PCA-DEA reducing the curse of dimensionality

The purpose of this chapter is to present the combined use of principal component analysis (PCA) and data envelopment analysis (DEA) with the stated aim of reducing the curse of dimensionality that occurs in DEA when there is an excessive number of inputs and outputs in relation to the number of decision-making units. Various PCA-DEA formulations are developed in the chapter utilizing the results of principal component analyses to develop objective, assurance region type constraints on the DEA weights. The first set of models applies PCA to grouped data representing similar themes, such as quality or environmental measures. The second set of models, if needed, applies PCA to all inputs and separately to all outputs, thus further strengthening the discrimination power of DEA. A case study of municipal solid waste managements in the Oulu district of Finland, which has been frequently analyzed in the literature, will illustrate the different models and the power of the PCA-DEA formulation. In summary, it is clear that the use of principal components can noticeably improve the strength of DEA models.