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A multiplier bound approach to assess relative efficiency in DEA without slacks

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  • Ramón, Nuria
  • Ruiz, José L.
  • Sirvent, Inmaculada

Abstract

In this paper, we propose a new approach to deal with the non-zero slacks in data envelopment analysis (DEA) assessments that is based on restricting the multipliers in the dual multiplier formulation of the used DEA model. It guarantees strictly positive weights, which ensures reference points on the Pareto-efficient frontier, and consequently, zero slacks. We follow a two-step procedure which, after specifying some weight bounds, results in an "Assurance Region"-type model that will be used in the assessment of the efficiency. The specification of these bounds is based on a selection criterion among the optimal solutions for the multipliers of the unbounded DEA models that tries to avoid the extreme dissimilarity between the weights that is often found in DEA applications. The models developed do not have infeasibility problems and we do not have problems with the alternate optima in the choice of weights that is made. To use our multiplier bound approach we do not need a priori information about substitutions between inputs and outputs, and it is not required the existence of full dimensional efficient facets on the frontier either, as is the case of other existing approaches that address this problem.

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  • Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2010. "A multiplier bound approach to assess relative efficiency in DEA without slacks," European Journal of Operational Research, Elsevier, vol. 203(1), pages 261-269, May.
  • Handle: RePEc:eee:ejores:v:203:y:2010:i:1:p:261-269
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    3. Dariush Akbarian, 2020. "Avoiding dissimilarity between the weights of the optimal DEA solutions," OPSEARCH, Springer;Operational Research Society of India, vol. 57(2), pages 364-375, June.
    4. Wade D. Cook & Juan Du & Joe Zhu, 2017. "Units invariant DEA when weight restrictions are present: ecological performance of US electricity industry," Annals of Operations Research, Springer, vol. 255(1), pages 323-346, August.
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    6. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2010. "On the choice of weights profiles in cross-efficiency evaluations," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1564-1572, December.
    7. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2011. "Reducing differences between profiles of weights: A "peer-restricted" cross-efficiency evaluation," Omega, Elsevier, vol. 39(6), pages 634-641, December.
    8. Alcaraz, Javier & Aparicio, Juan & Monge, Juan Fco & Ramón, Nuria, 2022. "Weight profiles in cross-efficiency evaluation based on hypervolume maximization," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    9. An, Qingxian & Zhang, Qiaoyu & Tao, Xiangyang, 2023. "Pay-for-performance incentives in benchmarking with quasi S-shaped technology," Omega, Elsevier, vol. 118(C).
    10. Kalinichenko, Olena & Amado, Carla A.F. & Santos, Sérgio P., 2022. "Exploring the potential of Data Envelopment Analysis for enhancing pay-for-performance programme design in primary health care," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1084-1100.
    11. Aparicio, Juan & Monge, Juan F., 2022. "The generalized range adjusted measure in data envelopment analysis: Properties, computational aspects and duality," European Journal of Operational Research, Elsevier, vol. 302(2), pages 621-632.
    12. Ruiz, José L. & Sirvent, Inmaculada, 2012. "On the DEA total weight flexibility and the aggregation in cross-efficiency evaluations," European Journal of Operational Research, Elsevier, vol. 223(3), pages 732-738.

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    Keywords

    DEA AR Non-zero weights Zero-slacks;

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