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  • 2020-2024  (16)
  • 2015-2019
  • 2005-2009  (7)
  • 2023  (16)
  • 2005  (7)
  • English  (23)
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  • 2020-2024  (16)
  • 2015-2019
  • 2005-2009  (7)
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  • English  (23)
  • 1
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    A Column-Generation Approach to Line Planning in Public Transport (2005)
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    Publication Date: 2020-12-15
    Description: The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize operating costs, the passengers want to minimize travel times. We propose a n ew multi-commodity flow model for line planning. Its main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically. We discuss properties of this model and investigate its complexity. Results with data for the city of Potsdam, Germany, are reported.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 2
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    Fare Planning for Public Transport (2005)
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    Publication Date: 2020-12-15
    Description: In this paper we introduce the fare planning problem for public transport which consists in designing a system of fares maximizing revenue. We propose a new simple general model for this problem. It i s based on a demand function and constraints for the different fares. The constraints define the structure of the fare system, e.g., distance dependent fares or zone fares. We discuss a simple example with a quadratic demand function and distance dependent fares. Then we introduce a more realistic discrete choice model in which passengers choose between different alternatives depending on the numb er of trips per month. We demonstrate the examples by computational experiments.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 3
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    Public Transport to the fORe! (2005)
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    Publication Date: 2020-12-15
    Description: Can OR methods help the public transport industry to break even? The article gives evidence that there exist significant potentials in this direction, which can be harnessed by a combination of modern mathematical methods and local planning knowledge. Many of the planning steps in public transport are classical combinatorial problems, which can be solved in unprecedented size and quality due the rapid progress in large-scale optimization. Three examples on vehicle scheduling, duty scheduling, and integrated vehicle and duty scheduling illustrate the level that has been reached and the improvements that can be achieved today. Extensions of such methods to further questions of strategic, online, and market-oriented planning are currently investigated. In this way, OR can make a significant contribution to answer the basic but extremely difficult question ``What is a good public transport network?.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 4
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    A Column Generation Approach to Airline Crew Scheduling (2005)
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    Publication Date: 2020-03-09
    Description: The airline crew scheduling problem deals with the construction of crew rotations in order to cover the flights of a given schedule at minimum cost. The problem involves complex rules for the legality and costs of individual pairings and base constraints for the availability of crews at home bases. A typical instance considers a planning horizon of one month and several thousand flights. We propose a column generation approach for solving airline crew scheduling problems that is based on a set partitioning model. We discuss algorithmic aspects such as the use of bundle techniques for the fast, approximate solution of linear programs, a pairing generator that combines Lagrangean shortest path and callback techniques, and a novel rapid branching'' IP heuristic. Computational results for a number of industrial instances are reported. Our approach has been implemented within the commercial crew scheduling system NetLine/Crew of Lufthansa Systems Berlin GmbH.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 5
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    An Auctioning Approach to Railway Slot Allocation (2005)
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    Publication Date: 2020-08-05
    Description: We present an approach to implement an auction of railway slots. Railway network, train driving characteristics, and safety requirements are described by a simplified, but still complex macroscopic model. In this environment, slots are modelled as combinations of scheduled track segments. The auction design builds on the iterative combinatorial auction. However, combinatorial bids are restricted to some types of slot bundles that realize positive synergies between slots. We present a bidding language that allows bidding for these slot bundles. An integer programming approach is proposed to solve the winner determination problem of our auction. Computational results for auction simulations in the Hannover-Fulda-Kassel area of the German railway network give evidence that auction approaches can induce a more efficient use of railway capacity.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 6
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    Optimal Fares for Public Transport (2005)
    Details
    Publication Date: 2020-12-15
    Description: The \emph{fare planning problem} for public transport is to design a system of fares that maximize the revenue. We introduce a nonlinear optimization model to approach this problem. It is based on a d iscrete choice logit model that expresses demand as a function of the fares. We illustrate our approach by computing and comparing two different fare systems for the intercity network of the Netherlands.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 7
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    Routing in Line Planning for Public Transportation (2005)
    Details
    Publication Date: 2020-12-15
    Description: The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists in finding lines and corresponding frequencies in a network such that a giv en demand can be satisfied. There are two objectives. Passengers want to minimize travel times, the transport company wishes to minimize operating costs. We investigate three variants of a multi-commo dity flow model for line planning that differ with respect to passenger routings. The first model allows arbitrary routings, the second only unsplittable routings, and the third only shortest path rou tings with respect to the network. We compare these models theoretically and computationally on data for the city of Potsdam.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Format: application/postscript
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    OPUS
  • 8
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    Non-Linear Charge Functions for Electric Vehicle Scheduling with Dynamic Recharge Rates (2023)
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    Publication Date: 2023-09-05
    Description: The ongoing electrification of logistics systems and vehicle fleets increases the complexity of associated vehicle routing or scheduling problems. Battery-powered vehicles have to be scheduled to recharge in-service, and the relationship between charging time and replenished driving range is non-linear. In order to access the powerful toolkit offered by mixed-integer and linear programming techniques, this battery behavior has to be linearized. Moreover, as electric fleets grow, power draw peaks have to be avoided to save on electricity costs or to adhere to hard grid capacity limits, such that it becomes desirable to keep recharge rates dynamic. We suggest a novel linearization approach of battery charging behavior for vehicle scheduling problems, in which the recharge rates are optimization variables and not model parameters.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 9
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    Non-Linear Battery Behavior in Electric Vehicle Scheduling Problems (2023)
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    Publication Date: 2023-10-04
    Description: The currently most popular approach to handle non-linear battery behavior for electric vehicle scheduling is to use a linear spline interpolation of the charge curve. We show that this can lead to approximate models that underestimate the charge duration and overestimate the state of charge, which is not desirable. While the error is of second order with respect to the interpolation step size, the associated mixed-integer linear programs do not scale well with the number of spline segments. It is therefore recommendable to use coarse interpolation grids adapted to the curvature of the charge curve, and to include sufficient safety margins to ensure solutions of approximate models remain feasible subjected to the exact charge curve.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 10
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    K-Shortest Simple Paths Using Biobjective Path Search (2023)
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    Publication Date: 2024-02-21
    Description: In this paper we introduce a new algorithm for the k-Shortest Simple Paths (K-SSP) problem with an asymptotic running time matching the state of the art from the literature. It is based on a black-box algorithm due to Roditty and Zwick (2012) that solves at most 2k instances of the Second Shortest Simple Path (2-SSP) problem without specifying how this is done. We fill this gap using a novel approach: we turn the scalar 2-SSP into instances of the Biobjective Shortest Path problem. Our experiments on grid graphs and on road networks show that the new algorithm is very efficient in practice.
    Language: English
    Type: article , doc-type:article
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