Cost Efficiency Measures with Trapezoidal Fuzzy Numbers in Data Envelopment Analysis Based on Ranking Functions: Application in Insurance Organization and Hospital

Cost efficiency CE evaluates the ability to produce current outputs at minimal cost, given its input prices. In ordinary CE model, the input prices are assumed to be definite. In recent years, various attempts have been made to measuring CE when the input prices are as trapezoidal fuzzy numbers. The main contribution of this paper is to provide a new approach for generalizing the CE of decision making units in data envelopment analysis when the input prices are trapezoidal fuzzy numbers, where concepts of fuzzy linear programming problems and CE, are directly used. Here, the author used the linear ranking functions to compare fuzzy numbers. The proposed method is illustrated with two application examples and proves to be persuasive and acceptable in real world systems.

[1]  K. Ganesan,et al.  Fuzzy linear programs with trapezoidal fuzzy numbers , 2006, Ann. Oper. Res..

[2]  Magnus Tambour,et al.  The Impact of Internal Markets on Health Care Efficiency: Evidence from Health Care Reforms in Sweden , 1999 .

[3]  S. H. Nasseri,et al.  A fuzzy primal simplex algorithm and its application for solving flexible linear programming problems , 2010 .

[4]  Teresa León,et al.  A fuzzy mathematical programming approach to the assessment of efficiency with DEA models , 2003, Fuzzy Sets Syst..

[5]  B. Hollingsworth,et al.  Efficiency measurement of health care: a review of non‐parametric methods and applications , 1999, Health care management science.

[6]  Joe Zhu,et al.  Efficiency evaluation with strong ordinal input and output measures , 2003, Eur. J. Oper. Res..

[7]  Ali Ebrahimnejad,et al.  Bounded Linear Programs with Trapezoidal Fuzzy Numbers , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[9]  Jian-Bo Yang,et al.  Interval efficiency assessment using data envelopment analysis , 2005, Fuzzy Sets Syst..

[10]  A. Mostafaee,et al.  Cost efficiency measures in data envelopment analysis with data uncertainty , 2010, Eur. J. Oper. Res..

[11]  A. Memariani,et al.  Reducing weight flexibility in fuzzy DEA , 2005, Appl. Math. Comput..

[12]  S. H. Nasseri,et al.  A primal-dual method for linear programming problems with fuzzy variables , 2010 .

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

[14]  Nezam Mahdavi-Amiri,et al.  Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables , 2007, Fuzzy Sets Syst..

[15]  Rahmah Mohd Amin,et al.  Measuring efficiency of teaching hospitals in Malaysia , 2011 .

[16]  J. M. Harris,et al.  Do mergers enhance the performance of hospital efficiency? , 2000, J. Oper. Res. Soc..

[17]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

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

[19]  E. Biørn,et al.  The Effect of Activity-Based Financing on Hospital Efficiency: A Panel Data Analysis of DEA Efficiency Scores 1992–2000 , 2003, Health care management science.

[20]  Shawna Grosskopf,et al.  The effects of teaching on hospital productivity , 2001 .

[21]  Nezam Mahdavi-Amiri,et al.  Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems , 2009 .

[22]  Joe Zhu,et al.  Incorporating health outcomes in Pennsylvania hospital efficiency: an additive super-efficiency DEA approach , 2014, Ann. Oper. Res..

[23]  Ali Ebrahimnejad,et al.  A dual simplex method for bounded linear programmes with fuzzy numbers , 2010, Int. J. Math. Oper. Res..

[24]  Baoding Liu Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[25]  Ali Ebrahimnejad,et al.  Using complementary slackness property to solve linear programming with fuzzy parameters , 2009 .

[26]  Minwir Al-Shammari,et al.  A multi‐criteria data envelopment analysis model for measuring the productive efficiency of hospitals , 1999 .

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

[28]  D. Niakas,et al.  Balancing efficiency of health services and equity of access in remote areas in Greece. , 2006, Health policy.

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

[30]  Liam O'Neill,et al.  Multifactor efficiency in Data Envelopment Analysis with an application to urban hospitals , 1998, Health care management science.

[31]  M. Vila,et al.  A general model for fuzzy linear programming , 1989 .

[32]  Shawna Grosskopf,et al.  Competitive effects on teaching hospitals , 2004, Eur. J. Oper. Res..

[33]  Hideo Tanaka,et al.  On Fuzzy-Mathematical Programming , 1973 .

[34]  Mary A. Weiss,et al.  Economies of Scope in Financial Services: A DEA Efficiency Analysis of the US Insurance Industry , 2010 .

[35]  H. B. Valami Cost efficiency with triangular fuzzy number input prices: An application of DEA , 2009 .

[36]  M. Farrell The Measurement of Productive Efficiency , 1957 .

[37]  Dimitris K. Despotis,et al.  Data envelopment analysis with imprecise data , 2002, Eur. J. Oper. Res..

[38]  Lourdes Campos,et al.  Linear programming problems and ranking of fuzzy numbers , 1989 .

[39]  M. Farrell,et al.  THE MEASUREMENT OF PRODUCTIVITY EFFICIENCY , 1957 .

[40]  R. Färe,et al.  The measurement of efficiency of production , 1985 .

[41]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[42]  Chiang Kao,et al.  Interval efficiency measures in data envelopment analysis with imprecise data , 2006, Eur. J. Oper. Res..

[43]  S. Chanas The use of parametric programming in fuzzy linear programming , 1983 .

[44]  Gholam Reza Jahanshahloo,et al.  Efficiency Analysis and Ranking of DMUs with Fuzzy Data , 2002, Fuzzy Optim. Decis. Mak..

[45]  Robert G. Dyson,et al.  A generalisation of the Farrell cost efficiency measure applicable to non-fully competitive settings , 2008 .

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

[47]  James J. Buckley,et al.  Evolutionary algorithm solution to fuzzy problems: Fuzzy linear programming , 2000, Fuzzy Sets Syst..

[48]  Jeffrey P Harrison,et al.  The Improving Efficiency Frontier of Religious Not-for-Profit Hospitals , 2006, Hospital topics.

[49]  H. Zimmermann Fuzzy programming and linear programming with several objective functions , 1978 .

[50]  Mashaallah Mashinchi,et al.  Linear programming with fuzzy variables , 2000, Fuzzy Sets Syst..

[51]  Shujie Yao,et al.  On technical efficiency of China's insurance industry after WTO accession , 2007 .

[52]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[53]  M. Wen,et al.  Fuzzy data envelopment analysis (DEA): Model and ranking method , 2009 .

[54]  Joe Zhu,et al.  Imprecise data envelopment analysis (IDEA): A review and improvement with an application , 2003, Eur. J. Oper. Res..