A Branch-and-Cut Approach for Solving Railway Line-Planning Problems

Goossens, Jan-Willem; Hoesel, Stan van; Kroon, Leo

doi:10.1287/trsc.1030.0051

Cited by 124 publications

(87 citation statements)

References 7 publications

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“…Moreover, if we assume that the LOPs are price taking and myopic entities, the LOP bid updating again leads us to the validity of equations (10). We shall now prove the convergence to the optimal resource prices, with respect to any given vector of capacity proportions, and any given vector of LOP bids.…”

Section: Lemma 2 For Any (Fixed) Vector F Of Capacity Proportions Thmentioning

confidence: 87%

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Incentive-Compatible Robust Line Planning

Bessas

Kontogiannis

Zaroliagis

2009

Robust and Online Large-Scale Optimization

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Abstract. The problem of robust line planning requests for a set of origin-destination paths (lines) along with their frequencies in an underlying railway network infrastructure, which are robust to fluctuations of real-time parameters of the solution. In this work, we investigate a variant of robust line planning stemming from recent regulations in the railway sector that introduce competition and free railway markets, and set up a new application scenario: there is a (potentially large) number of line operators that have their lines fixed and operate as competing entities issuing frequency requests, while the management of the infrastructure itself remains the responsibility of a single entity, the network operator. The line operators are typically unwilling to reveal their true incentives, while the network operator strives to ensure a fair (or socially optimal) usage of the infrastructure, e.g., by maximizing the (unknown to him) aggregate incentives of the line operators.By investigating a resource allocation mechanism (originally developed in the context of communication networks), we show that a socially optimal solution can be accomplished in certain situations via an anonymous incentive-compatible pricing scheme for the usage of the shared resources that is robust against the unknown incentives and the changes in the demands of the entities.This brings up a new notion of robustness, which we call incentive-compatible robustness, that considers as robustness of the system its tolerance to the entities' unknown incentives and elasticity of demands, aiming at an eventual stabilization to an equilibrium point that is as close as possible to the social optimum.

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Section: Lemma 2 For Any (Fixed) Vector F Of Capacity Proportions Thmentioning

confidence: 87%

“…The line planning problem has been mostly studied under two main approaches (see e.g., [7,10]). In the cost-oriented approach, the goal is to minimize the costs of the public transportation company, under the constraint that all customers can be transported.…”

Section: Introductionmentioning

confidence: 99%

Incentive-Compatible Robust Line Planning

Bessas

Kontogiannis

Zaroliagis

2009

Robust and Online Large-Scale Optimization

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“…A branch & cut approach (neglecting the upper frequency requirements) based on the models of Claessens et al (1998) and Bussieck (1998) is proposed in Goossens et al (2004) and Goossens (2004). Practical experiences with the Dutch Railway system show that the approach runs in reasonable time for real-world instances.…”

Section: Cost-oriented Modelsmentioning

confidence: 99%

Line planning in public transportation: models and methods

2011

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The problem of defining suitable lines in a public transportation system (bus, railway, tram, or underground) is an important real-world problem that has also been well researched in theory. Driven by applications, it often lacks a clear description, but is rather stated in an informal way. This leads to a variety of different published line planning models. In this paper, we introduce some of the basic line planning models, identify their characteristics, and review literature on models, mathematical approaches, and algorithms for line planning. Moreover, we point out related topics as well as current and future directions of research.Keywords Line planning · Public transportation · Mathematical programming The line planning problem in public transportationGiven the increasing demand for mobility, an efficient organization of public (passenger) transportation becomes more and more important. This is reflected not only in practice but also by an increasing number of research papers dealing with the optimization of public transport. The goal of the optimization process is on the one hand, to offer a high quality of service for the passengers while, on the other hand, the costs for setting up and running the transit system should be small.As noted by many authors (see e.g., Ceder and Wilson 1986;Liebchen and Möhring 2007;Desaulniers and Hickman 2007), the planning process in public transportation consists of several consecutive planning phases. As shown in Fig. 1, the process starts A. Schöbel (B)

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“…Lines are selected from a line pool or as paths of a infrastructure (or underlying) network and the objectives can be cost-oriented (e.g. see [5]) and customers-oriented (e.g. see [15]).…”

Section: Introductionmentioning

confidence: 99%

GRASP algorithms for the robust railway network design problem

et al. 2011

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This paper analyzes the solvability of a railway network design problem and its robust version. These problems are modeled as integer linear programming problems with binary variables, and their solutions provide topological railway networks maximizing the trip coverage in the presence of a competing mode, both assuming that the network works fine and that links can fail, respectively. Since these problems are computationally intractable for realistic sizes, GRASP heuristics are proposed for finding good feasible solutions. The results obtained in a computational experience indicate that our GRASP algorithms are suitable for railway network design problems.

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A Branch-and-Cut Approach for Solving Railway Line-Planning Problems

Cited by 124 publications

References 7 publications

Incentive-Compatible Robust Line Planning

Incentive-Compatible Robust Line Planning

Line planning in public transportation: models and methods

GRASP algorithms for the robust railway network design problem

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