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A minimum violations ranking method

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, College of Charleston, 175 Calhoun Street-RSS 339, Charleston, SC, 29401, USA

    Kathryn E. Pedings & Amy N. Langville

  2. Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan

    Yoshitsugu Yamamoto

Authors
  1. Kathryn E. Pedings
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  2. Amy N. Langville
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  3. Yoshitsugu Yamamoto
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Corresponding author

Correspondence to Amy N. Langville.

Additional information

This research was supported in part by NSF grant CAREER-CCF-0546622.

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Pedings, K.E., Langville, A.N. & Yamamoto, Y. A minimum violations ranking method. Optim Eng 13, 349–370 (2012). https://doi.org/10.1007/s11081-011-9135-5

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  • DOI: https://doi.org/10.1007/s11081-011-9135-5

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