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Road disruptions frequently occur in practice, resulting in a productivity loss of bus services and widespread passenger delays. These negative impacts are significant, especially when multiple routes are influenced at the same time. In order to mitigate these impacts, this paper proposes a multi-route coordination approach that collaboratively adjusts multiple bus routes and optimizes bus timetables to provide effective alternative bus services for passengers. Three adjusting strategies are adopted for bus routes with varying passenger demand: detouring, short-running, and cancellation. To address the multi-route coordination problem, a column-generation-based two-stage framework is developed. Concretely, a column generation technique is utilized in the first stage to iteratively generate candidate adaptive bus routes and passenger paths. Following that, an integrated integer programming model is built in the second stage to simultaneously determine bus timetables and the combinations of those adaptive bus routes. After realizing the low computational efficiency for large-scale problems, this paper designs a customized decomposition algorithm based on set partitioning to solve the presented model and obtain near-optimal solutions efficiently. Finally, the proposed methodology is applied to an illustrative Sioux Falls network and a real-world bus network in Beijing to verify its validity and effectiveness. Three comparative analyses are conducted to discuss the advantages of the three adjusting strategies, to investigate the benefits of coordinating bus timetables, and to explore the applicability of different adjusting strategies, respectively. • A multi-route coordination problem for bus systems in response to road disruptions. • A column-generation-based two-stage framework to address the problem. • A customized decomposition algorithm based on set partitioning for model solving. • The framework and algorithm are applied to a real-world bus network in Beijing. [ABSTRACT FROM AUTHOR]

With more and more interchange stations in a large-scale metro network, passengers tend to transfer between different metro lines from origination to destination, sometimes even more than once. Passenger waiting time is one of the critical standards for measuring the quality of urban public transport services. To support high service quality, this paper proposes a mixed integer nonlinear programming (MINLP) model for the train timetable generation problem of a metro network that minimizes the transfer waiting times and access passenger waiting times. In the mathematical formulation of the model, the transfer walking times at the interchange stations between two connected lines are treated as uncertain parameters. The robust train timetable generation model is formulated to optimize timetables by adjusting arrival and departure times of each train in the metro network to reduce access and transfer passenger waiting times. A robust counterpart is further derived that transforms the formulated robust model into a deterministic one. Moreover, a generalized Benders decomposition technique based approach is developed to decompose the robust counterpart into a subproblem and a master problem. The subproblem is a convex quadratic programming problem that can be solved efficiently. Finally, two sets of numerical examples, consisting of a small case and a large-scale case based on a real-world portion of the Beijing metro network, are performed to demonstrate the validity and practicability of the proposed model and solution approach. • Train timetable coordination with uncertain transfer walking time is considered. • A mixed integer nonlinear programming model is formulated for train timetable problem. • A generalized Benders decomposition algorithm is designed. • The proposed method reduces the passenger waiting times for metro networks. [ABSTRACT FROM AUTHOR]

Carefully coordinating train timetables of different operating lines can help reduce transfer delays, which in turn reduces station crowding and improves overall service quality. This paper explores the optimization to train timetable and skip-stop plans that aims to minimize the total passenger waiting time and station crowding. The problem is formulated as a mixed-integer non-linear programming model. To effectively address the complexity of the model, a decomposition and approximate dynamic programming approach is designed to convert the original network-level problem into a series of small-scale subproblems, one for each operating line, to be solved quickly in a distributed manner. The effectiveness and practicability of the model and algorithm are demonstrated on two case networks: a small-scale synthetic network of three metro lines and a real-world network based on Beijing metro. The computational results illustrate that the proposed strategy to generate train timetables and skip-stop plans can effectively reduce passenger waiting time and station crowing. The proposed decomposition and approximate dynamic programming approach is also shown to perform more efficiently than traditional heuristic algorithms, such as genetic algorithm and simulated annealing algorithm for large-scale networks. • The optimization of train timetable and skip-stop plans of metro networks is considered. • A mixed-integer nonlinear programming model is formulated for this problem. • A decomposition and approximate dynamic programming approach is designed. • The optimized strategy reduces passenger waiting time and station crowing. [ABSTRACT FROM AUTHOR]

