Document Type : Research Paper


1 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran


The data envelopment analysis (DEA) is a mathematical programming technique, which is used for evaluating relative efficiency of decision making units (DMUs). However, the DEA does not provide more information about the efficient DMUs. Recently, some researchers have been carried out in the background of using DEA models to generate local weights of alternatives from pairwise comparison matrices used in the analytic hierarchy process (AHP). In this paper, an application of a common set of weights is used for determining priorities in the AHP. First, we determine DEA efficient alternatives as DMUs. Then, these alternatives are ranked according to the efficiency score weighted by the common set of weights in the AHP. This application is applied successfully and the result is valid and assured. A numerical example is utilized to illustrate the capability of this procedure.


[1]                 Charnes, A.,Cooper, W.W. and Rhodes, (1978). Measuring the efficiency of decision making units. European Journal of operational research, Vol. 2, pp.                                429-444.
[2]                 Saaty, T. L. (1980). The Analytic Hierarchy Process. McGraw-Hill Company, NewYork.
[3]                 Andersen, P. and Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, Vol. 39, No. 10, pp. 1261–1264.
19        Deriving Priorities the Alternatives in an Analytic Hierarchy Process
[4]                 Sexton, T. R., Silkman, R. H. and Hogan, A. J. (1986). Data envelopment analysis: Critique and extensions. In R. H. Silkman (Ed.), Measuring efficiency: An assessment of data envelopment analysis (pp. 73–105). San Francisco: Jossey-Bass.
[5]                 Dyson, R. G. and Thanassoulis, E. (1988). Reducing weight flexibility in DEA.
Journal of the Operations Research Society, Vol. 39, pp. 563–576.
[6]                 Ertay, T., Ruan, D. and Tuzkaya, U. R. (2006). Integrating data envelopment analysis and analytic hierarchy for the facility layout design in manufacturing systems. Information Sciences, Vol. 176, pp. 237–262.
[7]                 Karsak, E. E. and Ashika, S. S. (2005). Practical common weight multi-criteria decision making approach with an improved discriminating power for technology selection.  International  Journal  of   Production   Research,   Vol.   43,   No.   8,   pp. 1537–1554.
[8]                 Karsak, E. E. and Ashika, S. S. (2008). Improved common weight MCDM model for technology selection. International Journal of Production Research, Vol. 46, No. 24, pp. 6933–6944.
[9]                 Li, X. B. and Reeves, G. R. (1999). A multiple criteria approach to data envelopment analysis. European Journal of Operational Research, Vol. 115, pp. 507–517.
[10]             Roll Y. and Golany, B. (1993). Alternate methods of treating factor weights in DEA.
Omega, Vol. 21, pp. 99–109.
[11]             Thompson, R. G., Langemeier, L. N., Lee, C. T. and Thrall, R. M. (1990). The role of multiplier bounds in efficiency analysis with application to Kansas farming. Journal of Econometrics, Vol. 46, pp. 93–108.
[12]             Thompson, R. G., Singleton, F. D., Thrall, R. M. and Smith, B. A. (1986). Comparative site evaluations for locating a high energy physics lab in Texas. Interfaces, Vol. 16, pp. 35–49.
[13]             Cook, W., Kress, M. and Seiford, L. (1992). Prioritization models for frontier decision-making units in DEA. European Journal of Operational Research,Vol. 59, pp. 319–23.
[14]             Mehrabian, S., Alirezaee, M. R. and Jahanshahloo, G. R. (1999). A complete efficiency ranking of decision making units in data envelopment analysis. Computational Optimization and Applications, Vol. 14, pp. 261–266.
[15]             Jahanshahloo, G. R., Junior, H. V., Hosseinzadeh Lotfi, F. and Akbarian, D. (2007). A new DEA ranking system based on changing the reference set. European Journal of Operational Research, Vol. 181, pp. 331–337.
[16]             Liu, F. F. and Peng, H. H. (2006). Ranking of units on the DEA frontier with common weights. Computers and Operations Research. doi:10.1016/j.cor.2006.09.006.
[17]             Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., Khanmohammadi, M., Kazemimanesh,
M. and Rezaie, V. (2010). Ranking of units by positive ideal DMU with common weights. Expert Systems with Applications, Vol. 37, pp. 7483–7488.
[18]             Liu, F. H. F. and Peng, H. H. (2008). Ranking of DMUs on the DEA frontier with common weights. Computers and Operations Research, Vol. 35, No. 5, pp. 1624– 1637.
[19]             Mirhedayatian, M.S. and Farzipoor Saen, R. (2011). A new approach for weight derivation using data envelopment analysis in the analytic hierarchy process. Journal of the Operational Research Society, Vol. 62, pp. 1585–1595.
[20]             Lin, M.I., Lee, Y. D. and Ho, T. N. (2011). Applying integrated DEA/AHP  to evaluate the economic performance of local governments in China. European Journal of Operational Research,Vol. 209, pp. 129–140.
S. Khoshfetrat and F. Hosseinzadeh-Lotfi /IJRIE 3(4) (2014) 13-20            20
[21]             Grošelj, P., Malovrh, S. P. and Stirn,L.Z. (2011). Methods based on data envelopment analysis for deriving group priorities in analytic hierarchy process. CEJOR, Vol. 19, pp. 267–284.
[22]             Wang, Y.M. and Chin, K.S. (2009). A new data envelopment analysis method for priority determination and group decision making in the analytic hierarchy process. European Journal of Operational Research,Vol. 195, pp. 239–250.