An extended data envelopment analysis model: Appending an additional input to make all decision making units at least weakly efficient

This paper proposes an extended Data Envelopment Analysis (DEA) model in which an additional input is appended to the original DEA model. For each DMU, the additional input takes the value of (0,1) as close as possible to one under the condition that all efficient DMUs in the original CCR model remain efficient and that all DMUs which are not efficient be at least weakly efficient in the extended CCR model. It is shown that the additional input value of any inefficient DMU is the reciprocal of the radial distance to the boundary of a production possibility set in the original BCC model.