Step by step search for achievable intermediate targets in zero sum data envelopment analysis

Classic DEA models do not assume any kind of production equilibrium for the whole set of decision-making units (DMUs), i.e., the production of a given DMU does not affect the production of the others. Nevertheless, in some cases, the equilibrium should be addressed. In this paper we propose modifications in the classic DEA BCC model in order to consider that the sum of outputs is constant. The idea behind this approach can be thought of as a zero sum game, in which every player's gains must be lost by one or more players. We present the proposed model, its general formulation and the output proportional reduction strategy. This is a non-linear model, which is solved through theorems that allows the immediate computation of targets and efficiencies, knowing the classic DEA model solution. However, some practical barriers can be found when trying to achieve the computed targets. We also propose a step-by-step search for achievable intermediate targets, which are on the iso-efficiency layers. This search can be done by a sole DMU or by co-operating DMUs.