Cross AHP/DEA method for ranking Decision Making Units

Document Type : Research Paper

Authors

1 Assistant Prof. of IUST, Dep. of Mathematics, Tehran, Iran

2 M.Sc. Student in Applied Mathematics, University of Science and Technology, Tehran, Iran

3 Ph.D. Student in Applied Mathematics, University of Science and Technology, Tehran, Iran

Abstract

All the basic models in Data Envelopment Analysis divide the Decision Making Units to two categories: efficient and inefficient. So, there is no separation for the efficient units. In The Analytical Hierarchy Process in spite of complete ranking of units, the process of pairwise comparison matrix making is based on experts’ ideas, causes error and inconsistency in resulted matrix. In this paper first we suggest a combined method called cross AHP/DEA method for ranking the units that not only uses the strength of The Analytical Hierarchy Process and Data Envelopment Analysis methods in presenting a rational ranking, but also covers the older methods problems noticeably and then we explained properties and advantages of our method in comparison to other methods. Finally, for better comparison we designed some numerical examples.

Keywords


Andersen, P., Petersen, N.C., 1993. A procedure for ranking efficient units in data envelopment analysis. Management Science, 39: 1261–1264.
Cooper, William W., Seiford Lawrence M., Tone Kaoru, (2000). Data Envelopment Analysis, Second Edition, Springer.
Cooper, W.W., Seiford, L.M., Tone, K., 2006. Introduction to Data Envelopment Analysis and Its Uses. Springer Science1Business Media Inc., New York.
Friedman, L., Sinuany-Stern, Z., 1997. Scaling units via the canonical correlation analysis in the DEA context. European Journal of Operational Research, 100: 629–637.
Ganley, J.A., Cubbin, S.A., 1992. Public Sector Efficiency Measurement: Applications of Data Envelopment Analysis. North-Holland Publishing, Amsterdam.‎‎
Jahanshahloo G.R, HosseinzadehLotfi F, Shoja. N., Tohidi. G, Razavyan. S. (2004). Ranking using L1-norm in data envelopment analysis, Applied Mathematics and Computation 153, 215–224.
Jahanshahloo G.R., HosseinzadehLotfi .F, Jafari. Y, Maddahi. R, (2011) Selecting symmetric weights as a secondary goalin DEA cross-efficiency evaluation. Applied Mathematical Modelling, 35, 544–549.
Jahanshahloo, G.R., Junior, H.V., Lotfi, F.H., Akbarian, D., 2007. A new DEA ranking system based on changing the reference set. European Journal of Operational Research, 181(1): 331–337.
Ramanathan, R., 2006. Data envelopment analysis for weight derivation and aggregation in the analytic hierarchy process. Computers and Operations Research, 33, 1289–1307.
Sexton, T.R., Silkman, R.H., Hogan, A.J., 1986. Data Envelopment Analysis. Jossey-Bass, San Francisco.
Sinuany-Stern, Z., Mehrez, A., Hadad, Y., 2000. An AHP/DEA methodology for ranking decision-making units. International Transactions in Operational Research, 7, 109–124.
Wang, Y.M., Liu, J., Elhagh, T.M.S., 2008b. An integrated AHP–DEA methodology for bridge risk assessment. Computers and Operations Research, 54, 513–525.‎‎‎‎