In product development, the identification of critical design requirements (DRs) is key to satisfying customer needs because it helps produce more successful products in a shorter time. Quality function deployment (QFD) is a tool used in product development to systematically determine the DRs so as to attain higher customer satisfaction. In the QFD process, the simultaneous optimisation of more than one conflicting objective is generally required. However, it is very difficult for decision makers to determine the goal value of each objective in imprecise and uncertain environments. In order to overcome this problem, the present study proposes a fuzzy mixed-integer goal programming model that determines a combination of optimal DR values. Different from the existing fuzzy goal programming models, the values of the DRs in the proposed model are taken as discrete. Finally, a new Decision Support System is developed. The new system integrates QFD and mathematical programming, enabling the design team to effectively compare product design alternatives and make product development easier and faster. The proposed methodology is illustrated using a real-world application in the Turkish white goods industry.