5. Conclusions
We introduced a new methodology based on the product-mix problem to assess the production performance of firms, which is related to the well-known Data Envelopment Analysis approach, thereby complementing its results with information about the value of technical coefficients. As in DEA the new approach assumes a common technology, offering novel analytical possibilities to researchers interested in this field by introducing the ability of performing efficiency evaluation. An outstanding feature of the new approach is, therefore, the possibility of estimating the technical coefficients in the evaluation process, thereby determining the underlying relationship between each pair of inputs and outputs. The new approach can be readily implemented as it departs from the product-mix problem used by process engineers in many industrial and primary sectors, particularly manufacturing and agriculture. The derived piece-wise linear output production set, based on the Tshebishev metric, is compared with the Directional Distance Function in the context of Data Envelopment Analysis. As a result of this comparison we prove that the new approach yields a production possibility set representing an outer approximation of that corresponding to DEA (vice versa, DEA is an inner approximation of the former), which extends to their efficient subsets.
