Approximation algorithms for distance constrained vehicle routing problems

  • Authors:

  • Viswanath Nagarajan;R. Ravi

  • Affiliations:

  • IBM T.J. Watson Research Center, Yorktown Heights, New York 10598;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

  • Venue:
  • Networks
  • Year:
  • 2012

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Abstract

We study the distance constrained vehicle routing problem (DVRP) (Laporte et al., Networks 14 (1984), 47–61, Li et al., Oper Res 40 (1992), 790–799): given a set of vertices in a metric space, a specified depot, and a distance bound D, find a minimum cardinality set of tours originating at the depot that covers all vertices, such that each tour has length at most D. This problem is NP-complete, even when the underlying metric is induced by a weighted star. Our main result is a 2-approximation algorithm for DVRP on tree metrics; we also show that no approximation factor better than 1.5 is possible unless P = NP. For the problem on general metrics, we present a $(O(\log {1 \over \varepsilon }),1 + \varepsilon )$ **image** -bicriteria approximation algorithm: i.e., for any ε 0, it obtains a solution violating the length bound by a 1 + ε factor while using at most $O(\log {1 \over \varepsilon })$ **image** times the optimal number of vehicles. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012 © 2012 Wiley Periodicals, Inc.