Title:
A Tchebycheff DEA model

Authors:
1) Gabriel Tavares
2) Carlos Henggeler Antunes

Abstract: 
In this study a new Data Envelopment Analysis (DEA) model is proposed that 
minimizes the Loo (or Tchebycheff) distance of each Decision Making Unit 
(DMU) to the efficient frontier. This model is obtained by using the same 
constraints of the additive model but with a different objective function. 
-This function is based on the LĄ metric and, contrary to the additive 
model, relies on the minimization of the distance of the actual operation 
point to the observed extreme frontier. This last issue is important since 
a better efficiency evaluation can be achieved with this model with respect 
to the additive model. The conditions in which the normal (instead of the 
augmented) Tchebycheff distance could be used to guarantee the attainment 
of efficient solutions are shown. Simple graphical examples (in 2D and 3D) 
are used to illustrate the proposed DEA model.