This paper introduces a methodology that permits presentation of the results of data envelopment analysis (DEA) graphically. A specialized form of multi-dimensional scaling, Co-Plot, enables presentation of the DEA results in a two-dimensional space, hence in a clear, understandable manner. When plotting ratios rather than original data, DEA efficient units can be visualized clearly, as well as their connections to specific variables and/or ratios. Furthermore, Co-Plot can be used in an exploratory data analysis to identify outliers, whose data require additional scrutiny, and potentially inconsequential variables that could be aggregated or removed from the analysis with little effect on the subsequent DEA results. The Co-Plot diagram of ratios presents super-efficient observations on an outer ring or sector of the plot and all reasonably efficient units on a slightly inner ring/sector, surrounding the remaining inefficient decision-making units. First, the well-known 35 Chinese Cities dataset is provided as an illustration. Second, a simulation study tests the applicability of Co-Plot to present the results of DEA.
Bibliographical noteFunding Information:
The authors would like to thank Ekaterina Yazhemsky and David Talby for excellent research assistance and the Recanati Foundation for partial funding of this work.
- Data envelopment analysis
- Multi-dimensional scaling