Using Multivariate Methods to Incorporate Environmental Variables for Local and Global Efficiency Performance Analysis

Abstract Enterprises typically referred to as decision making units (DMUs) seldom operate in similar environments. Within a relative performance point of view, if DMUs operating in different environments are compared, the units that operate in less desirable environments are at a disadvantage. In order to ensure that the performance comparison is reasonable within an efficiency measurement approach, a two-stage framework is presented in this research. The first stage uses multivariate methods (robust PCA, fuzzy clustering, and discriminant analysis) to group the DMUs based on the values of the environmental (non-discretionary) variables. The second stage incorporates one of the several efficiency measurement models to carry out relative performance analysis. The concept of local and global frontiers is explored and its significance towards making strategic resource allocation decisions is addressed. The approach proposed in this research is used to evaluate the efficiency performance of Greek municipalities that has been previously analyzed in the literature.

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

[2]  Ali S. Hadi,et al.  Finding Groups in Data: An Introduction to Chster Analysis , 1991 .

[3]  J. Edward Jackson,et al.  A User's Guide to Principal Components. , 1991 .

[4]  H. Kaiser.  The Application of Electronic Computers to Factor Analysis , 1960 .

[5]  Carl J. Huberty,et al.  Applied MANOVA and discriminant analysis , 2006 .

[6]  Rajiv D. Banker,et al.  Efficiency Analysis for Exogenously Fixed Inputs and Outputs , 1986, Oper. Res..

[7]  Konstantinos P. Triantis,et al.  Efficiency Performance and Dominance in Influential Subsets: An Evaluation using Fuzzy Clustering and Pair-wise Dominance , 2004 .

[8]  Konstantinos P. Triantis,et al.  The Identification of Influential Subsets in Regression Using a Fuzzy Clustering Strategy , 1999, Technometrics.

[9]  Peter J. Rousseeuw,et al.  Finding Groups in Data: An Introduction to Cluster Analysis , 1990 .

[10]  H. Kaiser.  The varimax criterion for analytic rotation in factor analysis , 1958 .

[11]  Léopold Simar,et al.  Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach , 2005 .

[12]  Harold O. Fried,et al.  Incorporating the Operating Environment Into a Nonparametric Measure of Technical Efficiency , 1999 .

[13]  Mia Hubert,et al.  ROBPCA: A New Approach to Robust Principal Component Analysis , 2005, Technometrics.

[14]  J. Dunn.  Some Recent Investigations of a New Fuzzy Partitioning Algorithm and its Application to Pattern Classification Problems , 1974 .

[15]  Konstantinos P. Triantis,et al.  Engineering Applications of Data Envelopment Analysis , 2011 .

[16]  Emmanuel Thanassoulis,et al.  Data Envelopment Analysis:the mathematical programming approach to efficiency analysis , 2008 .

[17]  John Ruggiero,et al.  Non-discretionary inputs in data envelopment analysis , 1998, Eur. J. Oper. Res..

[18]  K. Triantis,et al.  A fuzzy clustering approach used in evaluating technical efficiency measures in manufacturing , 1992 .

[19]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[20]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[21]  Tena I. Katsaounis,et al.  Analyzing Multivariate Data , 2004, Technometrics.

[22]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[23]  P. Green,et al.  Analyzing multivariate data , 1978 .

[24]  W. Oates,et al.  THE RISING COST OF LOCAL PUBLIC SERVICES: SOME EVIDENCE AND REFLECTIONS , 1969, National Tax Journal.

[25]  Antreas D. Athanassopoulos,et al.  Assessing Aggregate Cost Efficiency And The Related Policy Implications For Greek Local Municipalities , 1998 .

[26]  John Ruggiero,et al.  On the measurement of technical efficiency in the public sector , 1996 .

[27]  I. Jolliffe.  Principal Component Analysis , 2005 .

[28]  Alexandra Medina-Borja,et al.  Large-scale data envelopment analysis (DEA) implementation: a strategic performance management approach , 2007, J. Oper. Res. Soc..

[29]  Konstantinos P. Triantis,et al.  Engineering Applications of Data Envelopment Analysis: Issues and Opportunities , 2004 .

[30]  P. W. Wilson,et al.  Estimation and inference in two-stage, semi-parametric models of production processes , 2007 .

[31]  Konstantinos P. Triantis,et al.  Performance Measurement of Highway Maintenance Operation Using Data Envelopment Analysis: Environmental Considerations , 2009 .

[32]  Konstantinos P. Triantis,et al.  Evaluating the Productive Efficiency of Dynamical Systems , 2007, IEEE Transactions on Engineering Management.

[33]  A. C. Rencher.  Methods of multivariate analysis , 1995 .

[34]  Harold O. Fried,et al.  The Measurement of Productive Efficiency and Productivity Growth , 2008 .

[35]  Tormod Næs,et al.  The flexibility of fuzzy clustering illustrated by examples , 1999 .

[36]  Michael P. Windham,et al.  Cluster Validity for the Fuzzy c-Means Clustering Algorithrm , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[37]  W. Peizhuang.  Pattern Recognition with Fuzzy Objective Function Algorithms (James C. Bezdek) , 1983 .