Purpose: The purpose of this research is to develop a concurrent supplier selection model to minimize the purchasing cost and fuzzy quality loss considering process capability and assembled product specification. Design/methodology/approach: This research integrates fuzzy quality loss in the model to concurrently solve the decision making in detailed design stage and manufacturing stage. Findings: The resulted model can be used to concurrently select the optimal supplier and determine the tolerance of the components. The model balances the purchasing cost and fuzzy quality loss. Originality/value: An assembled product consists of many components which must be purchased from the suppliers. Fuzzy quality loss is integrated in the supplier selection model to allow the vagueness in final assembly by grouping the assembly into several grades according to the resulted assembly tolerance