Confrontation of Different Objectives in the determination of train scheduling (original) (raw)
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An integer programming model for analysing impacts of different train types on railway line capacity
The evaluation of railway line capacity is an important problem, which effects majority of problems in rail transportation planning. The railway capacity is dependent on infrastructure, traffic, and operating parameters. A key factor affecting railway line capacity is the impact of different train types. As the combination of different train types increases, more interference is generated. In this paper, for evaluation of train type interactions on railway line capacity, an integerprogramming model for both line and line section is presented. The problem is formulated as a multicommodity network design model on a space-discrete time network. The railway capacity is calculated using data typically available to planners. The inputs of the model are the characteristic of each train type and railway line attributes. The model determines railway capacity based on train type mixes. In addition, this model considers impact of train types on capacity and waiting time. In order to show the features of the model, a case study is implemented in Iran Railways. The capacity tends to increase nonlinearly with small incremental changes in parameters. The mixture of train types reduces the railway line capacity. The proposed model can help railway managers for long-term planning.
Train Scheduling in High Speed Railways: Considering Competitive Effects
Procedia - Social and Behavioral Sciences, 2014
The railway planning problem is usually studied from two different points of view: macroscopic and microscopic. We propose a macroscopic approach for the high-speed rail scheduling problem where competitive effects are introduced. We study train frequency planning, timetable planning and rolling stock assignment problems and model the problem as a multi-commodity network flow problem considering competitive transport markets. The aim of the presented model is to maximize the total operator profit.
Train Scheduling in Public Rail Transport
2000
This thesis deals with train scheduling problems with an emphasis on public rail transport. In particular, we assume a periodic schedule and a fixed railroad track network, which is common for public rail transport. A train schedule consists of arrival and departure times for the lines at certain points of the traffic network, e.g. railroad stations. The minimization of operational cost for the realization of a schedule forms a central part of this thesis. We introduce a mixed integer linear programming model for this objective. A direct solution of instances of real-world size is not possible with today's hard- and software. With the help of a decomposition idea, we are able to find solutions of acceptable quality for those instances in a reasonable amount of time. Therefore, we split the instance into an optimization component and a feasibility component. Both subproblems are integrated into a branch-and-bound algorithm. With these methods, we can produce solutions of practica...
An integrated train scheduling and infrastructure development model in railway networks
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The evaluation of the railway infrastructure capacity is an important task of railway companies. The goal is to nd the best infrastructure development plan for scheduling new train services. The question addressed by the present study is how the existing railway infrastructure can be upgraded to decrease the total delay of existing and new trains with minimum cost. To answer this question, a mixed-integer programming formulation is extended for the integrated train scheduling and infrastructure development problem. The train timetabling model deals with the optimum schedule of trains on a railway network and determines the best stop locations for both the technical and religious services. We developed two heuristics based on variable xing strategies to reduce the complexity of the problem. To evaluate the e ect of railway infrastructure development on the schedule of new trains, a sequential decomposition is adopted for Iranian railway network. The outcomes of the empirical analysis performed in this study allow to gain bene cial insights by identifying the bottleneck corridors. The result of the proposed methodology shows that it can signi cantly decrease the total delay of new trains with the most emphasis on the bottleneck sections.
In the last 15 years, the use of rail infrastructure by different train operating companies (shared railway system) has been proposed as a way to improve infrastructure utilization and to increase efficiency in the railway industry. Shared use requires coordination between the infrastructure manager and multiple train operators in a competitive framework, so that regulators must design appropriate capacity pricing and allocation mechanisms. However, capacity utilization in the railway industry cannot be known in the absence and understanding of operations. Therefore assessment of capacity requires the determination of the train timetable, which eliminates any potential conflicts between the train operators’ requests to use infrastructure capacity. Although there is a broad literature that proposes train timetabling methods for dedicated railway systems, there are few models that can be used for shared competitive railway systems. This paper proposes a train timetabling model for shared railway systems explicitly considering a variable number of trains, with large flexibility margins (train operators’ willingness to deviate from their desired timetable), and a variety of train services traveling along different routes. The train operators’ demand to schedule trains is assumed to be exogenous. The model is formulated and solved both as a mixed integer linear programming (MILP) problem (using a commercial solver) and as a dynamic programming (DP) problem. We solve the DP formulation with a novel algorithm based on a linear programming (LP) approach to approximate dynamic programming (ADP) that can solve much larger problems than commercial MILP solvers. This model can be used to evaluate the best possible train timetable under alternative capacity pricing and allocation mechanism. We use the results to understand the interactions between capacity planning and capacity operations in shared railway systems. Understanding this interactions is important to be able to design effective capacity pricing and allocation mechanisms. In this paper we describe the timetabling model and analyze an auction mechanism to price and allocate capacity in a case study based on the Northeast Corridor, in the U.S. to show how the competing demands and the decisions of the infrastructure manager under this mechanism impact the operations on the shared railway system for all stakeholders.
Optimization in railway scheduling
Train scheduling has been a significant issue in the railway industry. Over the last few years, numerous approaches and tools have been developed to aid in the management of railway infrastructure. In this paper, we describe some techniques, which was developed in a project in collaboration with the Spanish Railway Infractructure Manager (ADIF). We formulate train scheduling as constraint optimization problems and present two filtering techniques for these problem types. These filtering techniques are developed to speed up and direct the search towards suboptimal solutions in periodic train scheduling problems. The feasibility of our problem-oriented techniques are confirmed with experimentation using real-life data. The results show that these techniques enables MIP solvers such as LINGO and ILOG Concert Technology (CPLEX c ⃝ ) to terminate earlier with good solutions.
The demand-dependent optimization of regular train timetables
Electronic Notes in Discrete Mathematics, 2004
Regular timetables, in which the trains arrive and depart at constant intervals, have been adopted in various European countries, because of the simpler and fairer service they allow. The design of such a timetable has recently received a certain attention in the literature. This paper extends the commonly adopted model to take into account the reciprocal influence between the quality of a timetable and the transport demand captured by the railway with respect to alternative means of transport. The resulting mixed-integer non linear model remains non convex even after relaxing the integrality constraints. We solve it by a branch-and-bound algorithm based on Outer Approximation and a heuristic algorithm exploiting the decomposition and reciprocal update of two submodels. Preliminary computational results concern a regional network in Northwestern Italy.
Dynamic revenue management in a passenger rail network under price and fleet management decisions
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Cost optimal periodic train scheduling
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For real world railroad networks, we consider minimizing operational cost of train schedules which depend on choosing different train types of diverse speed and cost. We develop a mixed integer linear programming model for this train scheduling problem. For practical problem sizes, it seems to be impossible to directly solve the model within a reasonable amount of time. However, suitable decomposition leads to much better performance. In the first part of the decomposition, only the train type related constraints stay active. In the second part, using an optimal solution of this relaxation, we select and fix train types and try to generate a train schedule satisfying the remaining constraints. This decomposition idea provides the cornerstone for an algorithm integrating cutting planes and branchand-bound. We present computational results for railroad networks from Germany and the Netherlands.
Discrete optimization in public rail transport
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