The School Bus Problem on Trees
 Adrian Bock,
 Elyot Grant,
 Jochen Könemann,
 Laura Sanità
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The School Bus Problem is an NPhard 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 4approximation 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 setcover 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.
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 Title
 The School Bus Problem on Trees
 Journal

Algorithmica
Volume 67, Issue 1 , pp 4964
 Cover Date
 20130901
 DOI
 10.1007/s004530129711x
 Print ISSN
 01784617
 Online ISSN
 14320541
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Vehicle routing
 Approximation algorithm
 Setcover formulation
 Industry Sectors
 Authors

 Adrian Bock ^{(1)}
 Elyot Grant ^{(2)}
 Jochen Könemann ^{(2)}
 Laura Sanità ^{(2)}
 Author Affiliations

 1. EPFL, Lausanne, Switzerland
 2. University of Waterloo, Waterloo, Canada