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A new family of models with generalized orientation in data envelopment analysis

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  • V. J. Bolos
  • R Benitez
  • V. Coll-Serrano

Abstract

In the framework of data envelopment analysis, we review directional models \citep{Chambers1996, Chambers1998, Briec1997} and show that they are inadequate when inputs and outputs are improved simultaneously under constant returns to scale. Conversely, we introduce a new family of quadratically constrained models with generalized orientation and demonstrate that these models overcome this limitation. Furthermore, we extend the Farrell measure of technical efficiency using these new models. Additionally, we prove that the family of generalized oriented models satisfies some desired monotonicity properties. Finally, we show that the new models, although being quadratically constrained, can be solved through linear programs in a fundamental particular case.

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  • V. J. Bolos & R Benitez & V. Coll-Serrano, 2025. "A new family of models with generalized orientation in data envelopment analysis," Papers 2512.02630, arXiv.org.
    • Handle: RePEc:arx:papers:2512.02630
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    References listed on IDEAS

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    1. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
    2. Bolós, V.J. & Benítez, R. & Coll-Serrano, V., 2024. "Chance constrained directional models in stochastic data envelopment analysis," Operations Research Perspectives, Elsevier, vol. 12(C).
    3. Vicente J. Bolós & Rafael Benítez & Vicente Coll-Serrano, 2023. "Continuous models combining slacks-based measures of efficiency and super-efficiency," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(2), pages 363-391, June.
    4. Juan Aparicio & José Ruiz & Inmaculada Sirvent, 2007. "Closest targets and minimum distance to the Pareto-efficient frontier in DEA," Journal of Productivity Analysis, Springer, vol. 28(3), pages 209-218, December.
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    6. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
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