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Cross-efficiency evaluation capable of dealing with negative data: A directional distance function based approach

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  • Ruiyue Lin

Abstract

Cross-efficiency evaluation is a commonly used technique for ranking decision making units (DMUs) in data envelopment analysis while it is just applicable to the non-negative data set. Based on the range directional measure (RDM), we explore the duality relation regarding the maximum slacks formulation of RDM and define cross-efficiencies on the basis of the equivalences with some fractional programming problems. The newly defined cross-efficiency evaluation is under the variable returns to scale condition. It can handle negative values in inputs and outputs well and the resulting cross-efficiencies as well as cross-efficiency scores are between 0 and 1 for all DMUs. It provides self- and peer-evaluations of DMUs by measuring the inefficiency in both inputs and outputs simultaneously. In addition, we propose a corresponding model that implements the benevolent criterion to select weights. A numerical example demonstrates the validity and effectiveness of the proposed cross-efficiency evaluation in dealing with negative data.

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  • Ruiyue Lin, 2020. "Cross-efficiency evaluation capable of dealing with negative data: A directional distance function based approach," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(3), pages 505-516, March.
    • Handle: RePEc:taf:tjorxx:v:71:y:2020:i:3:p:505-516
    DOI: 10.1080/01605682.2019.1567652
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    Cited by:

    1. Radojko LUKIC, 2022. "Measurement and Analysis of the Dynamics of Financial Performance and Efficiency of Trade in Serbia Based on the DEA Super-Radial Model," REVISTA DE MANAGEMENT COMPARAT INTERNATIONAL/REVIEW OF INTERNATIONAL COMPARATIVE MANAGEMENT, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 23(5), pages 630-645, December.
    2. Borrás, Fernando & Ruiz, José L. & Sirvent, Inmaculada, 2023. "Peer evaluation through cross-efficiency based on reference sets," Omega, Elsevier, vol. 114(C).
    3. Radojko LUKIC, 2024. "Economic Performance of the Economy of Kosovo and Metohija," Management and Economics Review, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 9(1), pages 120-137, February.
    4. Sweksha Srivastava & Abha Aggarwal & Pooja Bansal, 2024. "Efficiency Evaluation of Assets and Optimal Portfolio Generation by Cross Efficiency and Cumulative Prospect Theory," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 129-158, January.
    5. Feng Li & Han Wu & Qingyuan Zhu & Liang Liang & Gang Kou, 2021. "Data envelopment analysis cross efficiency evaluation with reciprocal behaviors," Annals of Operations Research, Springer, vol. 302(1), pages 173-210, July.

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