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1 results

  • Probabilistic Analysis of Unit-Demand Vehicle Routeing Problems

  • Part of
  • Agustín Bompadre, Moshe Dror, James B. Orlin
  • Journal:
    Journal of Applied Probability / Volume 44 / Issue 1 / March 2007
    Published online by Cambridge University Press:
    14 July 2016, pp. 259-278
    Print publication:
    March 2007
    • Article
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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.