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![Figure 1. Transport planning process [5]](profile/Fernando-Lopez-Irarragorri/publication/317916215/figure/fig8/AS:668721320300560@1536446995884/Transport-planning-process-5_Q320.jpg)
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![Figure 3. Types of synchronization nodes [13]](profile/Fernando-Lopez-Irarragorri/publication/317916215/figure/fig1/AS:509708529934337@1498535391826/Types-of-synchronization-nodes-13_Q320.jpg)
The urban transport planning process has four main activities: Network design, Timetable construction, Vehicle scheduling and Crew scheduling; each activity has subactivities. In this paper the authors work with the subactivities of timetable construction: minimal frequency calculation and departure time scheduling. The authors propose to solve bot...
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Citations
... Shrivastava et al. [13] developed an integrated model for suburban train and public bus operations in which a genetic algorithm is used to assign the optimally coordinated timetable for feeder buses based on the given suburban train timetable in a "scheduling sub-model". Avila-Torres et al. [14] developed a dual-objective fuzzy planning model to address traffic demand uncertainty. They considered factors like departure frequency, schedule, operating cost, and cycle synchronization. ...
In order to enhance passenger willingness to choose buses for commuting and to reduce the operating costs and tailpipe emissions of bus companies, a bus scheduling model is established. The model aims to minimize the sum of the operating costs of the bus company, the costs associated with the loss of passengers’ interest, and the cost of tailpipe emissions. It considers constraints such as maintaining an average load factor of the buses above 60%, ensuring a departure interval of greater than 5 min during non-peak hours and less than 30 min during peak hours, and limiting the maximum number of buses allocated to a route. The passenger flow is divided into peak hours and nonpeak hours according to the survey of passenger flow during each period of a bus operation on a route in Nanjing City, China. A genetic algorithm is employed to solve the proposed bus scheduling model and determine the total costs during peak and non-peak hours. After designing the parameters of the genetic algorithm, optimal departure intervals and bus numbers for a day’s operation cycle on a given route are calculated using a weighting method.
... From the works in traditional timetabling, there are several approaches that couple the timetabling problem with the frequency setting problem (Furth and Wilson, 1981;Peeters and Kroon, 2001;Ávila-Torres et al., 2018;Silva-Soto and Ibarra-Rojas, 2021) or the timetabling problem with the vehicle scheduling problem (Ceder, 2011;Ibarra-Rojas et al., 2014;Schmid and Ehmke, 2015;Fonseca et al., 2018). Nevertheless, scheduling methods do not consider the impact of the determined timetables on vehicle flow in a common corridor of the public transport network. ...
The trips of a high-frequency urban rail line are typically planned with the aim of achieving even time headways. This results in reliable services for each urban rail line, where successive trips have the same time headway. Maintaining even time headways for each service line has significant advantages for the passengers of the line, but it might result in safety issues, vehicle bunching, and increased transfer times at a common corridor served by multiple urban rail lines. This study investigates the problem of urban rail corridor coordination and develops an exact optimization method for coordinating the vehicle trips of different lines that serve stations along a joint corridor. The proposed formulation is a non-convex mathematical program which is reformulated as a mixed-integer quadratic program with a convex objective function. A branch-and-bound algorithm coupled with the Active-set method is proposed for solving the model to global optimality. Results from a toy network and a case study of the light rail service in The Hague, The Netherlands, demonstrate the improvement potential of time headways at a common corridor, while accounting for the effect on the variation of time headways at isolated segments of the individual service lines.
... A distinct line of works has proposed the simultaneous optimisation of bus frequencies and timetables [19][20][21][22]. Other works, such as [23,24], tried to determine simultaneously the route network design, the bus frequencies, and the timetable assignment by integrating the strategic and tactical planning phases. ...
Bus scheduling is a well-known NP-hard problem, and it is addressed with the use of heuristic solution methods or graphical approaches. In this study, the author proposes an improved formulation of the bus scheduling problem that considers the vehicle availability, the vehicle capacity and the allowed headway variability among successive trip dispatches. His formulation expands the classic bus scheduling model formulation by including the aforementioned features. In his study, the bus scheduling problem is understood as the problem of setting the optimal dispatching times for a set of pre-determined daily trips of a particular bus line. His model facilitates the search of solutions that can improve the waiting times of passengers while meeting the operational requirements and avoiding overcrowding. His proposed mathematical program is proved to be non-convex, and it is solved with heuristic solution methods because numerical optimisation approaches cannot guarantee a globally optimal solution. The performance of his approach is tested in a case study using real operational data from bus line 302 in Singapore. A simulation-based evaluation demonstrates potential gains of up to 20% on average passenger waiting times and a major reduction in refused passenger boardings because of overcrowding.
... A distinct line of works has proposed the simultaneous optimization of the route network design, the frequency setting, and the timetabling problems ( Yan et al., 2006;Zhao and Zeng, 2008). Other works, such as Furth and Wilson (1981); Gallo and Miele (2001); Peeters and Kroon (2001) and´Avilaand´ and´Avila- Torres et al. (2017), proposed the simultaneous optimization of bus frequencies and timetables. Contrary to the above, most works on timetable optimization, such as Sun et al. (2015); Wang et al. (2017) and Yu et al. (2017), decouple the frequency settings problem from the timetabling problem and solve them in sequential order. ...
