Data Envelopment Analysis Journal > Vol 5 > Issue 2

## Multidimensional Visualization of Data Envelopment Analysis Models

Alexander P. Afanasiev, Institute for Information Transmission Problems of the Russian Academy of Sciences, Russia, apa@iitp.ru , Vladimir E. Krivonozhko, National University of Science and Technology MISiS, Russia, krivonozhkove@mail.ru , Finn R. Førsund, Department of Economics, University of Oslo, Norway, finn.forsund@econ.uio.no , Andrey V. Lychev, National University of Science and Technology MISiS, Russia, lychev@misis.ru

Suggested Citation
Alexander P. Afanasiev, Vladimir E. Krivonozhko, Finn R. FĂ¸rsund and Andrey V. Lychev (2021), "Multidimensional Visualization of Data Envelopment Analysis Models", Data Envelopment Analysis Journal: Vol. 5: No. 2, pp 339-361. http://dx.doi.org/10.1561/103.00000040

Publication Date: 17 Aug 2021
© 2021 A. P. Afanasiev et al.

Subjects

Keywords
Data envelopment analysisproduction possibility setfrontiervisualizationmerger of units

#### Journal details

In this article:
 1 Introduction 2 DEA Background 3 Three-Dimensional Frontier Visualization of the BCC Model 4 Computational Experiments 5 Conclusions References

#### Abstract

Production theory in economics is based on production employing multiple inputs to produce multiple outputs. The boundary of the production possibility set contains the efficient units and is called the frontier production function. The non-parametric data envelopment analysis (DEA) has become an important tool for estimating the frontier production function. The production possibility set in DEA models is a polyhedral set that is a convex combination of extreme points and extreme rays. However, even for a modest number of variables very high numbers of facets may occur. In order to explore properties of frontier functions, visualization is a most helpful tool. An algorithm is developed that starts with an initial vertex, and revise until the final three-dimensional result. The algorithm constructs the sections for a finite number of steps. The performance of the algorithm is tried on data for electric utilities. The consequence of merging units is also analyzed.

DOI:10.1561/103.00000040