Path-based DEA models and a single-stage approach for finding an efficient benchmark
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Published
Sep 21, 2024
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Abstract
In data envelopment analysis (DEA) each model for efficiency evaluation can be formulated in two forms - the envelopment and the multiplier form that are in a primal-dual relationship. The general class of path-based DEA models, which also includes nonlinear convex models, is formulated in the envelopment form. In general, models of this class do not project onto the strongly efficient frontier, and hence a two-stage procedure is used to find a strongly efficient benchmark for the assessed unit. In this paper, we use the multiplier form of general path-based models to formulate a single-stage optimisation procedure for finding a strongly efficient benchmark. We illustrate the numerical tractability of the proposed approach on an environmental data set of 27 EU countries.
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Hrdina, J., Trnovská, M., & Halická, M.
(2024).
Path-based DEA models and a single-stage approach for finding an efficient benchmark.
Proceedings Of The Conference Algoritmy, , 169 - 178.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/2167/1038
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References
[1] 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.
[2] R. G. Chambers, Y. Chung, and R. Färe, Benefit and distance functions, Journal of Economic Theory, 70 (1996), pp. 407–419.
[3] R. G. Chambers, Y. Chung, and R. Färe, Profit, directional distance functions, and Nerlovian efficiency, Journal of Optimization Theory and Applications, 98 (1998), pp. 351–364.
[4] 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.
[5] R. Färe, S. Grosskopf, and C. A. K. Lovell, The Measurement of Efficiency of Production, Springer Netherlands, 1985.
[6] 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.
[7] M. Grant, S. Boyd, and Y. Ye, Cvx: Matlab software for disciplined convex programming, version 2.0 beta, 2013.
[8] 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.
[9] 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.
[10] P. J. Korhonen and M. Luptacik, Eco-efficiency analysis of power plants: An extension of data envelopment analysis, European journal of operational research, 154 (2004), pp. 437–446.
[11] G. Papaioannou and V. V. Podinovski, A single-stage optimization procedure for data envelopment analysis, European Journal of Operational Research, 313 (2024), pp. 1119–1128.
[12] M. Trnovská, M. Halická, and J. Hrdina, Path-based dea models in multiplier form and returns-to-scale analysis, (2024). https://www.researchgate.net/publication/377273268_Path-based_DEA_models_in_multiplier_form_and_returns-to-scale_ analysis.
[13] 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.
[14] 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.
[2] R. G. Chambers, Y. Chung, and R. Färe, Benefit and distance functions, Journal of Economic Theory, 70 (1996), pp. 407–419.
[3] R. G. Chambers, Y. Chung, and R. Färe, Profit, directional distance functions, and Nerlovian efficiency, Journal of Optimization Theory and Applications, 98 (1998), pp. 351–364.
[4] 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.
[5] R. Färe, S. Grosskopf, and C. A. K. Lovell, The Measurement of Efficiency of Production, Springer Netherlands, 1985.
[6] 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.
[7] M. Grant, S. Boyd, and Y. Ye, Cvx: Matlab software for disciplined convex programming, version 2.0 beta, 2013.
[8] 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.
[9] 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.
[10] P. J. Korhonen and M. Luptacik, Eco-efficiency analysis of power plants: An extension of data envelopment analysis, European journal of operational research, 154 (2004), pp. 437–446.
[11] G. Papaioannou and V. V. Podinovski, A single-stage optimization procedure for data envelopment analysis, European Journal of Operational Research, 313 (2024), pp. 1119–1128.
[12] M. Trnovská, M. Halická, and J. Hrdina, Path-based dea models in multiplier form and returns-to-scale analysis, (2024). https://www.researchgate.net/publication/377273268_Path-based_DEA_models_in_multiplier_form_and_returns-to-scale_ analysis.
[13] 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.
[14] 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.