Choosing weights in optimal solutions for DEA-BCC models by means of a N-dimensional smooth frontier

Abstract

The DEA (Data Envelopment Analysis) smoothed frontier was introduced to solve the problem of multiple optimal solutions in the extreme efficient DMUs (Decision Making Units), which hinders the knowledge of the substitution rates (tradeoffs). It consists of changing the original frontier (piecewise linear) for a smoothed one, being as close as possible to the original one, and having continuous partial derivates at every point. First, a solution was developed only for the BCC (Banker, Charnes and Cooper) model with either a single input or a single output. Then, it was generalized for the N-dimensional BCC model with simultaneous multiplicity of inputs and outputs, but limited by the fact that the polynomial of the output needs to be a linear one. The present article presents a general model, which not only expunges the limitations of the previous models but also includes them.