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Testing the Efficiency of Two Pairwise Comparison Methods in Discrete Multiple Criteria Problems

Risto Lahdelma, Pekka Salminen, Markku Kuula, Testing the Efficiency of Two Pairwise Comparison Methods in Discrete Multiple Criteria Problems. European Journal on Operational Research (145), 496-508, 2003.

Abstract:

In so-called pairwise comparison methods, the decision-maker (DM) makes holistic binary comparisons among feasible decision alternatives. The goal is to identify the best (most preferred) alternative using a minimal amount of comparisons. In the worst case, m-1 comparisons are required to identify the best among m alternatives. The efficiency of a pairwise comparison method is measured in terms of the number of saved comparisons with respect to the worst case. We test the efficiency of two pairwise comparison methods. The methods studied are Salminen's piecewise linear prospect theory (PLP) method and the convex cone method by Korhonen, Wallenius, and Zionts (KWZ). The PLP method models the DMs preferences by a piecewise linear difference function. The KWZ method assumes a quasi-concave utility or value function. These methods are tested using randomly generated data sets with 50, 100, 150, and 200 alternatives and from 2 up to 6 criteria. The DM's preference statements are simulated using linear, quadratic, and Chebycheff value functions and piecewise linear difference functions. The efficiency measurements can be used for evaluating whether it is feasible to apply the methods in a real-life application with given number of alternatives and criteria. The results indicate that pairwise comparison methods are not as efficient as reported in the literature. Both methods lose their efficiency very rapidly with increasing number of criteria.

BibTeX entry:

@ARTICLE{jLaSaKu02a,
  title = {Testing the Efficiency of Two Pairwise Comparison Methods in Discrete Multiple Criteria Problems},
  author = {Lahdelma, Risto and Salminen, Pekka and Kuula, Markku},
  journal = {European Journal on Operational Research},
  number = {145},
  pages = {496-508},
  year = {2003},
  keywords = {Multiple criteria analysis, discrete optimisation, pairwise comparison methods},
}

Belongs to TUCS Research Unit(s): Algorithmics and Computational Intelligence Group (ACI)

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