Multidimensional Visualization of Data Envelopment Analysis Models

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.