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Abstract According to the concept of physical integration as understood in axiomatic design, design parameters of a product should be integrated into a single physical part or a few parts with the aim of reducing the information content, while still satisfying the independence of functional requirement. However, no specific method is suggested in the literature for determining the optimal degree of physical integration in a given design. This is particularly important with the current advancement in technologies such as additive manufacturing. As new manufacturing technologies allow physical elements to be integrated in new ways, new methods are needed to help designers optimize physical integration given the specific constraints and conflicts of each design. This study proposes an algorithm that uses graph partitioning to allow a designer to optimize the integration of functional requirements into a target number of parts, with the goal of minimizing the co-allocation of incompatible functional requirements in the same part. The operation and viability of the algorithm are demonstrated via two numerical examples and a practical example of designing a pencil. 

Digitization, connected networks, embedded software, and smart devices have resulted in a major paradigm shift in business models. Transformative service-based business models are dominating the market, where advancement in technology has paved the way for offering not only a set of new services but also altering product functionalities and services over time. This paradigm shift calls for new design approaches. Designers should be able to design flexible products and services that can adapt to a wide range of consumer needs over time. To address the need for designing for flexibility, the objective of this study is to develop a graph coloring technique that can model changes in the functional requirements of a product and determine the minimum number of physical parts needed to meet future functionalities. This technique relies on vertex labeling by the designer and the construction of a core graph combining key elements of all desired iterations, which is then colored by label. One numerical example and one real-world example are provided to show the application of the proposed model.