Multiple Criteria Decision Making (MCDM), Cross-efficiency Data Envelopment Analysis (DEA), Rank reversal, and Least Common Multiple (LCM)


This paper presents that the rank reversal occurs in other popular MCDM approach as well, cross-efficiency evaluation of data envelopment analysis (DEA), which has been alternative method for ranking decision making units (DMU) in the data envelopment analysis (DEA). This paper also attempts to illustrate that the proposed least common multiple (LCM) approach successfully addresses these rank reversal problems in decision support systems area.

Full Text : PDF

  • Barzilai, J. & Golany, B., 1994. AHP rank reversal, normalization and aggregation rules, INFOR, 32(2),  57-63.
  • Belton, V. & Gear, T., 1983. On a shortcoming of Saaty’s method of analytic hierarchies. Omega, 11 (3), 228-230.
  • Charnes, A., Cooper, W. & Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429-444.
  • Doyle, J. & Green, R., 1994. Efficiency and cross-efficiency in DEA. Journal of the Operational Research Society, 45, 567-578.
  • Dyer, J. & Wendell, R., 1985. A critique of the Analytic Hierarchy Process. Technical Report, 84/85, 4-24. Department of Management. The University of Texas at Austin.
  • Lootsma, F., 1999. Multi-criteria decision analysis via ratio and difference judgment. Kluwer Academic Publishers: Dordrecht.
  • Perez, J., Jimeno, J. & Mokotoff, E., 2006. Another potential shortcoming of AHP.  TOP, 14(1), 99-111.
  • Saaty, T.L. & Sagir, M., 2009. An essay on rank preservation and reversal.  Mathematical and Computer Modelling, 49,  1230-1243.
  • Schoner, B., Wedley, W.C., & Choo, E.U., 1993. A unified approach to AHP with linking pins. European Journal of Operational Research, 64, 384-392.
  •    Sexton, T. Silkman, R. & Hogan, A., 1986. Data envelopment analysis: Critique and extensions. Jossey-Bass, San Francisco, CA.
  • Shin, Y.B. & Lee, S.H., 2012. Note on an approach to preventing rank reversals with addition or deletion of an Analytic Hierarchy Process. Journal of Education Review, 3(1), 66-72.   
  • Wong, Y. & Beasley, J., 1990. Restricting weight flexibility in data envelopment analysis. Journal of the Operational Research Society, 41(9), 829-835.