Multiplicative Duality Theory in Production Economics

Charnes et al. (1982, 1983) introduced a multiplicative model for efficiency measurement under Data Envelopment Analysis (DEA) framework. Later, Coelli and Peyrach (2009) presented the Multiplicative Directional Distance Function which was recovered by Mehdiloozad et al. (2014) to draw the Generalized Multiplicative Directional Distance Function. In this paper, we propose a general duality framework based upon the so-called Exponential Distance Function endowed with a multiplicative convexity structure. The notion of allocative and overall efficiency are considered from a multiplicative view point. Some non-linear duality results are established. Along this line, a connection to the Cobb-Douglas functional form is proposed