Optimal scale sizes in input–output allocative data envelopment analysis models

In production theory, industrial units do business in such a way that they use minimum amount of resources to produce maximum amount of products. So, inefficient units decrease their inputs level and increase their outputs level to meet the efficient frontier. By changing inputs and outputs, achieving an optimal scale size (OSS) in industrial units is one of the most important attempts and has attracted considerable attention among researchers. In this paper, an optimal scale size in input–output allocative DEA model is defined to each production firm in which the costs of inputs and the revenues of outputs are considered. We first rearrange the average-revenue efficiency measure that combines scale and output allocative efficiencies. Next, we simultaneously consider both of inputs and outputs in a new average-cost/revenue efficiency measure (ACRE). It has been shown that the proposed ACRE measure is the ratio of the profitability efficiency to ray average productivity. A numerical heuristic procedure is proposed to calculate a relatively good approximation of the new OSS in a convex and continuous technology set. To illustrate the real applicability of the proposed approach, we use a real case on 39 electricity distribution companies.