Supply chain includes all activities associated with the flow and transformation of goods from the raw material stage through to the end user. Supplier selection is one of the most important parts of supply chain management (SCM). For selecting suppliers, data envelopment analysis (DEA), as a multiple criteria decision making tool, has been applied for several times. However, sometimes in supplier selection problem, there may exist some criteria that are beyond the control of a management. These criteria are called non-discretionary or exogenously fixed factors. Since in traditional treatment of non-discretionary inputs in DEA, free reign is given when deciding for each decision making unit (DMU) which outputs and inputs to emphasise, many different avenues are present by which a DMU can appear efficient. Therefore, it is common to have many DMUs that are relatively efficient. In addition, since each DMU has its own set of weights, all of its weight might be put on a single output and input. As a result, the objective of this paper is to propose a cross-efficiency model which is able to consider non-discretionary inputs. A numerical example demonstrates the application of the proposed model in supplier selection context.