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An Extended Formulation for the Line Planning Problem

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Operations Research Proceedings 2015

Part of the book series: Operations Research Proceedings ((ORP))

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Abstract

In this paper we present a novel extended formulation for the line planning problem that is based on what we call “configurations” of lines and frequencies. Configurations account for all possible options to provide a required transportation capacity on an infrastructure edge. The proposed configuration model is strong in the sense that it implies several facet-defining inequalities for the standard model: set cover, symmetric band, MIR, and multicover inequalities. These theoretical findings can be confirmed in computational results. Further, we show how this concept can be generalized to define configurations for subsets of edges; the generalized model implies additional inequalities from the line planning literature.

Supported by the Research Center Matheon “Mathematics for key technologies”.

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Author information

Authors and Affiliations

  1. Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Heide Hoppmann

Authors
  1. Heide Hoppmann
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Correspondence to Heide Hoppmann .

Editor information

Editors and Affiliations

  1. Department of Business Administration, University of Vienna, Vienna, Austria

    Karl Franz Dörner

  2. Decision Sciences and Statistics (IDS) Department, ESSEC Business School of Paris, Cergy Pontoise Cedex, France

    Ivana Ljubic

  3. Department of Statistics and Operations Research, University of Vienna, Vienna, Austria

    Georg Pflug

  4. Operations Research and Control Systems, TU Wien, Vienna, Austria

    Gernot Tragler

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Hoppmann, H. (2017). An Extended Formulation for the Line Planning Problem. In: Dörner, K., Ljubic, I., Pflug, G., Tragler, G. (eds) Operations Research Proceedings 2015. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-42902-1_2

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