Data envelopment analysis models with limited variable or constant sum

In this work we present two DEA (Data Envelopment Analysis) models in which a new input (or output) is to be fairly assigned to all units (DMUs - Decision Making Units) of a corporation. An interesting characteristic of those proposed models is that the way this distribution is influenced by both inputs and outputs used in each DMU. The models were built in accordance with the geometric shape of CCR frontier and they can be convex or concave, depending on the nature of the variables we intend to share. We show that, under this assumption, it becomes relatively easy the distribution of a new input (or output) among several DMUs, considering that each DMU will receive the new input (or output) fraction in order to become efficient, forcing its position on the specific frontier.