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**Data envelopment analysis with imprecise data.**
*(English)*
Zbl 1030.90055

Summary: In original Data Envelopment Analysis (DEA) models, inputs and outputs are measured by exact values on a ratio scale. W. W. Cooper, K. S. Park, and G. Yu [Manag. Sci. 45, 597-607 (1999)] recently addressed the problem of imprecise data in DEA, in its general form. We develop in this paper an alternative approach for dealing with imprecise data in DEA. Our approach is to transform a nonlinear DEA model to a linear programming equivalent, on the basis of the original data set, by applying transformations only on the variables. Upper and lower bounds for the efficiency scores of the units are then defined as natural outcomes of our formulations. It is our specific formulation that enables us to proceed further in discriminating among the efficient units by means of a post-DEA model and the endurance indices. We then proceed still further in formulating another post-DEA model for determining input thresholds that turn an inefficient unit to an efficient one.

### MSC:

90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |

90C31 | Sensitivity, stability, parametric optimization |

90B50 | Management decision making, including multiple objectives |

### Software:

DEA
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\textit{D. K. Despotis} and \textit{Y. G. Smirlis}, Eur. J. Oper. Res. 140, No. 1, 24--36 (2002; Zbl 1030.90055)

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### References:

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