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Dual structures for the additive DEA model

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  • Chambers, Robert G.

Abstract

We show that the weighted additive DEA score (WA) for the additive DEA model is simultaneously the (dual) support function for a translation of the DEA technology and the gauge of the dual polar set of the translated technology. Those results are used: to show that WA and the indicator function for the translated technology form a dual conjugate pair; to show that WA and the translated technology’s gauge function form a dual polar pair; to develop a simple but exact link between WA and the profit function for the DEA technology; to show that WA and the directional distance function form a dual polar pair; and to develop an exact decomposition of profit inefficiency that extends the Cooper, Pastor, Aparicio, and Borras (2011) and Aparicio et al. (2016) decomposition.

Suggested Citation

  • Chambers, Robert G., 2023. "Dual structures for the additive DEA model," European Journal of Operational Research, Elsevier, vol. 307(2), pages 984-989.
    • Handle: RePEc:eee:ejores:v:307:y:2023:i:2:p:984-989
    DOI: 10.1016/j.ejor.2022.10.026
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    References listed on IDEAS

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    1. Cooper, William W. & Seiford, Lawrence M. & Zhu, Joe, 2000. "A unified additive model approach for evaluating inefficiency and congestion with associated measures in DEA," Socio-Economic Planning Sciences, Elsevier, vol. 34(1), pages 1-25, March.
    2. Aparicio, Juan & Pastor, Jesus T. & Vidal, Fernando, 2016. "The weighted additive distance function," European Journal of Operational Research, Elsevier, vol. 254(1), pages 338-346.
    3. 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.
    4. Bala, Kamel & Cook, Wade D., 2003. "Performance measurement with classification information: an enhanced additive DEA model," Omega, Elsevier, vol. 31(6), pages 439-450, December.
    5. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
    6. Cooper, W.W. & Pastor, Jesus T. & Aparicio, Juan & Borras, Fernando, 2011. "Decomposing profit inefficiency in DEA through the weighted additive model," European Journal of Operational Research, Elsevier, vol. 212(2), pages 411-416, July.
    7. 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.
    8. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
    9. Ang, Sheng & Chen, Chien-Ming, 2016. "Pitfalls of decomposition weights in the additive multi-stage DEA model," Omega, Elsevier, vol. 58(C), pages 139-153.
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