The efficiency of a transport system depends on several elements, such as available technology, governmental policies, the planning process, and control strategies. Indeed, the interaction between these elements is quite complex, leading to intractable decision making problems. The planning process and real-time control strategies have been widely studied in recent years, and there are several practical implementations with promising results. In this paper, we review the literature on Transit Network Planning problems and real-time control strategies suitable to bus transport systems. Our goal is to present a comprehensive review, emphasizing recent studies as well as works not addressed in previous reviews.

Planning, operation, and control of bus transport systems: A literature review

In this paper, we propose a vehicle-scheduling model for electric transit buses with either battery swapping or fast charging at a battery station, and a vehicle-scheduling model with the maximum route distance constraint for compressed natural gas, diesel, or hybrid-diesel buses. Both of these scheduling models are NP-hard. We develop column-generation-based algorithms to solve the scheduling problems. We conduct extensive case studies based on real-world instances and instances randomly generated in a practical setting. Our computational experiments show that our algorithms demonstrate very good computational performances. We also use real-world transit data to systematically analyze the number of buses needed, the total operational costs, and the vehicle emissions generated when compressed natural gas, diesel, hybrid, or electric buses are used in service.

Transit Bus Scheduling with Limited Energy

On an exact method for the constrained shortest path problem

Planning a public transportation system is a multi-objective problem which includes among others line planning, timetabling, and vehicle scheduling. For each of these planning stages, models are known and advanced solution techniques exist. Some of the models focus on costs, others on passengers’ convenience. Setting up a transportation system is usually done by optimizing each of these stages sequentially. In this paper we argue that instead of optimizing each single step further and further it would be more beneficial to consider the whole process in an integrated way. To this end, we develop and discuss a generic, bi-objective model for integrating line planning, timetabling, and vehicle scheduling. We furthermore propose an eigenmodel which we apply for these three planning stages and show how it can be used for the design of iterative algorithms as heuristics for the integrated problem. The convergence of the resulting iterative approaches is analyzed from a theoretical point of view. Moreover, we propose an agenda for further research in this field.

An eigenmodel for iterative line planning, timetabling and vehicle scheduling in public transportation

It is complex and difficult to perform the vehicle scheduling of urban bus lines, which is important to reduce the operational cost and improve the quality of public transportation services. One has to assign vehicles to cover a set of trips contained in a timetable while minimizing multiple objectives that may conflict with each other. Existing approaches combine these objectives in a weighted fashion to form a single objective and then use a single-objective optimization approach to solve it. However, they can only produce one solution, and it is not easy to assign a proper weight for each objective to obtain a superior solution that can balance different objectives. In this paper, a methodology is presented to create a set of Pareto solutions for this problem. First, a set of candidate vehicle blocks is generated. Then, multiple block subsets are selected from this candidate set by an improved multiobjective genetic algorithm combined with a departure-time adjustment procedure to obtain multiple Pareto solutions. To encode a solution, we propose a coding scheme that has a relatively short coding length and low decoding complexity. This approach is applied to a real-world vehicle scheduling problem of a bus line in Nanjing, China. Experiments show that this approach is able to quickly produce satisfactory Pareto solutions that outperform the actually used experience-based solution.

Vehicle Scheduling of an Urban Bus Line via an Improved Multiobjective Genetic Algorithm

This paper discusses the integrated vehicle-and crew-scheduling problem in public transit with multiple depots. It is well known that the integration of both planning steps discloses additional flexibility that can lead to gains in efficiency, compared to sequential planning. We present a new modeling approach that is based on a time-space network representation of the underlying vehicle-scheduling problem. The integrated problem is solved with column generation in combination with Lagrangian relaxation. The column generation subproblem is modeled as a resource-constrained shortest-path problem based on a novel time-space network formulation. Feasible solutions are generated by a heuristic branch-and-price method that involves fixing service trips to depots. Numerical results show that our approach outperforms other methods from the literature for well-known test problems.

