Data Envelopment Analysis with Uncertain Inputs and Outputs

Data envelopment analysis (DEA), as a useful management and decision tool, has been widely used since it was first invented by Charnes et al. in 1978. On the one hand, the DEA models need accurate inputs and outputs data. On the other hand, in many situations, inputs and outputs are volatile and complex so that they are difficult to measure in an accurate way. The conflict leads to the researches of uncertain DEA models. This paper will consider DEA in uncertain environment, thus producing a new model based on uncertain measure. Due to the complexity of the new uncertain DEA model, an equivalent deterministic model is presented. Finally, a numerical example is presented to illustrate the effectiveness of the uncertain DEA model.

[1]  Kai Yao,et al.  A New Option Pricing Model for Stocks in Uncertainty Markets , 2011 .

[2]  William W. CooperKyung IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA , 1999 .

[3]  Tomoe Entani,et al.  Dual models of interval DEA and its extension to interval data , 2002, Eur. J. Oper. Res..

[4]  N. Petersen Data Envelopment Analysis on a Relaxed Set of Assumptions , 1990 .

[5]  Baoding Liu,et al.  Uncertain Multiobjective Programming and Uncertain Goal Programming , 2015 .

[6]  Hong Kam Lo,et al.  An energy-efficient scheduling and speed control approach for metro rail operations , 2014 .

[7]  William W. Cooper,et al.  IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units) , 2001, J. Oper. Res. Soc..

[8]  Gang Yu,et al.  An Illustrative Application of Idea (Imprecise Data Envelopment Analysis) to a Korean Mobile Telecommunication Company , 2001, Oper. Res..

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

[10]  Baoding Liu Uncertain Risk Analysis and Uncertain Reliability Analysis , 2010 .

[11]  X. Chen,et al.  Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optim Decis Making , 2010 .

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

[13]  Shu-Cherng Fang,et al.  Fuzzy data envelopment analysis (DEA): a possibility approach , 2003, Fuzzy Sets Syst..

[14]  R. Banker Maximum likelihood, consistency and data envelopment analysis: a statistical foundation , 1993 .

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

[16]  Andreas Behr Stochastic Data Envelopment Analysis , 2015 .

[17]  Ziyou Gao,et al.  A green train scheduling model and fuzzy multi-objective optimization algorithm , 2013 .

[18]  Chiang Kao,et al.  Fuzzy efficiency measures in data envelopment analysis , 2000, Fuzzy Sets Syst..

[19]  Baoding Liu Extreme value theorems of uncertain process with application to insurance risk model , 2013, Soft Comput..

[20]  Baoding Liu Fuzzy Process, Hybrid Process and Uncertain Process , 2008 .

[21]  Kaoru Tone,et al.  A slacks-based measure of efficiency in data envelopment analysis , 1997, Eur. J. Oper. Res..

[22]  L. Zadeh Fuzzy sets as a basis for a theory of possibility , 1999 .

[23]  Abraham Charnes,et al.  Management Models and Industrial Applications of Linear Programming , 1961 .

[24]  Lawrence M. Seiford,et al.  A DEA Bibliography (1978–1992) , 1994 .

[25]  Byeong-Ho Gong,et al.  Finite sample evidence on the performance of stochastic frontiers and data envelopment analysis using panel data , 1992 .

[26]  S. Grosskopf Statistical inference and nonparametric efficiency: A selective survey , 1996 .

[27]  Baoding Liu Some Research Problems in Uncertainty Theory , 2009 .

[28]  Zhiguo Zeng,et al.  Belief reliability: a new metrics for products’ reliability , 2013, Fuzzy Optim. Decis. Mak..

[29]  Boaz Golany,et al.  Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions , 1985 .

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

[31]  P. W. Wilson,et al.  Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models , 1998 .

[32]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[33]  Peijun Guo,et al.  Fuzzy DEA: a perceptual evaluation method , 2001, Fuzzy Sets Syst..

[34]  Baoding Liu,et al.  Uncertain multilevel programming: Algorithm and applications , 2015, Comput. Ind. Eng..

[35]  Léopold Simar,et al.  Aspects of statistical analysis in DEA-type frontier models , 1996 .

[36]  Yuan Gao,et al.  Connectedness Index of uncertain Graph , 2013, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[37]  Baoding Liu Uncertain Risk Analysis and Uncertain Reliability Analysis , 2010 .

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

[39]  N. Petersen,et al.  Chance constrained efficiency evaluation , 1995 .

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

[41]  X. Chen,et al.  Existence and uniqueness theorem for uncertain differential equations , 2010, Fuzzy Optim. Decis. Mak..

[42]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[43]  Yuhan Liu,et al.  Expected Value of Function of Uncertain Variables , 2010 .

[44]  Jati K. Sengupta,et al.  Efficiency measurement in stochastic input-output systems† , 1982 .