Data Envelopment Analysis under Uncertainty and Risk
Data Envelopment Analysis (DEA) is one of the most
widely used technique for evaluating the relative efficiency of a set
of homogeneous decision making units. Traditionally, it assumes that
input and output variables are known in advance, ignoring the critical
issue of data uncertainty. In this paper, we deal with the problem
of efficiency evaluation under uncertain conditions by adopting the
general framework of the stochastic programming. We assume that
output parameters are represented by discretely distributed random
variables and we propose two different models defined according to a
neutral and risk-averse perspective. The models have been validated
by considering a real case study concerning the evaluation of the
technical efficiency of a sample of individual firms operating in
the Italian leather manufacturing industry. Our findings show the
validity of the proposed approach as ex-ante evaluation technique
by providing the decision maker with useful insights depending on
his risk aversion degree.
[1] Charnes A, Cooper W W, Rhodes, E. Measuring the efficiency of
decision making units. European Journal of Operational Research 1978;
6: 429-444.
[2] Paradi J C, Asmild M, Simak P. Using Dea and worst practice DEA in
credit risk evaluation. Journal of Productivity Analysis 2004; 21: 153-
165.
[3] Premachandra I M, Chen Y, Watson J. Dea as a tool for predicting
corporate failure and success: A case of bankruptcy assessment. Omega
2011; 39: 620-626.
[4] Charnes A, Cooper W W. Chance constrained programming. Management
Science 1959; 5(1): 73-79.
[5] Land K C, Lovell C A K, Thore S. Chance-constrained Data Envelopment
Analysis. Managerial and Decision Economics 1993; 14: 541-554.
[6] Olesen O B, Petersen N C. Chance constrained efficiency evaluation.
Management Science 1995; 41: 442-457.
[7] Olesen O B. Comparing and combining two approaches for chance
constrained DEA. Journal of Productivity Analysis 2006; 26(2): 103-
119.
[8] Sengupta J K. Data Envelopment Analysis for efficiency measurement
in the stochastic case. Computers and Operations Research 1987; 14:
117-129.
[9] Sengupta J K. Efficiency measurement in stochastic input-output systems.
International Journal of Systems Science 1982; 13: 273-287.
[10] Sueyoshi T. Stochastic DEA for restructure strategy: an application to a
Japanese petroleum company. Omega 2000; 28: 385-398.
[11] Bruni M E, Beraldi P, Conforti D, Tundis E. Probabilistically constrained
models for efficiency and dominance in DEA. International Journal of
Production Economics 2009; 117(1): 219-228.
[12] Ruszczy'nski A, Shapiro A. Stochastic Programming, Handbook in
Operations Research and Management Science. Elsevier Science, Amsterdam,
2003.
[13] Ogryczak W, Ruszczy'nski A. Dual stochastic dominance and related
mean-risk models. SIAM Journal on Optimization 2002; 13:60-78.
[14] Markowitz H M. Portfolio selection. Journal of Finance 1952; 7: 77-91.
[15] Rocafellar R, Uryasev V. Conditional value at risk for general loss
distributions. Journal of Banking and Finance 2000; 26:1443-1471.
[16] Artzner P, Delbaen F, Eber J M, Heath D. Coherent measures of risk.
Mathematical Finance 1999; 9(3): 203-228.
[17] Shabbir A, Convexity and decomposition of mean-risk stochastic programs.
Mathematical Programming 2006; 106(3): 433-446.
[18] Notyan N, Ruszczy'nski A. Valid inequalities and restrictions for
stochastic programming problems with first order stochastic dominance
constraints. Mathematical Programming 2008; 114: 433-446.
[19] Beraldi P, De Simone F, Violi A. Generating scenario trees: a parallel
integrated simulation-optimization approach. Journal of Computational
and Applied Mathematics 2010; 23(9): 2322-2331.
[20] Beraldi P, Bruni M E. New stochastic programming DEA formulations.
Technical Report N. 1 - Laboratory of Financial Engineering 2011;
University of Calabria, Italy.
[21] Kaut M, Wallace S. Evaluation of scenario generation methods for
stochastic programming. Pacific Journal of Optimization 2007; 3(2):
257-271.
[1] Charnes A, Cooper W W, Rhodes, E. Measuring the efficiency of
decision making units. European Journal of Operational Research 1978;
6: 429-444.