A Time-Space Network Approach for the Integrated Vehicle-and Crew-Scheduling Problem with Multiple Depots

We discuss timetables in ex-urban bus traffic that consist of many trips serviced every day together with some exceptions that do not repeat daily. Traditional optimization methods for vehicle and crew scheduling in such cases usually produce schedules that contain irregularities which are not desirable especially from the point of view of the bus drivers. We propose a solution method which improves regularity while partially integrating the vehicle and crew scheduling problems. The approach includes two phases: first we solve the LP relaxation of a set covering formulation, using column generation together with Lagrangean relaxation techniques. In a second phase, we generate integer solutions using a new combination of local branching and various versions of follow-on branching. Numerical tests with artificial and real instances show that regularity can be improved significantly with no or just a minor increase of costs.

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Branching strategies to improve regularity of crew schedules in ex-urban public transit

Fahrplane regionaler Busunternehmen bestehen aus vielen Fahrten, die jeden Tag durchgefuhrt werden, und Ausnahmen, die sich nicht taglich wiederholen, wie z.B. Schul- oder Baderfahrten. Mit traditionellen Optimierungsansatzen fur die Umlauf- und Dienstplanung entstehen dabei in der Praxis unerwunschte unregelmasige Dienstplane fur Busfahrer. Fur partiell integrierte Umlauf- und Dienstplanungsprobleme im Regionalverkehr schlagen wir zur Erzeugung kostenminimaler und regelmasiger Dienstplane ein zweistufiges Verfahren vor. In der ersten Phase wird mit einem Column Generation Verfahren die LP-Relaxation einer Set Partitioning Formulierung gelost. Wir stellen dabei algorithmische Aspekte des Column Generation Verfahrens wie die Verwendung des Volume Algorithmus zur schnellen, approximativen Losung linearer Programme und Beschleunigungsverfahren dar. Weiterhin beschreiben wir neuartige Spaltenmanagementtechniken auf Basis der primalen/dualen Informationen des Volume- Algorithmus. In der zweiten Phase erzeugen wir ganzzahlige Losungen durch eine neuartige Kombination von Local Branching Cuts und verschiedener Branching-Strategien. Die durchgefuhrten Tests mit kunstlichen und realen Instanzen zeigen, dass deutlich regelmasigere Dienstplane bei geringfugiger Erhohung der operativen Gesamtkosten effizient generiert werden konnen.

Local Branching und Branching-Strategien für Umlauf- und Dienstplanung im Regionalverkehr mit unregelmäßigen Fahrplänen

We discuss timetables in ex-urban bus traffic that consist of many trips serviced every day together with some exceptions that do not repeat daily. Traditional optimization methods for vehicle and crew scheduling in such cases usually produce schedules that contain irregularities which are not desirable especially from the point of view of the bus drivers. We propose a solution method which improves regularity while partially integrating the vehicle and crew scheduling problems. The approach includes two phases: first we solve the LP relaxation of a set partitioning formulation, using column generation together with Lagrangean relaxation techniques. In a second phase we generate integer solutions using a new combination of local branching and various versions of follow-on branching. Numerical tests with artificial and real instances show that regularity can be improved significantly with no or just a minor increase of costs.

08. Branching Strategies to Improve Regularity of Crew Schedules in Ex-Urban Public Transit

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Ingmar Steinzen

Papers

A Time-Space Network Approach for the Integrated Vehicle-and Crew-Scheduling Problem with Multiple Depots

Branching strategies to improve regularity of crew schedules in ex-urban public transit

Local Branching und Branching-Strategien für Umlauf- und Dienstplanung im Regionalverkehr mit unregelmäßigen Fahrplänen

08. Branching Strategies to Improve Regularity of Crew Schedules in Ex-Urban Public Transit

Optimierungssysteme für die Dienstplanung im ÖPNV