Supplier selection in an outsourcing environment is a challenging task as it depends upon various dimensions. To this effect, the study presents a hybrid approach in which in the first phase, various supplier selection dimensions are identified and the structural relationship among them is modelled by applying interpretive structural modelling (ISM) approach. In phase two, the driver-dependence power of various dimensions is analysed using the MICMAC approach. From the results, it is observed that owing to high dependence power dimensions "Cost," "Quality", and "Service" dimensions are important from the customer's point of view for supplier selection. So, in order to help the managers to address the risk associated with these dimensions, qualitative analysis based on fuzzy set theory has been carried out by considering three potential suppliers. The simulation experiments conducted with different combinations of "Cost," "Quality", and "Service" dimensions show that the supplier selection process is a tedious task and may vary with the organizational needs. The approach proposed in the study can be adopted by the supply chain professionals to address supplier selection problems.