Timetables are typically generated based on passenger demand and travel time expectations. This work incorporates the travel time and passenger demand uncertainty to generate robust timetables that minimize the possible loss at worst-case scenarios. We solve the resulting minimax problem with a genetic algorithm that uses sequential quadratic programming to evaluate the worst-case performance of each population member. Our approach is tested on a bus line in Singapore demonstrating an improvement potential of 5% on service regularity and excessive trip travel times.
... Several works have jointly addressed the bus frequency settings problem and the bus timetabling problem [11], [12], [13], [14], [15]. Nevertheless, in most cases the optimization of the timetable of a bus line is perceived as a standalone problem and is generally decoupled from the from the frequency settings problem [16], [17], [18]. ...
Bus operators plan the dispatching times of their daily trips based on the average values of their travel times. Given the trip travel time uncertainty though, the performance of the daily operations is different than expected impacting the service regularity and the expected waiting times of passengers at stops. To address this problem, this work develops a model that considers the travel time uncertainty when planning the dispatching times of trips. In addition, it introduces a minimax approach combining Monte Carlo evaluations with a Genetic Algorithm for computing dispatching times which are robust to travel time variations. This approach is tested in a circular bus line of a major bus operator in Asia Pacific (APAC) using 4 months of Automated Vehicle Location (AVL) and Automated Fare Collection (AFC) data for analyzing the travel time uncertainty and computing robust dispatching times. In addition, 1 month of data is used for validation purposes demonstrating a potential service regularity improvement of 5.5% in the average case and ≃22% in worst-case scenarios.
... Since it may be inappropriate to assume that the demands of products are independent random variables, this paper intends to remove such an assumption in accordance with the practical situation of the multi-product newsvendor problems [5]. Different from the existent results, the dynamic correlation of demands will be incorporated into an optimization model of newsvendor problems in this paper. ...
Aiming at the influence of demand uncertainty and stochastic carbon trading price on the choice of intermodal transportation route for reefer containers, a hybrid robust stochastic optimization model with minimum economic cost is established, and a Monte Carlo sampling-based catastrophic adaptive genetic algorithm is designed to test the reasonableness and validity of the model. The results show that: influenced by the regret value constraint, the robust optimization of demand uncertainty will increase the total cost of reefer container multimodal transportation, while the increase of carbon trading price stochasticity doesn’t necessarily mean the increase of cost, and the reasonable setting of carbon trading price stochasticity and the trade-off between the maximum regret value and the economic cost, so that the cold-chain logistics and transportation enterprises can easily deal with the fluctuation of the demand of the freight transportation market, and also respond to the low-carbon requirements.
In many European metropolitan areas, the urban transit system is a mixture of schedule- and frequency-based services. This study proposes an integrated transit frequency and schedule design problem (ITFSDP), where frequencies and schedules are simultaneously determined, and develops a biobjective model for the ITFSDP to minimize operation costs and total passenger-perceived generalized travel cost. Meanwhile, the passengers’ route choice behavior is described by the bounded stochastic user equilibrium (BSUE). The in-vehicle congestion effect is represented using a set of constraints that differ in terms of the sitting and standing costs as sitting and standing passengers perceive crowding differently. This set of constraints captures the realistic behavioral feature that having occupied a seat, users remain seated at subsequent stops in the same vehicle. The problem is formulated as a mixed integer nonlinear programming problem, which is subsequently linearized to a mixed integer linear programming problem and solved using a branch and bound algorithm. A column generation and reduction phase is embedded in the solution algorithm to obtain the bounded choice set according to the BSUE constraints. Experiments are conducted to illustrate the model’s properties and the performance of the solution method. In particular, we demonstrate a Braess-like paradoxical phenomenon in the context of transit scheduling and highlight that well-synchronized transit services can deteriorate the network performance in terms of the total passengers’ generalized travel cost when considering passenger congestion costs because of crowding.
Urban public transport is a very complex system, and with the development of urbanization, there are many new urban traffic characteristics. Making bus routes and scheduling strategies more efficient, scientific and accurate has a positive impact on the actual operation of public transport. To solve the urban public transport line design problem, this paper describes the implicit law of the characteristics of public transport travel from a deep perspective and analyzes the forms, influencing factors and existing problems of bus dispatching. By establishing a multiobjective public transport dispatching optimization model, starting from bus companies, passengers and government departments, public transportation operating costs comprehensively consider the interests of various parties and finally realize the optimization objective of minimizing fixed costs, fuel costs, carbon emission costs and time window penalty costs. The objective function is set reasonably, and the generation and optimization method of the initial line set in the public transport line design problem is improved; suitable constraint conditions and evaluation indicators are considered. This paper attempts to control the overall length of the bus line on the premise of fully meeting the travel needs of passengers. By solving the multiobjective problem on the same network and comparing different multiobjective optimization algorithms, the effectiveness of the method is evaluated. Additionally, an improved multiobjective adaptive particle swarm optimization (MOAPSO) is proposed, which has the characteristics of faster convergence, higher efficiency and low computational complexity. The simulation experimental results show that the proposed algorithm in this paper can obtain a better Pareto optimal solution set and can effectively solve the multiobjective model. The departure interval conforms to the passenger flow distribution, which can effectively reduce costs and improve the travel service quality of passengers on a large-scale network.
