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Probabilistic Analysis of Unit-Demand Vehicle Routeing Problems

Part of: Algorithms - Computer Science Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Agustín Bompadre ,
Moshe Dror  and
James B. Orlin
Agustín Bompadre*
Affiliation:
Operations Research Center, MIT
Moshe Dror*
Affiliation:
Operations Research Center, MIT
James B. Orlin*
Affiliation:
Sloan School of Management, MIT
*
∗ Current address: Optiant Inc., 4 Van de Graaff Drive, Burlington, MA 01803, USA. Email address: [email protected]
∗∗ Current address: Department of Management Information Systems, Eller College of Management, University of Arizona, 430M McClelland Hall, 1130 E. Helen Street, PO Box 210108, Tucson, AZ 85721-0108, USA.
∗∗∗ Postal address: Sloan School of Management, MIT, 50 Memorial Drive, Cambridge, MA 02142, USA.
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Abstract

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We analyze the unit-demand Euclidean vehicle routeing problem, where n customers are modeled as independent, identically distributed uniform points and have unit demand. We show new lower bounds on the optimal cost for the metric vehicle routeing problem and analyze them in this setting. We prove that there exists a constant ĉ > 0 such that the iterated tour partitioning heuristic given by Haimovich and Rinnooy Kan (1985) is a (2 - ĉ)-approximation algorithm with probability arbitrarily close to 1 as the number of customers goes to ∞. It has been a longstanding open problem as to whether one can improve upon the factor of 2 given by Haimovich and Rinnooy Kan. We also generalize this, and previous results, to the multidepot case.

Keywords

Vehicle routeing problemheuristicprobabilistic analysis of algorithms

MSC classification

Primary: 68W40: Analysis of algorithms
Secondary: 90B06: Transportation, logistics
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007 , pp. 259 - 278
Copyright
Copyright © Applied Probability Trust 2007 

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