Full Ranking of Decision Making Units by Relaying Hyperplane on the Set of Produce Possibility

Document Type : Research Paper


1 Department of Mathematics, Science and Research Branch, IAU, Hesarak, poonak

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

3 Department of mathematics, Mathemathics and Computer Science College, Kharazmi University, Tehran, Iran


The exit methods for producing common weight in DEA are complicated or they can’t produce full ranking for Decision Making Units (DMUs). Wang and et al introduced two methods based on regresion analysis for finding common weights. In these method they fined set of common weight so that the efficeincy which is computed by set of common weight for all units, are always smaller or and equal to obtained optimistic efficeincy from CCR model. In this methods we are trying to make the computed efficeincy by common weight closer to obtained optimistic efficeincy from CCR model, and or in other words the goal of obtaining unique hyperplane as all distance of DMUs from this hyperplane will be minimal. In this paper by using an example, we show that the obtained hyperplane from suggested methods of Wang is passing throug PPS. In other words, in introduced method of proposed hyperplane for ranking, isn’t relaying PPS, neccessarly. At the end, we introduce a new method for ranking the decision makind units that is a correspond hyperplane of relaying common weight set on PPS and finally we can use this techniqe for real data.


  1. A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444 (1978)
  2. L. Friedman, Z. Sinuany-Stern, Scaling units via the canonical correlation analysis in the DEA context. European Journal of Operational Research, 100, 629–637 (1997).
  3. J. A. Ganley, S. A. Cubbin, Public sector efficiency measurement: Applications of data envelopment analysis. Amsterdam: North-Holland (1992).
  4. A. Hashimoto, D. A. Wu, A DEA-compromise programming model for comprehensive ranking. Journal of the Operations Research Society of Japan, 47, 73–81 (2004).
  5. G. R. Jahanshahloo, A. Memariani, F. Hosseinzadeh Lotfi, H. Z. Rezai, A note on some DEA models and finding efficiency and complete ranking using common set of weights. Applied Mathematics and Computation, 166, 265–281 (2005).
  6. C. Kao, H. T. Hung, Data envelopment analysis with common weights: The compromise solution approach. Journal of the Operational Research Society, 56, 1196– 1203 (2005).
  7. F. H. F. Liu, H. H. Peng, Ranking of units on the DEA frontier with common weights. Computers and Operations Research, 35, 1624–1637 (2008).
  8. Z. Sinuany-Stern, A. Mehrez, A. Barboy, Academic departments’ efficiency in DEA. Computers and Operations Research, 21, 543–556 (1994).
  9. Z. Sinuany-Stern, L. Friedman, DEA and the discriminant analysis of ratios for ranking units. European Journal of Operational Research, 111, 470–478 (1998).
  10. Y. M. Wang, Y. Luo, Y. X. Lan, Common weights for fully ranking decision making units by regression analysis. Expert System with Applications 38, 9122–9128 (2011).
  11. Y. M. Wang, Y. Luo, L. Liang, Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis. Journal of Computational and Applied Mathematics, 223, 469–484 (2009).