{"title":"Data Envelopment Analysis under Uncertainty and Risk","authors":"P. Beraldi, M. E. Bruni","volume":66,"journal":"International Journal of Computer and Information Engineering","pagesStart":811,"pagesEnd":817,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/11764","abstract":"Data Envelopment Analysis (DEA) is one of the most\nwidely used technique for evaluating the relative efficiency of a set\nof homogeneous decision making units. Traditionally, it assumes that\ninput and output variables are known in advance, ignoring the critical\nissue of data uncertainty. In this paper, we deal with the problem\nof efficiency evaluation under uncertain conditions by adopting the\ngeneral framework of the stochastic programming. We assume that\noutput parameters are represented by discretely distributed random\nvariables and we propose two different models defined according to a\nneutral and risk-averse perspective. The models have been validated\nby considering a real case study concerning the evaluation of the\ntechnical efficiency of a sample of individual firms operating in\nthe Italian leather manufacturing industry. Our findings show the\nvalidity of the proposed approach as ex-ante evaluation technique\nby providing the decision maker with useful insights depending on\nhis risk aversion degree.","references":"[1] Charnes A, Cooper W W, Rhodes, E. Measuring the efficiency of\ndecision making units. European Journal of Operational Research 1978;\n6: 429-444.\n[2] Paradi J C, Asmild M, Simak P. Using Dea and worst practice DEA in\ncredit risk evaluation. Journal of Productivity Analysis 2004; 21: 153-\n165.\n[3] Premachandra I M, Chen Y, Watson J. Dea as a tool for predicting\ncorporate failure and success: A case of bankruptcy assessment. Omega\n2011; 39: 620-626.\n[4] Charnes A, Cooper W W. Chance constrained programming. Management\nScience 1959; 5(1): 73-79.\n[5] Land K C, Lovell C A K, Thore S. Chance-constrained Data Envelopment\nAnalysis. Managerial and Decision Economics 1993; 14: 541-554.\n[6] Olesen O B, Petersen N C. Chance constrained efficiency evaluation.\nManagement Science 1995; 41: 442-457.\n[7] Olesen O B. Comparing and combining two approaches for chance\nconstrained DEA. Journal of Productivity Analysis 2006; 26(2): 103-\n119.\n[8] Sengupta J K. Data Envelopment Analysis for efficiency measurement\nin the stochastic case. Computers and Operations Research 1987; 14:\n117-129.\n[9] Sengupta J K. Efficiency measurement in stochastic input-output systems.\nInternational Journal of Systems Science 1982; 13: 273-287.\n[10] Sueyoshi T. Stochastic DEA for restructure strategy: an application to a\nJapanese petroleum company. Omega 2000; 28: 385-398.\n[11] Bruni M E, Beraldi P, Conforti D, Tundis E. Probabilistically constrained\nmodels for efficiency and dominance in DEA. International Journal of\nProduction Economics 2009; 117(1): 219-228.\n[12] Ruszczy'nski A, Shapiro A. Stochastic Programming, Handbook in\nOperations Research and Management Science. Elsevier Science, Amsterdam,\n2003.\n[13] Ogryczak W, Ruszczy'nski A. Dual stochastic dominance and related\nmean-risk models. SIAM Journal on Optimization 2002; 13:60-78.\n[14] Markowitz H M. Portfolio selection. Journal of Finance 1952; 7: 77-91.\n[15] Rocafellar R, Uryasev V. Conditional value at risk for general loss\ndistributions. Journal of Banking and Finance 2000; 26:1443-1471.\n[16] Artzner P, Delbaen F, Eber J M, Heath D. Coherent measures of risk.\nMathematical Finance 1999; 9(3): 203-228.\n[17] Shabbir A, Convexity and decomposition of mean-risk stochastic programs.\nMathematical Programming 2006; 106(3): 433-446.\n[18] Notyan N, Ruszczy'nski A. Valid inequalities and restrictions for\nstochastic programming problems with first order stochastic dominance\nconstraints. Mathematical Programming 2008; 114: 433-446.\n[19] Beraldi P, De Simone F, Violi A. Generating scenario trees: a parallel\nintegrated simulation-optimization approach. Journal of Computational\nand Applied Mathematics 2010; 23(9): 2322-2331.\n[20] Beraldi P, Bruni M E. New stochastic programming DEA formulations.\nTechnical Report N. 1 - Laboratory of Financial Engineering 2011;\nUniversity of Calabria, Italy.\n[21] Kaut M, Wallace S. Evaluation of scenario generation methods for\nstochastic programming. Pacific Journal of Optimization 2007; 3(2):\n257-271.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 66, 2012"}