Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis

It has been widely recognized that data envelopment analysis (DEA) lacks discrimination power to distinguish between DEA efficient units. This paper proposes a new methodology for ranking decision making units (DMUs). The new methodology ranks DMUs by imposing an appropriate minimum weight restriction on all inputs and outputs, which is decided by a decision maker (DM) or an assessor in terms of the solutions to a series of linear programming (LP) models that are specially constructed to determine a maximin weight for each DEA efficient unit. The DM can decide how many DMUs to be retained as DEA efficient in final efficiency ranking according to the requirement of real applications, which provides flexibility for DEA ranking. Three numerical examples are investigated using the proposed ranking methodology to illustrate its power in discriminating between DMUs, particularly DEA efficient units.

[1]  B. Golany,et al.  Controlling Factor Weights in Data Envelopment Analysis , 1991 .

[2]  T. Sexton,et al.  Data Envelopment Analysis: Critique and Extensions , 1986 .

[3]  Yao Chen,et al.  Ranking efficient units in DEA , 2004 .

[4]  Rodney H. Green,et al.  Efficiency and Cross-efficiency in DEA: Derivations, Meanings and Uses , 1994 .

[5]  Abraham Charnes,et al.  Programming with linear fractional functionals , 1962 .

[6]  J. Cubbin,et al.  Public Sector Efficiency Measurement: Applications of Data Envelopment Analysis , 1992 .

[7]  Rodney H. Green,et al.  Cross-Evaluation in DEA - Improving Discrimiation Among DMUs , 1995 .

[8]  C. A. Knox Lovell,et al.  Equivalent standard DEA models to provide super-efficiency scores , 2003, J. Oper. Res. Soc..

[9]  Shanling Li,et al.  A super-efficiency model for ranking efficient units in data envelopment analysis , 2007, Appl. Math. Comput..

[10]  B. Golany,et al.  Alternate methods of treating factor weights in DEA , 1993 .

[11]  T.-H. Chen,et al.  Slack-based ranking method: an interpretation to the cross-efficiency method in DEA , 2008, J. Oper. Res. Soc..

[12]  F. Hosseinzadeh Lotfi,et al.  A new DEA ranking system based on changing the reference set , 2007, Eur. J. Oper. Res..

[13]  P. Andersen,et al.  A procedure for ranking efficient units in data envelopment analysis , 1993 .

[14]  Zilla Sinuany-Stern,et al.  Scaling units via the canonical correlation analysis in the DEA context , 1997, Eur. J. Oper. Res..

[15]  Zilla Sinuany-Stern,et al.  DEA and the discriminant analysis of ratios for ranking units , 1998, Eur. J. Oper. Res..

[16]  Zilla Sinuany-Stern,et al.  Review of ranking methods in the data envelopment analysis context , 2002, Eur. J. Oper. Res..

[17]  Rajiv D. Banker,et al.  The super-efficiency procedure for outlier identification, not for ranking efficient units , 2006, Eur. J. Oper. Res..

[18]  Richard H. Silkman,et al.  Measuring efficiency : an assessment of data envelopment analysis , 1986 .

[19]  Zilla Sinuany-Stern,et al.  An AHP/DEA methodology for ranking decision making units , 2000 .

[20]  Lawrence M. Seiford,et al.  INFEASIBILITY OF SUPER EFFICIENCY DATA ENVELOPMENT ANALYSIS MODELS , 1999 .

[21]  Zilla Sinuany-Stern,et al.  Academic departments efficiency via DEA , 1994, Comput. Oper. Res..

[22]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[23]  Fuh-Hwa Franklin Liu,et al.  Ranking of units on the DEA frontier with common weights , 2008, Comput. Oper. Res..

[24]  Barton A. Smith,et al.  Comparative Site Evaluations for Locating a High-Energy Physics Lab in Texas , 1986 .

[25]  Russell G. Thompson,et al.  The role of multiplier bounds in efficiency analysis with application to Kansas farming , 1990 .

[26]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .