologically present the evolving research trends in MAEV studies from 2020 to 2025, as shown in Figure 6. The data reveal a consistent year-on-year growth in MAEV-related publications, suggesting that MAEVs will remain a prominent research focus beyond 2025. For optimized scheduling and charging infrastructure planning for autonomous modular public transport (AMB) systems, Chang et al. [64] proposed collaborative optimization methods to improve the sustainability of urban public transport systems. Oargă et al. [65] discussed the energy efficiency advantages of Modular Autonomous Vehicles (MAVs) in the PT system. Hong et al. [66] established a data-driven model for modular vehicle scheduling in scenic areas. Focused on customized bus services, Guo et al. [31] proposed a two-stage optimization method to explore the potential application of MAEVs. Liu et al. [67] extended the traditional DF model to fit the definition of autonomous PT vehicle systems and verified its potential to minimize fleet size in large-scale, multi-line, and multi-terminal AMPT systems. Future research can focus on developing integrated scheduling frameworks that seamlessly incorporate both traditional and emerging transportation modes, ensuring efficient resource allocation across multi-modal networks.