Identification of inefficiencies in an additive model based IDEA (imprecise data envelopment analysis)

We employ an additive data envelopment analysis (DEA) model and assume, without loss of generality, all the input-output data are known in the form of arbitrary linear inequalities. This is referred to as an additive imprecise DEA (IDEA) model that involves treating a non-linear programming problem. The non-linear model is then transformed into a linear programming equivalent by methods we present in this paper. To achieve the purpose of this paper which is the identification of specific inefficiencies for the decision making units (DMUs) under consideration, we develop a two-stage method. In the first stage, we obtain an aggregated measure of inefficiencies from solving the linear version of the additive IDEA model. We then retrieve exact data based upon the optimal solutions obtained in the first stage. These exact data retrieved are then used in the next stage which implies that an ordinary additive DEA model is constructed. We can thus obtain the specific inefficiencies in terms of slacks as well as peer groups and scale sizes for every DMU to be considered.