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# Vehicle Scheduling Based on a Line Plan

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OASIcs.ATMOS.2018.15.pdf
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## Cite As

Rolf N. van Lieshout and Paul C. Bouman. Vehicle Scheduling Based on a Line Plan. In 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/OASIcs.ATMOS.2018.15

## Abstract

We consider the following problem: given a set of lines in a public transportation network with their round trip times and frequencies, a maximum number of vehicles and a maximum number of lines that can be combined into a vehicle circulation, does there exist a set of vehicle circulations that covers all lines given the constraints. Solving this problem provides an estimate of the costs of operating a certain line plan, without having to compute a timetable first. We show that this problem is NP-hard for any restriction on the number of lines that can be combined into a circulation which is equal to or greater than three. We pay special attention to the case where at most two lines can be combined into a circulation, which is NP-hard if a single line can be covered by multiple circulations. If this is not allowed, a matching algorithm can be used to find the optimal solutions, which we show to be a 16/15-approximation for the case where it is allowed. We also provide an exact algorithm that is able to exploit low tree-width of the so-called circulation graph and small numbers of vehicles required to cover single circulations.

## Subject Classification

##### ACM Subject Classification
• Applied computing → Transportation
• Mathematics of computing → Graph algorithms
##### Keywords
• Vehicle scheduling
• integrated railway planning
• (fractional) matching
• treewidth

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## References

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