A new mathematical model for the efficiency calculation

Abstract

During the past sixty years, a lot of effort has been made regarding the productive efficiency. Such endeavours provided an extensive bibliography on this subject, culminating in two main methods, named the Stochastic Frontier Analysis (parametric) and Data Envelopment Analysis (non-parametric). The literature states this methodology also as the benchmark approach, since the techniques compare the sample upon a chosen “more-efficient” reference. This article intends to disrupt such premise, suggesting a mathematical model that relies on the optimal input combination, provided by a differential equation system instead of an observable sample. A numerical example is given, illustrating the application of our model’s features.