项目间交互作用以及参数不确定性增加了项目组合选择问题的复杂性和求解难度。研究带有不确定项目收益交互和资源交互作用的项目组合选择问题。建立鲁棒性可调节的鲁棒优化模型，通过模型逐步推导，建立与之等价的线性混合整数规划模型。例举一个研发项目的算例，用CPLEX求解并对实验结果进行分析。结果表明，该方法可以灵活地控制最优解的鲁棒性，适用于不同风险偏好的决策者，为项目管理者提供决策支持。
Project portfolio selection (PPS) is one of the most important basic problems in the field of project management. PPS is to select a subset of projects from candidates subject to resource capacity and some other constraints to realize one or more goals. By integrating some features, such as project interactions, parameter uncertainty and multiple objectives.The PSS is more complex and difficult to be solved. In practice, project interaction is influenced by many factors among which the relationships are uncertain and complicated.Consequently, the project interaction is usually with severer uncertainty and its probability distribution is difficult to estimate. Therefore, in this paper, the PSS problem with uncertain project interaction is investigated. At first, without considering uncertainty, the programming model is formulated to maximize the total profits for the PSS with two types of project interactions including profit interaction and resource consumption interaction. Then, the uncertainty of project interactions is taken into consideration. The uncertainty is defined as an interval with nominal value and the half-interval width. Two controller parameters called objective robustness level and constraint robustness level are also defined,which vary in the interval [0, 1].The objective robustness level and constraint robustness level control the robustness of objective function and constraints against the level of conservatism respectively. Based on the definitions of uncertainty as well as robustness level, the general robust optimization model is formulated.To solve the model, its robust counter part as a linear mix integer programming is derived on the basis of optimization theory. A case of R&D project portfolio selection is illustrated and numerous experiments are conducted to investigate the relationship among two robustness levels and the objective. Experiments show that the method can adjust the robustness of solutions, and thus can provide project managers who have different risk preferences with decision support.
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