Suppliers ranking in the presence of undesirable outputs

In conventional usage of Data Envelopment Analysis (DEA) for supplier selection, it is assumed that producing more outputs relative to fewer inputs is a criterion of efficiency. However, in the presence of undesirable outputs, suppliers with more good (desirable) outputs and less bad (undesirable) outputs relative to fewer inputs should be recognised as efficient. In addition, to get a complete ranking among suppliers and also eliminate unrealistic weighting schemes among them, this paper proposes a cross-efficiency formulation of DEA, which can treat undesirable outputs. A numerical example demonstrates the application of the proposed model in supplier ranking context.