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DEA target setting using lexicographic and endogenous directional distance function approaches

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Abstract

Directional Distance Function (DDF) is an approach often used in data envelopment analysis (DEA) due to its clear interpretation and to the flexibility provided by the possibility of choosing the projection direction towards the efficient frontier. In this paper two new DDF approaches are considered. The first one uses an exogenous directional vector and a multi-stage methodology that at each step uses the projection along the input and output dimensions of the directional vector that can be improved. This lexicographic DDF approach also computes a directional efficiency score and a directional inefficiency indicator for each input and output variable. The second approach is a non-linear optimization model that endogenously determines the directional vector so that the smallest improvement required to reach the efficient frontier is computed.

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Acknowledgements

This research was carried out with the financial support of the Spanish Ministry of Economy, Industry and Competitiveness, DPI2017-85343-P. N.S. acknowledges the support of a grant from the Ministry of Science, Research and Technology of the Islamic Republic of Iran. We would also like to thank the reviewers for their constructive and helpful remarks and suggestions.

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Authors and Affiliations

  1. Department of Industrial Management, University of Seville, Seville, Spain

    Sebastián Lozano

  2. Department of Mathematics, Kharazmi University, Tehran, Iran

    Narges Soltani

Authors
  1. Sebastián Lozano
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  2. Narges Soltani
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Correspondence to Sebastián Lozano.

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The authors declare that they have no conflict of interest.

Appendix

Appendix

Figures 4 and 5

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figure 4

Flowchart of the lexicographic radial approaches of Korhonen et al. (2018) and Coelli (1998)

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Fig. 5
figure 5

Flowchart of the proposed lexicographic DDF approach

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Lozano, S., Soltani, N. DEA target setting using lexicographic and endogenous directional distance function approaches. J Prod Anal 50, 55–70 (2018). https://doi.org/10.1007/s11123-018-0534-x

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