Path-based DEA models with directions defined using the anti-ideal point
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Sep 21, 2024
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Abstract
Data envelopment analysis (DEA) is a non-parametric technique for relative efficiency evaluation. It formulates models in the form of optimisation problems where the objective function can be interpreted as an efficiency measure and the optimal value is the efficiency score. Path-based DEA models represent a subclass of models where the efficiency score is found by following a parametric path running towards the boundary of the technology set. In this paper, we focus on models where the parametric path is characterised by a direction vector defined using the anti-ideal point. We show that these models possess several desirable properties and are applicable even in the presence of negative data. The results are illustrated with both a simple example and numerical experiments on real environmental data sets from 27 European countries.
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Trnovská, M., Halická, M., & Szolgayová, J.
(2024).
Path-based DEA models with directions defined using the anti-ideal point.
Proceedings Of The Conference Algoritmy, , 159 - 168.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/2166/1037
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References
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[2] R. D. Banker, A. Charnes, and W. W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30 (1984), pp. 1078–1092.
[3] R. G. Chambers, Y. Chung, and R. Färe, Benefit and distance functions, Journal of Economic Theory, 70 (1996), pp. 407–419.
[4] R. G. Chambers, R. Fāure, and S. Grosskopf, Productivity growth in APEC countries, Pacific Economic Review, 1 (1996), pp. 181–190.
[5] J.-P. Chavas and T. L. Cox, A generalized distance function and the analysis of production efficiency, Southern Economic Journal, 66 (1999), pp. 294–318.
[6] R. Färe, S. Grosskopf, and C. A. K. Lovell, The Measurement of Efficiency of Production, Springer Netherlands, 1985.
[7] M. Grant and S. Boyd, Graph implementations for nonsmooth convex programs, in Recent Advances in Learning and Control, V. Blondel, S. Boyd, and H. Kimura, eds., Lecture Notes in Control and Information Sciences, Springer-Verlag Limited, 2008, pp. 95–110. http://stanford.edu/~boyd/graph_dcp.html.
[8] M. Grant, S. Boyd, and Y. Ye, Cvx: Matlab software for disciplined convex programming, version 2.0 beta, 2013.
[9] M. Halická and M. Trnovská, Negative features of hyperbolic and directional distance models for technologies with undesirable outputs, Central European Journal of Operations Research (CEJOR), 26 (2018), pp. 887–907.
[10] M. Halická, M. Trnovská, and A. Černỳ, On indication, strict monotonicity, and efficiency of projections in a general class of path-based data envelopment models, arXiv preprint arXiv:2311.16382, (2023).
[11] M. Halická, M. Trnovská, and A. Černý, A unified approach to radial, hyperbolic, and directional efficiency measurement in data envelopment analysis, European Journal of Operational Research, 312 (2024), pp. 298–314.
[12] K. Kerstens and I. Van de Woestyne, Negative data in dea: a simple proportional distance function approach, Journal of the Operational Research Society, 62 (2011), pp. 1413–1419.
[13] M. C. A. S. Portela, E. Thanassoulis, and G. Simpson, Negative data in DEA: A directional distance approach applied to bank branches, Journal of the Operational Research Society, 55 (2004), pp. 1111–1121.
[14] M. Trnovská and M. Halická, Applying path-based models to negative data with the focus on super-efficiency, (2023). https://www.researchgate.net/publication/375895714_Applying_path-based_models_to_negative_data_with_the_focus_on_super-efficiency.
[15] H. Zhou, Y. Yang, Y. Chen, and J. Zhu, Data envelopment analysis application in sustainability: The origins, development and future directions, European journal of operational research, 264 (2018), pp. 1–16.
[16] P. Zhou, B. W. Ang, and K. L. Poh, A survey of data envelopment analysis in energy and environmental studies, European journal of operational research, 189 (2008), pp. 1–18.