Efficiency bounds and efficiency classifications in imprecise DEA: An extension

Abstract

Park proposed a pair of mathematical data envelopment analysis (DEA) models to estimate the lower and upper bound of efficiency scores in the presence of imprecise data. This article illustrates that his approach suffers from some drawbacks: (i) it may convert weak ordinal data into an incorrect set of precise data; (ii) it utilizes various production frontiers to obtain an interval efficiency score for each decision making unit (DMU); (iii) in the absence of exact output data (pure ordinal output data), the approach leads to a meaningless model; (iv) the built model is infeasible with pure ordinal input data; (v) it may include free or unlimited production output which results in unreliable and suspicious results. Moreover, the utilized models by Park involve a positive lower bound (non-Archimedean epsilon) for the weights to deter them from being zero. However, the author ignored the requirement of determining a suitable value for the epsilon. This study constructs two new DEA models with a fixed and unified production frontier (the same constraint set) to compute the upper and lower bounds of efficiency. It is demonstrated that the suggested models can successfully capture the aforementioned shortcomings. Although these models are also epsilon-based, a new model is developed to obtain a suitable epsilon value for the proposed models. It is proved that the suggested approach effectively eliminates all the weaknesses. Additionally, a case study of Iranian Space Agency (ISA) industry is taken as an example to illustrate the superiority of the new approach over the previous ones.

Keywords:

• Data envelopment analysis
• imprecise data
• unified production frontier
• classification
• Iranian Space Agency

Notes

Acknowledgement

The research was supported by the Czech Science Foundation (ČACR 17-23495S).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 A general form of an ordinal data is $x_{\mathit{ij}}\le x_{\mathit{ik}},\mathrm{ }\forall j,k\in J$, nevertheless, for simplifying the presentation we use the notation employed by Zhu (2003).

2 The ordinal data of $x_{p1}\le x_{p2}\le \dots \le x_{\mathit{pn}}$ can be rescaled to ${0\le x}_{p1}^{\mathrm{\prime }}\le x_{p2}^{\mathrm{\prime }}\le \dots \le x_{\mathit{pn}}^{\mathrm{\prime }}=1$ by dividing all data to $x_{\mathit{pn}}(=\max \left\{x_{\mathit{pj}}:j=1,\dots ,n\right\})$ .

3 The $o^{\mathit{th}}$ unit vector having zero components, except for a 1 in the $o^{\mathit{th}}$ position (see Bazaraa, Jarvis, & Sherali (2010) p. 46).

4 $0_{\mathrm{s}}$ is the origin in ${\mathbb{R}}^{\mathrm{s}}$ space, i.e., $0_{\mathrm{s}}=\left(0,\dots ,0\right)\in {\mathbb{R}}^{\mathrm{s}}$.

5 Previously known as Times Higher Education–QS World University Rankings, for more details visit https://en.wikipedia.org/wiki/QS_World_University_Rankings

6 Based on ECSS-M-ST-40C, which is a standard for designing and constructing the satellites.