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Approximation results for min‐max path cover problems in vehicle routing

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  • Zhou Xu
  • Liang Xu
  • Chung‐Lun Li

Abstract

This article studies a min‐max path cover problem, which is to determine a set of paths for k capacitated vehicles to service all the customers in a given weighted graph so that the largest path cost is minimized. The problem has wide applications in vehicle routing, especially when the minimization of the latest service completion time is a critical performance measure. We have analyzed four typical variants of this problem, where the vehicles have either unlimited or limited capacities, and they start from either a given depot or any depot of a given depot set. We have developed approximation algorithms for these four variants, which achieve approximation ratios of max{3 ‐ 2/k,2}, 5, max{5 ‐ 2/k,4}, and 7, respectively. We have also analyzed the approximation hardness of these variants by showing that, unless P = NP, it is impossible for them to achieve approximation ratios less than 4/3, 3/2, 3/2, and 2, respectively. We have further extended the techniques and results developed for this problem to other min‐max vehicle routing problems.© 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Suggested Citation

  • Zhou Xu & Liang Xu & Chung‐Lun Li, 2010. "Approximation results for min‐max path cover problems in vehicle routing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(8), pages 728-748, December.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:8:p:728-748
    DOI: 10.1002/nav.20434
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    Cited by:

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    2. Wei Yu & Zhaohui Liu, 2019. "Better approximability results for min–max tree/cycle/path cover problems," Journal of Combinatorial Optimization, Springer, vol. 37(2), pages 563-578, February.

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