Uncertain mean-variance model for project portfolio selection problem with divisibility

The project portfolio selection problem considering divisibility is a new research problem rising in recent years. However, two deficiencies are discovered in current divisible project portfolio selection research, one is that researchers always ignore the already started exiting projects when selecting a project portfolio, and the other is that the project parameters are all considered as exact values which are not consistent with practice situation. Under this circumstance, the paper first discusses the dynamic project portfolio selection problem with project divisibility. Meanwhile, due to the lack of correlative historical data, some project parameters are given by experts’ estimates and are treated as uncertain variables. Therefore, a mean-variance mixed integer nonlinear optimal selection model is first developed in this paper to deal with the uncertain dynamic project portfolio selection problem with divisibility. For the convenience of computations, an equivalent mixed integer linear programming representation is proposed. Numerical examples with two scenarios are presented to shed light on the characteristics of the proposed model.