Super-efficiency in stochastic data envelopment analysis: An input relaxation approach

This paper addresses super-efficiency issue based on input relaxation model in stochastic data envelopment analysis. The proposed model is not limited to using the input amounts of evaluating DMU, and one can obtain a total ordering of units by using this method. The input relaxation super-efficiency model is developed in stochastic data envelopment analysis, and its deterministic equivalent, also, is derived which is a nonlinear program. Moreover, it is shown that the deterministic equivalent of the stochastic super-efficiency model can be converted to a quadratic program. As an empirical example, the proposed method is applied to the data of textile industry of China to rank efficient units. Finally, when allowable limits of data variations for evaluating DMU are permitted, the sensitivity analysis of the proposed model is discussed.

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

[2]  Zhimin Huang,et al.  Dominance stochastic models in data envelopment analysis , 1996 .

[3]  Lawrence M. Seiford,et al.  CHARACTERISTICS ON STOCHASTIC DEA EFFICIENCY : RELIABILITY AND PROBABILITY BEING EFFICIENT , 1999 .

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

[5]  Gholam Reza Jahanshahloo,et al.  Determining assurance interval for non-Archimedean element in the improving outputs model in DEA , 2004, Appl. Math. Comput..

[6]  Oliver Stein,et al.  A Semi-Infinite Programming Model In Data Envelopment Analysis , 2001 .

[7]  Patrick T. Harker,et al.  Note: Ranking DMUs with Infeasible Super-Efficiency DEA Models , 2002, Manag. Sci..

[8]  Peter Bogetoft,et al.  Incentive efficient production frontiers: an agency perspective on DEA , 1994 .

[9]  William W. Cooper,et al.  Chapter 13 Satisficing DEA models under chance constraints , 1996, Ann. Oper. Res..

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

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

[12]  Milan Martic,et al.  An application of DEA for comparative analysis and ranking of regions in Serbia with regards to social-economic development , 2001, Eur. J. Oper. Res..

[13]  M. Khodabakhshi,et al.  An input relaxation measure of efficiency in stochastic data envelopment analysis , 2009 .

[14]  K. Tone.  Continuous Optimization A slacks-based measure of super-efficiency in data envelopment analysis , 2002 .

[15]  William W. Cooper,et al.  Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis , 2002, J. Oper. Res. Soc..

[16]  William W. Cooper,et al.  Stochastics and Statistics , 2001 .

[17]  A. Charnes,et al.  Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis , 1984 .

[18]  Kenneth C. Land,et al.  Chance‐constrained data envelopment analysis , 1993 .

[19]  Mohammad Khodabakhshi,et al.  A super-efficiency model based on improved outputs in data envelopment analysis , 2007, Appl. Math. Comput..

[20]  W. Cooper,et al.  Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA , 1998 .

[21]  Joe Zhu.  Robustness of the efficient DMUs in data envelopment analysis , 1996 .

[22]  M. Khodabakhshi,et al.  CHANCE CONSTRAINED ADDITIVE INPUT RELAXATION MODEL IN STOCHASTIC DATA ENVELOPMENT ANALYSIS , 2010 .

[23]  Robert M. Thrall,et al.  Chapter 5 Duality, classification and slacks in DEA , 1996, Ann. Oper. Res..

[24]  W. Cooper,et al.  Using DEA to improve the management of congestion in Chinese industries (1981-1997) , 2001 .

[25]  M. Khodabakhshi,et al.  A one-model approach based on relaxed combinations of inputs for evaluating input congestion in DEA , 2009 .

[26]  Gholam Reza Jahanshahloo,et al.  Suitable combination of inputs for improving outputs in DEA with determining input congestion: Considering textile industry of China , 2004, Appl. Math. Comput..

[27]  Russell G. Thompson,et al.  Importance for DEA of zeros in data, multipliers, and solutions , 1993 .

[28]  M. Khodabakhshi,et al.  Estimating most productive scale size with stochastic data in data envelopment analysis , 2009 .

[29]  Kaoru Tone,et al.  A slacks-based measure of super-efficiency in data envelopment analysis , 2001, Eur. J. Oper. Res..

[30]  Gholam Reza Jahanshahloo,et al.  A Complete Efficiency Ranking of Decision Making Units in Data Envelopment Analysis , 1999, Comput. Optim. Appl..

[31]  M. Khodabakhshi,et al.  An additive model approach for estimating returns to scale in imprecise data envelopment analysis , 2010 .

[32]  A. Charnes,et al.  SENSITIVITY OF EFFICIENCY CLASSIFICATIONS IN THE ADDITIVE MODEL OF DATA ENVELOPMENT ANALYSIS , 1992 .

[33]  Betty L. Hickman,et al.  Effects of excluding the column being scored from the DEA envelopment LP technology matrix , 1997 .

[34]  Lawrence M. Seiford,et al.  Stability regions for maintaining efficiency in data envelopment analysis , 1998, Eur. J. Oper. Res..

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

[36]  R M Thrall,et al.  DUALITY CLASSIFICATION AND SLACKS IN DATA ENVELOPMENT ANALYSIS , 1996 .

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

[38]  Greg N. Gregoriou,et al.  An input-oriented super-efficiency measure in stochastic data envelopment analysis: Evaluating chief executive officers of US public banks and thrifts , 2010, Expert Syst. Appl..