A Value Efficiency-Based Target Setting Approach in Data Envelopment Analysis

Subject Areas : Statistics

Nasim Nasrabadi ¹

1 - Department of Mathematics-Faculty of Mathematical Science and Statistics-University of Birajnd-Birjand-Iran

Received: 2018-04-11 Accepted : 2018-09-01 Published : 2019-04-01

Keywords: تابع فاصله جهت‌دار, مرز کارای ارزش, واحد الگو, نزدیک‌ترین الگو, ارجحیت,

Abstract :

Basic models of Data Envelopment Analysis are intrinsically preference-free, in the sense that they consider all inputs and outputs and also all decision making units of the same importance. Although this property is beneficial in many ways, it has some drawbacks simultaneously, as the decision makers’ preferences are not taken into account in the process of evaluating units. To overcome this drawback many researchers have developed several techniques for incorporating the preferences into the evaluation model. One of the underlying approaches is value efficiency analysis, which evaluates decision making units by comparing them with the most preferred unit. The most preferred unit is a unit which satisfies the decision maker most. On the other hand, the issue of benchmarking is an important aspect in data envelopment analysis, as it enables the analyst to choose a target for each inefficient unit. The target unit for each unit is located on the efficient frontier and determines the path of improvement for that inefficient unit. In this paper, the issue of target setting based on the concept of value efficiency is investigated. We aim to develop a target setting model which is able to determine target units that are not only efficient but also value efficient, as well. Moreover, the targets are determined based on closest distance from the evaluated unit. Some properties of the model are also discussed. Finally, we perform the proposed model on a real data set of 42 Spanish Universities.

References:

 

[1] M. J. Farrell. The measurement of productive efficiency. Journal of the Royal Statistical Society. Series A (General) 120(3): 253-290 (1957).

 

‎[2] A. Charnes, W. W. Cooper, E. Rhodes. Measuring the efficiency of decision ‎making units. European Journal of Operational Research 2 (6): 429-444‎‏ (1978).

 

[3] R. D. Banker, A. Charnes, W. W. Cooper. Some models for estimating technical ‎and scale inefficiencies in data envelopment analysis, Management Science ‎30 (9): 1078-1092‎‏ (1984).

 

[4] J. Aparicio, J. L. Ruiz, I. Sirvent. Closest targets and minimum distance to the Pareto-efficient frontier in DEA. Journal of Productivity Analysis 28(3): 209-218 (2007).

 

[5] C. Baek, J. D. Lee. The relevance of DEA benchmarking information and the least-distance measure. Mathematical and Computer Modelling 49(1-2): 265-275 (2009).

 

[6] K. Ando, K., A. Kai, Y. Maeda, K. Sekitani. Least distance based inefficiency measures on the Pareto-efficient frontier in DEA. Journal of the Operations Research Society of Japan 55(1): 73-91 (2012).

 

[7] J. L. Ruiz, J. V. Segura, I. Sirvent. Benchmarking and target setting with expert preferences: An application to the evaluation of educational performance of Spanish universities. European Journal of Operational Research 242(2): 594-605 (2015).

 

[8] M. C. A. S., Portela, P. C. Borges, E.  Thanassoulis.  Finding closest targets in non-oriented DEA models: the case of convex and non-convex technologies. Journal of Productivity Analysis 19 (2-3): 251-269 (2003).

 

[9] R. Allen, A. Athanassopoulos, R. G.  Dyson, E. Thanassoulis. Weights restrictions and value judgements in data envelopment analysis: evolution, development and future directions. Annals of operations research 73: 13-34 (1997).

 

[10] V. V. Podinovski, A. D. Athanassopoulos, Assessing the relative efficiency of decision making units using DEA models with weight restrictions. Journal of the Operational Research Society 49(5): 500-508 (1998).

 

[11] M. Halme, T. Joro, P. Korhonen, S. Salo, J. Wallenius. A value efficiency approach to incorporating preference information in data envelopment analysis. Management Science 45(1): 103-115 (1999).

 

[12] P. Korhonen, R. Tainio, J.  Wallenius. Value efficiency analysis of academic research. European Journal of Operational Research 130(1): 121-132 (2001).

 

[13] T. Joro, P. Korhonen. Extension of data envelopment analysis with preference information. Springer 2015.

[14] W. W. Cooper, L. M. Seiford, K. Tone. Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software. Springer 2007.

 

[15] Y. H. Chung, R. Färe, S. Grosskopf. Productivity and undesirable outputs: a directional distance function approach. Journal of Environmental Management 51(3): 229-240 (1997).

 

[16] D. G. Luenberger.  Benefit functions and duality. Journal of mathematical economics 21(5): 461-481 (1992).

 

[17] D. G. Luenberger. Microeconomic theory. McGraw Hill, Boston 1995.

 

[18] R. Färe, S. Grosskopf.  Theory and application of directional distance functions. Journal of productivity analysis 13(2): 93-103 (2000).

 

[19] W. Briec. A graph-type extension of Farrell technical efficiency  measures. Journal of Productivity Analysis 8: 95–111 (1997).

 

[20] W. Briec. Holder distance function and the measurement of technical efficiency. Journal of Productivity Analysis 11: 111–132 (1997).

 

[21] R. Fare, S. Grosskopf. New directions: efficiency and productivity. Kluwer, Boston 2004.

 

[22] N. Adler, N. Volta.  Accounting for externalities and disposability: A directional economic environmental distance function. European Journal of Operational Research 250(1): 314-327 (2016).

 

[23] K. Wang, Y. Xian, C. Y. Lee, Y. M. Wei, Z. Huang. On selecting directions for directional distance functions in a non-parametric framework: A review. Annals of Operations Research. 1-34 (2017).

 

[24] R. Färe, S. Grosskopf. Directional distance functions and slacks-based measures of efficiency. European Journal of Operational Research 200(1): 320-322 (2010).

 

[25] R. Färe, S. Grosskopf. Directional distance functions and slacks-based measures of efficiency: Some clarifications. European Journal of Operational Research 206(3): 702-705 (2010).

 

 [26] R. Färe, S. Grosskopf, G. Whittaker. Directional output distance functions: endogenous directions based on exogenous normalization constraints. Journal of Productivity Analysis 40(3): 267-269 (2013).

 

[27] R. E. Steuer. Multiple criteria optimization: Theory, Computation and Applications Wiley 1986.

 

[28] A. Charnes, W. W. Cooper, J. J. Rousseau,  A. Schinnar. N. E. Terleckyj, D. Levy. A goal-focusing approach to intergenerational transfers of income. International Journal of Systems Sciences 17: 420-440 (1980).

 

[29] E. Zio, R.  Bazzo. A comparison of methods for selecting preferred solutions in multiobjective decision making, In Computational intelligence systems in industrial engineering. Atlantis Press. Paris 2012.

 

[30] J. Park, H. Bae, S. Lim. Stepwise benchmarking path selection in DEA. In Intelligent Decision Technologies. Springer, Berlin, Heidelberg 2012.

 

[31] S. Lozano, G. Villa.  Determining a sequence of targets in DEA. Journal of the Operational Research Society 56(12): 1439-1447 (2005).

 

[6] Miggen Cui, Yingzhen Lin.Nonlinear Numerical Analysis in the Reproducing Kernel Space.Nova Science Publishers, Inc (2008)