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In the current study, a model is proposed to evaluate the performance of these types of general two-stage network structures. To this end, we provide a linear model using fractional programming. In fact, previous models were often nonlinear models which were solved with heuristic methods. But, since the model presented in this paper is a linear model, then it can be solved easily as a linear programming problem. In order to clarify the newly proposed approach of this study, it has been applied to a case of regional Research and Development (R&amp;D) system related to 30 provincial level regions in China and results have been compared with the heuristic method of Li et al. 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