Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations

Nachtigall, Karl; Opitz, Jens

doi:10.4230/OASIcs.ATMOS.2008.1588

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Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations

Authors Karl Nachtigall, Jens Opitz

Part of: Volume: 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08) (ATMOS 2008)
Part of: Series: Open Access Series in Informatics (OASIcs)
Part of: Conference: Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2008-09-24

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Document Identifiers

DOI: 10.4230/OASIcs.ATMOS.2008.1588
URN: urn:nbn:de:0030-drops-15884

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Keywords

Periodic event scheduling problem
integer programming
modulo network simplex

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Abstract

In the last 15 years periodic timetable problems have found
much interest in the combinatorial optimization community. We will focus on the optimisation task to minimise a weighted sum of undesirable slack times. This problem can be formulated as a mixed integer linear problem, which for real world instances is hard to solve. This is mainly caused by the integer variables, the so-called modulo parameter. At first we will discuss some results on the polyhedral structure of the periodic timetable problem. These ideas allow to define a modulo simplex basic solution by calculating the basic variables from modulo equations. This leads to a modulo network simplex method, which iteratively improves the solution by changing the simplex basis.

Cite As Get BibTex

Karl Nachtigall and Jens Opitz. Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations. In 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08). Open Access Series in Informatics (OASIcs), Volume 9, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008) https://doi.org/10.4230/OASIcs.ATMOS.2008.1588

Author Details

Karl Nachtigall

Jens Opitz

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