, Volume 67, Issue 1, pp 49–64 | Cite as

The School Bus Problem on Trees

  • Adrian BockEmail author
  • Elyot Grant
  • Jochen Könemann
  • Laura Sanità


The School Bus Problem is an NP-hard vehicle routing problem in which the goal is to route buses that transport children to a school such that for each child, the distance travelled on the bus does not exceed the shortest distance from the child’s home to the school by more than a given regret threshold. Subject to this constraint and bus capacity limit, the goal is to minimize the number of buses required.

In this paper, we give a polynomial time 4-approximation algorithm when the children and school are located at vertices of a fixed tree. As a byproduct of our analysis, we show that the integrality gap of the natural set-cover formulation for this problem is also bounded by 4. We also present a constant factor approximation for the variant where we have a fixed number of buses to use, and the goal is to minimize the maximum regret.


Vehicle routing Approximation algorithm Set-cover formulation 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Adrian Bock
    • 1
    Email author
  • Elyot Grant
    • 2
  • Jochen Könemann
    • 2
  • Laura Sanità
    • 2
  1. 1.EPFLLausanneSwitzerland
  2. 2.University of WaterlooWaterlooCanada

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