This research study proposes a method to resolve issues with trade-offs between functionalities, which hinder the unconventional improvement of a product. As products have become increasingly complex, it has become difficult to grasp all the aspects of a product. To resolve the problematic trade-off issues of a complex product, it is necessary to model the product in an appropriate form and to gather knowledge from experts in each domain. Although there have been several models to tackle this issue, modeling still poses difficulties due to a lack of clear guidelines. This paper classifies models into three types: function-based, cognition-based, and physics-based models. Next, their roles and description guidelines are clarified. As a function-based model depicts the functionality of a product in a rather simple description, it is employed to specify significant trade-offs. A cognition-based model depicts the designers' recognition of physical phenomena, whereas a physics-based model rigorously depicts the physical phenomena. A cognition-based model is appropriate for ideation, while the physics-based model contributes to the objectivity of a model. This study proposes a strategy of complementary modeling and the use of cognition-and physics-based models. To support the ideation of a solution to the trade-offs, the theory of inventive problem solving (TRIZ) is applied. The proposed method is validated by a case study of continuously variable transmissions (CVT).