This paper deals with the train scheduling problem for metro networks taking into account time-dependent passenger origin–destination demands and train speed profiles. The aim is to adjust train schedules online according to time-dependent passenger demands so that passenger satisfaction and operational costs are jointly optimized. An extended passenger absorption model that explicitly includes time-dependent passenger origin–destination demands is developed, where the term "absorption" refers to passengers boarding trains. Then, the passenger absorption model is extended to a bi-level framework, where passenger demands and rolling stock availability are considered at the higher level, and detailed timetables and train speed profiles are included at the lower level. A bi-level model predictive control (MPC) approach is developed for the integrated problem. The optimization problems of both levels of the bi-level MPC approach can be converted into mixed-integer linear programming (MILP) problems, which enables us to solve them with existing MILP solvers. We then show that the recursive feasibility of both the higher-level and the lower-level optimization problems can be guaranteed. In this way, we can achieve real-time train scheduling for the metro system. Numerical experiments, based on real-life data from the Beijing metro network, illustrate the effectiveness of the extended passenger absorption model and the proposed bi-level MPC approach. • An extended passenger absorption model is developed to design train departure frequencies considering passenger demands. • A train scheduling model is presented to include detailed timetables, train speed profiles, and train orders. • A bi-level model predictive control approach is proposed for the train scheduling problem. [ABSTRACT FROM AUTHOR]

• Construct a unified model for integrating timetable, bus formation and vehicle scheduling problems. • Schedule autonomous modular vehicles (AMVs) in both directions simultaneously. • Design a decomposition-based iterative solution framework based on Alternating Direction Method of Multipliers (ADMM) algorithm to solve the origin model efficiently. • Solve the subproblem efficiently with a customized time-dependent shortest path algorithm. • Introduce AMVs into public transport systems can reduce overall system costs and increase vehicle utilization. This paper presents a joint optimization of the timetable, bus formation, and vehicle scheduling in a flexible public transport (PT) system that utilizes autonomous modular vehicles (AMVs). In this system, AMVs have the capability to detach or join with each other at intermediate stops along the route to dynamically adjust the bus formation (capacity). To increase vehicle utilization, a flexible scheduling strategy is proposed that allows AMVs to detach from one modular bus and join another modular bus in either direction of a bidirectional line. In particular, the penalty cost for each detachment or joining operation, as well as the limited number of available AMVs is explicitly considered. We formulate a unified model for the integrated optimization of the modular bus service (timetable and bus formation) and vehicle scheduling by introducing two types of decision variables. The objective is to minimize overall system costs, including passenger waiting time cost, operational costs, and detachment/joining penalty costs. The two types of decision variables are coupled by a vehicle resource consistency constraint, ensuring the conformity of the modular bus service and vehicle scheduling decisions. To tackle the complexity of our model, the Alternating Direction Method of Multipliers (ADMM) is employed to decompose it into two subproblems, which can be efficiently solved using a customized forward dynamic programming algorithm and a commercial solver. The model is validated using illustrative examples and a real-world instance from the Beijing Public Transport system, and it is compared with two benchmark models. Our results demonstrate the efficiency of the ADMM-based solution framework for solving the integrated optimization model. Furthermore, our findings indicate that the use of AMVs in PT systems can lead to reduced overall system costs and increased vehicle utilization. [ABSTRACT FROM AUTHOR]

