This paper defines a new distance function in production theory that generalizes several existing efficiency measures. The new distance function is inspired from the Atkinson inequality index and maximizes the generalized sum of netput expansions until an efficient point is reached. Along this line, many measures of technical efficiency are derived from the maximization of a utility function built on the Stone-Geary model. In particular, the directional distance function is expressed from the maximization of a suitable Leontief utility function. A generalized mean duality theorem is proven and a dual correspondence is developed between the generalized directional distance function and the profit function. It is then shown that, for every feasible production vectors, all previous dual correspondences are special cases of this correspondence.