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Efficient vectors in priority setting methodology

Author

Listed:
  • Susana Furtado

    (Universidade do Porto Rua Dr. Roberto Frias)

  • Charles R. Johnson

    (College of William and Mary)

Abstract

The Analytic Hierarchy Process (AHP) is a much discussed method in ranking business alternatives based on empirical and judgemental information. We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of pair-wise comparisons. It has been shown that the entry-wise geometric mean of all columns is efficient for any reciprocal matrix. Here, by combining some new basic observations with some known theory, we (1) give a method for inductively generating large collections of efficient vectors, and (2) show that the entry-wise geometric mean of any collection of distinct columns of a reciprocal matrix is efficient. We study numerically, using different measures, the performance of these geometric means in approximating the reciprocal matrix by a consistent matrix. We conclude that, as a general method to be chosen, independent of the data, the geometric mean of all columns performs well when compared with the geometric mean of proper subsets of columns.

Suggested Citation

  • Susana Furtado & Charles R. Johnson, 2024. "Efficient vectors in priority setting methodology," Annals of Operations Research, Springer, vol. 332(1), pages 743-764, January.
    • Handle: RePEc:spr:annopr:v:332:y:2024:i:1:d:10.1007_s10479-023-05771-y
    DOI: 10.1007/s10479-023-05771-y
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