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

In Data Envelopment Analysis, when there are more inputs and outputs, there are more efficient Decision Making Units. Because usually inputs or outputs are correlated, they should be selected appropriately. We propose using principal component analysis as a means of weighting inputs and/or outputs and summarizing them parsimoniously rather than selecting them. In principal components (PCs), many weights for original variables may have negative values. A denominator of the objective function in fractional programming 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.