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

Ruiyue Lin and Yue Liu

Omega, 2019, vol. 85, issue C, 26-34

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.

Keywords: Data envelopment analysis; Super-efficiency; Directional distance function; Infeasibility; Negative data; Variable returns to scale (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

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DOI: 10.1016/j.omega.2018.05.009

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