Characteristics of defining hyperplanes of variable returns to scale technology in DEA

Assume that we have DMUs each consuming inputs and producing outputs. Let be an -matrix and be a -matrix consisting of non-negative elements, containing observed input and output measures for the DMUs, respectively. We denote by (the jth column of ) the vector of inputs consumed by DMUj. A similar notation is used for outputs. Since, we are interested in BCC models in this paper, we represent the PPS of variable returns to scale (VRS) technology in the following manner: Based on the PPS of VRS technology the envelopment form of BCC model is in the following manner [BCC]: