Optimization and Engineering

, Volume 13, Issue 2, pp 349–370 | Cite as

A minimum violations ranking method

  • Kathryn E. Pedings
  • Amy N. LangvilleEmail author
  • Yoshitsugu Yamamoto


We present a rating method that, given information on the pairwise comparisons of n items, minimizes the number of inconsistencies in the ranking of those items. Our Minimum Violations Ranking (MVR) Method uses a binary linear integer program (BILP) to do this. We prove conditions when the relaxed LP will give an optimal solution to the original BILP. In addition, the LP solution gives information about ties and sensitivities in the ranking. Lastly, our MVR method makes use of bounding and constraint relaxation techniques to produce a fast algorithm for the linear ordering problem, solving an instance with about one thousand items in less than 10 minutes.


Minimum violations rating Linear ordering Integer programming Linear programming Optimization Ties Sensitivity 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Kathryn E. Pedings
    • 1
  • Amy N. Langville
    • 1
    Email author
  • Yoshitsugu Yamamoto
    • 2
  1. 1.Department of MathematicsCollege of CharlestonCharlestonUSA
  2. 2.Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukubaJapan

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