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Purpose This study aims to explore the innovative strategies of business model of the free-to-fee switch, the relationship between the business model innovation and customer knowledge and further develop a conceptual model. Design/methodology/approach This study adopts a multiple case study method with abductive research logic, following the replication logic to select samples. A total of eight outstanding companies with altogether 312 free-to-fee switch events were selected from 1998 to 2021. Findings A strategic matrix with four innovative business models for the free-to-fee switch is generated. The parallelism between the models and customer knowledge orientations is also found. Further, the study develops the conceptual model regarding customer knowledge orientation as a key mediation. Research limitations/implications The study highlights the conceptualization definition of customer knowledge orientation and its mediation effect to the business model innovation of free-to-fee switch, which is a new issue compared with previous research. Furthermore, it reveals that there exists organizational ambidexterity, which brings a new definition of customer knowledge orientation. Practical implications This study suggests how to integrate customer knowledge orientations to support the marketing process of the business model of free-to-fee switch. It also proposes a specific mechanism to conduct the free-to-fee switch with the introduction of four innovative strategic models and eight evolutional paths. Originality/value This study creatively proposes the strategic matrix and the conceptual model of business model innovation of free-to-fee switch. Moreover, a new conceptual definition of customer knowledge orientation is specified.

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Multi-material Topology Optimization is a simulation technique based on the principle of the finite element method which is able to determine the optimal distribution of two or more different materials in combination under thermal and mechanical loads. This paper develops a lightweight topology optimization formulation of multi-material structures considering displacement constraints based on independent, continuous and mapping (ICM) method. Furthermore, explicit expression of optimised formulation is derived, approximations of displacement and weight are given by the first and second order Taylor expansion. And the optimization problem is solved by sequential quadratic programming approach. The feasibility and effectiveness of proposed method are demonstrated by numerical examples. It is found that the best transfer path of load is provided using multi-material topology optimization. The results show that a clear topological structure is obtained and the best transfer path of load is provided after multi-material topology optimization. In addition, under the precondition of satisfying the displacement constraint condition, the weight of the optimized structure based on various materials is lighter. The weight of multi-material topology optimization structure decreases with the increase of displacement constraint. And the optimal topological structure of the multi-material is different with the component materials. Besides, the optimization model established by using the structural performance parameters as a constraint is more reliable and more suitable for practical engineering applications.