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The question, "How to assign projects to project managers?" is considered to be one of the most important questions in project management. Nevertheless, methods to answer this question have not yet been sufficiently addressed in the literature. In practice, even though the question is rather common, practitioners still seek an effective project assignment methodology - especially, for the assignments of project managers of multiple concurrent projects, such as a project manager of new product development projects in typical high-technology industries. To respond to this question, we performed an inductive study to develop a theoretical framework for project assignments, including some significant assignment criteria and processes. We found that to be effective in project assignments, management should consider strategic elements of the organization in project prioritization, project requirements and competencies of project managers in project manager-to-project matching, and some organizational/personal limitations regarding the assignment. An optimization model was developed to apply this framework. This model can assist in assigning projects to project managers for the better performances of projects, project managers, and the organization.