Under fairly general assumptions requiring neither a differentiable frontier nor a constant-returns-to-scale technology, this paper introduces a new definition of an optimal scale size based on the minimization of unit costs. The corresponding measure, average-cost efficiency, combines scale and allocative efficiency, and generalizes the measurement of scale economies in efficiency analysis while providing a performance criterion which is stricter than both cost efficiency and scale efficiency measurement. The average-cost efficiency is not reliant upon the uniformity of the firms’ input-price vector, and we supply procedures to compute it in both convex and non-convex production technologies. Empirical illustration of the theoretical results is given with reference to large sets of production units. average-cost efficiency constant returns to scale data envelopment analysis decision making unit free disposal hull most productive scale size overall efficiency/cost efficiency optimal scale size technical and scale radial efficiency variable returns to scale 
Average-cost efficiency and optimal scale sizes in non-parametric analysis