Imperfect and defective outputs in production process

Data envelopment analysis (DEA) has been proven as an excellent data-oriented effciency analysis method when multiple inputs and outputs are present in a set of decision making units (DMUs). In conventional DEA we assume that the produced outputs are perfect. However in real applications, there are systems which their produced outputs are possibly imperfect and defective. These outputs enter the system as inputs once again and after rebuilding, they will be completed. The present paper proposes a modication of the standard DEA model to incorporate such imperfect outputs. Numerical example is used to demonstrate the approach.