Frequency optimization in public transportation with strict capacity constraints. A bilevel programming approach
In this thesis, we consider the problem of frequency optimization in public transit systems based on buses. The objective of the problem is to determine the time interval between subsequent buses for a set of transportation lines. The solutions should satisfy a given origin-destination demand while...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2024 |
| País: | Uruguay |
| Institución: | Universidad de la República |
| Repositorio: | COLIBRI |
| Idioma: | inglés |
| OAI Identifier: | oai:colibri.udelar.edu.uy:20.500.12008/55043 |
| Acceso en línea: | https://hdl.handle.net/20.500.12008/55043 |
| Access Level: | acceso abierto |
| Palabra clave: | Transporte Transporte público con capacidades Optimización de frecuencias Programación lineal entera mixta Programación binivel Transportation Public transport capacity Transit frequency optimization Mixed integer linear programming Bilevel programming |
| Sumario: | In this thesis, we consider the problem of frequency optimization in public transit systems based on buses. The objective of the problem is to determine the time interval between subsequent buses for a set of transportation lines. The solutions should satisfy a given origin-destination demand while considering the interests of users and operators in the context of constraints pertaining to infrastructure, budget, and service performance. To consider congestion on the transportation lines (that is, when the lines operate at the limit of their capacities in relation to the attracted demand), we extend an existing model by adding a constraint on bus capacities while respecting user choice on the lines that can drive users to their destinations. The resulting formulation is bilevel and is then transformed, by means of applying optimality conditions on the lower level, into a mixed integer linear programming formulation (MILP) that can be solved to optimality over small instances using state-of-the-art MILP techniques. To study the nature of the model, we analyze different variants of the proposed bilevel formulation. Furthermore, we compare solutions and evaluate their feasibility of being applied to real-world scenarios. In order to do that, we apply the model to a small test case and to a real one published in the literature. To provide a better level of service to the users of the system, we study the effects of adding to the proposed formulation a constraint on the maximum waiting times of the users allowed at the bus stops. We conclude that a bilevel approach should be considered whenever bus capacities are contemplated; thus, there is a need for models that incorporate the behavior of the users, the waiting times at the stops, and bus capacities. To the best of our knowledge, the simultaneous inclusion of all of the aforementioned aspects in a single mathematical programming formulation has not been studied. Moreover, by using a test case corresponding to an actual city, we explore some underlying issues that arise whenever bus capacities and different fleet sizes are considered. By studying measures such as line capacities and maximum waiting times, with the aid of visual inspection, problematic sectors of the line network can be quickly identified. This allows a more thorough discussion of the issues that could arise in real-life contexts and helps devise alternative solutions. Finally, we analyze the limit regarding the size of the instances that can be resolved by the proposed model. |
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