Application of principal component analysis for parsimonious summarization of DEA inputs and/or outputs

Abstract

In Data Envelopment Analysis (DEA), when there are more inputs and outputs, there are more efficient Decision Making Units (DMUs). For example, if the specific inputs or outputs advantageous for a particular DMU are used, the DMU will become efficient. Usually the variables used as inputs or outputs are correlated. Therefore, the inputs and outputs should be selected appropriately by experts who know their characteristics very well. People who are less familiar with those characteristics require tools to assist in the selection. We propose using principal component analysis as a means of weighting inputs and/or outputs and summarizing parsimoniously them rather than selecting them. A basic model and its modification are proposed. In principal component analysis, many weights for the variables that define principal components (PCs) have negative values. This may cause a negative integrated input that is a denominator of the objective function in fractional programming. The denominator should be positive. In the basic model, a condition that the denominator must be positive is added. When the number of PCs is less than the number of original variables, a part of original information is neglected. In the modified model, a part of the neglected information is also used.