A Generalized Multiplicative Directional Distance Function for Efficiency Measurement in DEA

Abstract

For measuring technical efficiency relative to a log-linear technology, a generalized multiplicative directional distance function (GMDDF) is developed using the framework of multiplicative directional distance function (MDDF). Furthermore, a computational procedure is suggested for its estimation. This GMDDF-based measure serves as a comprehensive measure of efficiency in revealing Pareto-efficient targets as it accounts for all possible input and output slacks. This measure satisfies several desirable properties of an ideal efficiency measure such as strong monotonicity, unit invariance, translation invariance, and positive affine transformation invariance. This measure can be easily implemented in any standard DEA software and provides the decision makers with the option of specifying preferable direction vectors for incorporating their decision-making preferences. Finally, to demonstrate the ready applicability of our proposed measure, we conduct an illustrative empirical analysis based on real-life data set of 20 hardware computer companies in India.

Keywords: Data envelopment analysis, Multiplicative directional distance function, Generalized multiplicative directional distance function, Log-convexity, Piece-wise log-linear technology