Selective convexity in extended GDEA models

An extension of generalized data envelopment analysis (GDEA) model has been introduced in this paper. In this generalization different cases of production possibility set (PPS) of the extended generalized data envelopment analysis (EGDEA) model are investigated. The proposed EGDEA model evaluates the decision’s making units (DMUs) either with full convexity assumption imposed on inputs and outputs (CCR and BCC models) or without convexity assumption for each input and output (FDH model). We have proposed a model in EGDEA, which can treat each input and output individually with respect to the convexity assumption. The concept of selective convexity in data envelopment analysis (DEA) has been utilized in the proposed EGDEA model.In the following discussion, we assume that there exist n DMUs to be evaluated. Each DMU consumes varying amounts of m different inputs to produce p different outputs. Specifically, DMUj consumes amounts of inputs (i=1,…,m) and produces amounts of outputs (k=1,…,p). for these constants, which generally take the form of observed data, we assume for each (i=1,…,m) and for each k=1,…,p . Further, we assume that there are no duplicated in observed data. The output matrix for the n DMUs is denoted by Y, and the input matrix for the n DMUs denoted by X . and are amounts of inputs and outputs of DMUo , which is evaluated.