The subway and bus together contribute to the structure of public transport network in a metropolis. However, integrated service of public transport is not satisfied due to the lower timetable synchronization between these two modes at transfer stations. In this paper, a double-layer public transport network composed of subway/bus lines and stations is first created. Then, two stages are included in the timetable optimization process. In the first stage, a user equilibrium assignment model and a capacity restriction iterative algorithm are employed to obtain the passenger distribution in the subway–bus public transport transfer network. Based on this distribution, with the consideration of the synchronization and section service level, a mixed-integer linear programming (MILP) model is applied to optimize the timetables of the subway and bus networks in the second stage. Computational results using real Automatic Fare Collection System (AFC) data from the public transport system in Beijing are reported, and these results show that the suggested model is efficient in improving passenger service levels. • Two stages (passenger assignment and timetabling) are in the optimization. • A double-layer network is constructed to describe subway/bus lines and stations. • A user equilibrium is for passengers distribution in the double-layer network. • Four types of space-time relationship of synchronization are considered. • Synchronization and section service level are included in the model objectives. [ABSTRACT FROM AUTHOR]

To our knowledge, the previous studies did not answer the following questions: how much does window analysis differ from the original Data Envelopment Analysis (DEA) approaches and how to develop DEA window analysis? To address these questions, we propose three intermediate approaches (cross-sectional approach, window efficiency analysis and window index approach) and statistically compare their performances. The underlying concern is that we need to examine whether a metrological bias exists in our study. The concern is important in guiding policy issues such as energy policy and climate change. Empirically, the proposed approaches are applied to measure the unified efficiency of fossil fuel power plants at a provincial level in China from 2007 to 2017, since these plants are important energy consumers and CO 2 emitters. We obtain two important implications. First, considerable differences were confirmed among the three approaches, thus implying an existence of the methodological bias. Second, Beijing (the capital of China) outperformed the other provinces in terms of their measures, since the government has paid serious attention to air pollution emitted from fossil fuel power plants. The governmental regulation in Beijing is a good example of pollution prevention in China. It is expected that the success on Beijing will be disseminated to the other provinces. This paper proposed three approach, i.e. one conventional approach (cross-sectional approach) and two new approaches (window efficiency analysis and window index approach). The two new approaches were capable of measuring efficiency shifts or technology shifts over time. Empirically, these approaches were adopted to evaluate the performance of Chinese fossil fuel power plants. Image 1 • We evaluate the performance of China's fossil fuel power plants from 2007 to 2017. • Three formulations are utilized for DEA intermediate approach. • The first policy effort was put on Beijing and gradually on other provinces. • China made a progress on economic and environmental measures during this period. [ABSTRACT FROM AUTHOR]

• The scheduling problem of EBs for multiple vehicle types is proposed and defined as the MVT-E-VSP. • Differences in technical characteristics of various EV types are considered in the modeling. • The insertion of recharging trips and the substitution between EV types are considered. • The findings provide some guidance on the scheduling of EBs for multiple vehicle types and the deployment of chargers. The effective scheduling of electric buses (EBs) for multiple vehicle types is essential for the sustainable practice of public transport. This paper proposes a new methodology for the electric vehicle scheduling problem with multiple vehicle types (MVT-E-VSP) in public transport based on a given multi-vehicle-type timetable. First, with explicit consideration of differences in driving range, recharging duration and energy consumption of EBs for multiple vehicle types, an optimization model is established to minimize annual total scheduling costs, including the purchase costs of EBs and chargers, the operating costs of deadheading and timetabled trips, etc. Then, a heuristic procedure is developed to find the optimal solution considering recharging trips and the substitution between electric vehicle (EV) types. Finally, the proposed methodology is validated using a real-world transit network in Daxing District, Beijing. The optimization result provides transit agencies with guidance on the purchase and schedule of EBs for multiple vehicle types, as well as the deployment of chargers. Comparative analysis indicates the proposed method considering the substitution between EV types reduces annual total scheduling costs by 15.93% compared with the conventional method. Sensitivity analysis reveals that the current recharging power (240 kW) and discharging depth (80%) are approximately economical. [ABSTRACT FROM AUTHOR]