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Super-efficiency based on the directional distance function in the presence of negative data

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  • Lin, Ruiyue
  • Liu, Yue

Abstract

The problem of how to construct an appropriate direction for the directional distance function (DDF) based super-efficiency model arises in the data envelopment analysis field. By exploring the relationships between the optimal value of the DDF-based super-efficiency model and directions, this paper provides the conditions satisfied by the directions, with which the DDF-based super-efficiency model is capable of dealing with negative data and generates bounded super-efficiency scores. Based upon these conditions, two types of directions are put forward. No matter whether negative data exist or not, DDF-based super-efficiency models with these directions are feasible and generate bounded super-efficiency scores. They successfully address the infeasibility issue of the conventional radial super-efficiency model under the assumption of variable returns to scale. Super-efficiency models with the proposed directions are monotonous and unit-invariant. More importantly, compared with the current DDF-based super-efficiency model capable of dealing with negative data, the super-efficiency model with one type of direction is translation invariant for both inputs and outputs. Numerical examples demonstrate the validity and practicality of the proposed conditions and directions.

Suggested Citation

  • Lin, Ruiyue & Liu, Yue, 2019. "Super-efficiency based on the directional distance function in the presence of negative data," Omega, Elsevier, vol. 85(C), pages 26-34.
    • Handle: RePEc:eee:jomega:v:85:y:2019:i:c:p:26-34
    DOI: 10.1016/j.omega.2018.05.009
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    10. Kao, Chiang, 2020. "Measuring efficiency in a general production possibility set allowing for negative data," European Journal of Operational Research, Elsevier, vol. 282(3), pages 980-988.

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