Supplier selection with its proved importance on the successes of the buyer company is given a careful attention in the academic and real world applications. Due to the multiple criteria nature of the supplier selection problem, multiple criteria decision making (MCDM) tools like data envelopment analysis (DEA) are frequently used. However, analysts may face some criteria (e.g., undesirable outputs and dual-role factors) which cannot be modelled in a normal way in DEA. The objective of this paper is to discuss these issues in supplier selection context and consider them in a single model. Moreover, the final supplier selection model of this paper is run with a virtual decision making unit (DMU) which dominate other DMUs. The presence of such a DMU increases discrimination power of the model.