In this paper, the project portfolio selection problem which considers the divisibility of projects is discussed. In a conventional method, some essential and uncertain variables, such as return, investment and set up cost, are given by estimation of experts due to lack of historical data. To better solve the problem, uncertainty theory is introduced into this study. A mean-variance model is proposed to help decision makers find an optimal portfolio and its time schedule. Specially, the situation where all the uncertain parameters are normal distribution is discussed. For efficient computation, an equivalent mixed integer linear programming representation is proposed. Another mean-variance model without considering the divisibility is also proposed to see the contrast effect of net present value (NPV). At last, a numerical example under above two scenarios is demonstrated and the effect of risk level to the maximum expected NPV is discussed.
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