Ranking Decision Making Units in Data Envelopment Analysis
by Dr. Manolis N. Kritikos, Assistant Professor at Athens University of Economics and Business.
Data envelopment analysis (DEA) is a widely used non-parametric frontier analysis method for measuring the efficiency of a homogeneous group of decision making units (DMUs) on the basis of multiple inputs and outputs and does not require any subjective or economic parameters (weights, prices, etc). DEA proposed by Charnes et al. (1978) and developed by Banker et al. (1984). In DEA it is not necessary to know the production functions. It seeks to identify top performing units in a particular sector and develop possible ways to improve DMU's performances for those units that are far away from the efficiency frontier. The number of applications of DEA is large covering fields as diverse as finance, health, education, manufacturing, transportation etc. (Dotoli et al. (2015), Kritikos et al. (2010), Kritikos and Ioannou (2010).
The DEA methodology is computationally intensive, requiring the solution of a linear programming problem for each DMU by finding a set of the best weights for every DMU by maximizing its efficiency (Charnes et al., 1978). The efficiency calculated with the DEA method is an overestimation of the real efficiency of each DMU as each DMU can select the best input and output weights through solving the linear programming problem in order to get a higher efficiency.
The conventional data envelopment analysis (DEA) has been universally recognized as a useful tool of performance assessment and assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group of DMUs. However, DEA does not provide more information about efficient DMUs and it has been widely recognized that data envelopment analysis (DEA) lacks discrimination power to distinguish between DEA efficient units (Chen (2004)). To overcome this problem, researchers have presented several approaches for ranking the efficient units (Asghar and Aouni, 2012; Kao and Hung, 2005; Adler et al., 2002).
Kritikos (2017) developed a new methodology for ranking all decision making units in data envelopment analysis (DEA). The new approach seeks a common set of weights using a proposed linear programming model and is based on the TOPSIS approach (Behzadian et al., 2012) in multiple attribute decision making (MADM). Five artificial or dummy decision making units (DMUs) are defined, the ideal DMU (IDMU), the anti-ideal DMU (ADMU), the right ideal DMU (RIDMU), the left anti-ideal DMU (LADMU) and the average DMU (AVDMU). We form two comprehensive indexes for the AVDMU called the Left Relative Closeness (LRC) and the Right Relative Closeness (RRC) with respect to the RIDMU and LADMU. The LRC and RRC indexes are used in the new proposed linear programming model to estimate the common set of weights, the new efficiency of DMUs and finally an overall ranking for all the DMUs.
The results confirm that the proposed methodology has strong correlation with the literature ranking methods while it is much simpler in use and has better discrimination power than the comparable models. The recalculation of the efficiencies of DMUs using the proposed common weights gives efficiencies close to the efficiency score of the DEA (CCR) methodology. The new methodology presents a good average deviation from the ranking methodologies with the best correlations from the others and the best average deviation for the CCR ranking of the inefficient units.
Using the proposed methodology, we can expand the evaluation considering interval, fuzzy or stochastic data and to explore relevant ideas providing more insight into theory and methodology of DEA.
Adler, N., Friedman, L., Sinuany-Stern, Z., 2002. Review of ranking methods in the data envelopment analysis context. European Journal of Operational Research 140, 249-265.
Asghar, F. A., Aouni, B., 2012. New approaches for determining a common set of weights for a voting system. International Transactions in Operational Research, 19, 4, 521-550.
Banker, R.D., Charnes, A., Cooper, W.W., 1984. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 30, 1078-1092.
Behzadian, M., Khanmohammadi Otaghsara, S., Yazdami, M., & Ignatius, J. (2012). A state-of the-art survey of TOPSIS applications. Expert Systems with Applications, 39, 13051-13069.
Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429-444.
Chen, Y., 2004. Ranking efficient units in DEA. Omega 32, 213-219.
Dotoli, M., Epicoco, N., Falagario, M. and Sciancalepore, F., 2015. A stochastic cross-efficiency data envelopment analysis approach for supplier selection under uncertainty. International Transactions in Operational Research, DOI: 10.1111/ itor 12155.
Kao, C., Hung, H.T., 2005. Data envelopment analysis with common weights: The compromise solution approach. Journal of the Operational Research Society 56, 1196-1203.
Kritikos, M.N., 2017. A full ranking methodology in data envelopment analysis based on a set of dummy decision making units, Expert Systems with Applications, 77, 211-225.