[2] Paradi J C, Asmild M, Simak P. Using Dea and worst practice DEA in
credit risk evaluation. Journal of Productivity Analysis 2004; 21: 153-
165.
[3] Premachandra I M, Chen Y, Watson J. Dea as a tool for predicting
corporate failure and success: A case of bankruptcy assessment. Omega
2011; 39: 620-626.
[4] Charnes A, Cooper W W. Chance constrained programming. Management
Science 1959; 5(1): 73-79.
[5] Land K C, Lovell C A K, Thore S. Chance-constrained Data Envelopment
Analysis. Managerial and Decision Economics 1993; 14: 541-554.
[6] Olesen O B, Petersen N C. Chance constrained efficiency evaluation.
Management Science 1995; 41: 442-457.
[7] Olesen O B. Comparing and combining two approaches for chance
constrained DEA. Journal of Productivity Analysis 2006; 26(2): 103-
119.
[8] Sengupta J K. Data Envelopment Analysis for efficiency measurement
in the stochastic case. Computers and Operations Research 1987; 14:
117-129.
[9] Sengupta J K. Efficiency measurement in stochastic input-output systems.
International Journal of Systems Science 1982; 13: 273-287.
[10] Sueyoshi T. Stochastic DEA for restructure strategy: an application to a
Japanese petroleum company. Omega 2000; 28: 385-398.
[11] Bruni M E, Beraldi P, Conforti D, Tundis E. Probabilistically constrained
models for efficiency and dominance in DEA. International Journal of
Production Economics 2009; 117(1): 219-228.
[12] Ruszczy'nski A, Shapiro A. Stochastic Programming, Handbook in
Operations Research and Management Science. Elsevier Science, Amsterdam,
2003.
[13] Ogryczak W, Ruszczy'nski A. Dual stochastic dominance and related
mean-risk models. SIAM Journal on Optimization 2002; 13:60-78.
[14] Markowitz H M. Portfolio selection. Journal of Finance 1952; 7: 77-91.
[15] Rocafellar R, Uryasev V. Conditional value at risk for general loss
distributions. Journal of Banking and Finance 2000; 26:1443-1471.
[16] Artzner P, Delbaen F, Eber J M, Heath D. Coherent measures of risk.
Mathematical Finance 1999; 9(3): 203-228.
[17] Shabbir A, Convexity and decomposition of mean-risk stochastic programs.
Mathematical Programming 2006; 106(3): 433-446.
[18] Notyan N, Ruszczy'nski A. Valid inequalities and restrictions for
stochastic programming problems with first order stochastic dominance
constraints. Mathematical Programming 2008; 114: 433-446.
[19] Beraldi P, De Simone F, Violi A. Generating scenario trees: a parallel
integrated simulation-optimization approach. Journal of Computational
and Applied Mathematics 2010; 23(9): 2322-2331.
[20] Beraldi P, Bruni M E. New stochastic programming DEA formulations.
Technical Report N. 1 - Laboratory of Financial Engineering 2011;
University of Calabria, Italy.
[21] Kaut M, Wallace S. Evaluation of scenario generation methods for
stochastic programming. Pacific Journal of Optimization 2007; 3(2):
257-271.
@article{"International Journal of Information, Control and Computer Sciences:60798", author = "P. Beraldi and M. E. Bruni", title = "Data Envelopment Analysis under Uncertainty and Risk", abstract = "Data Envelopment Analysis (DEA) is one of the most
widely used technique for evaluating the relative efficiency of a set
of homogeneous decision making units. Traditionally, it assumes that
input and output variables are known in advance, ignoring the critical
issue of data uncertainty. In this paper, we deal with the problem
of efficiency evaluation under uncertain conditions by adopting the
general framework of the stochastic programming. We assume that
output parameters are represented by discretely distributed random
variables and we propose two different models defined according to a
neutral and risk-averse perspective. The models have been validated
by considering a real case study concerning the evaluation of the
technical efficiency of a sample of individual firms operating in
the Italian leather manufacturing industry. Our findings show the
validity of the proposed approach as ex-ante evaluation technique
by providing the decision maker with useful insights depending on
his risk aversion degree.", keywords = "DEA, Stochastic Programming, Ex-ante evaluation
technique, Conditional Value at Risk.", volume = "6", number = "6", pages = "810-6", }
