信息不确定下的主动打断项目组合选择问题鲁棒优化

在项目组合选择问题中,历史数据的缺乏以及预测和估计过程中出现的不可避免的误差,会导致模型中的参数无法被准确地估计,进而给决策带来巨大的风险.因此,构建合适的鲁棒优化模型,为企业提供能有效应对参数不确定性的鲁棒解,对企业的风险防范具有极其重要的现实意义.本文首先对确定参数下的主动打断项目组合选择问题数学模型的特点进行了分析.进一步地,介绍了鲁棒优化问题中不确定情境集的概念,并给出了允许管理者根据其偏好确定不确定情境集大小的方法,构建了全新的基于情境的鲁棒优化模型,进而计算出在所规定的不确定情境集内的最坏情境下能保持可行性与最优性的鲁棒解,实现了鲁棒性与最优性间的权衡,最后,通过GAMS/BARON进行了算例分析,验证了模型的合理性与有效性.从理论上,本文首次将鲁棒优化理论扩展到了主动打断项目组合选择问题中,针对现有的项目组合选择问题鲁棒优化理论仅能应对有限个可行解的不足之处,提出了一类新的鲁棒优化方法,使其能够应对具有无穷多可行解的主动打断项目组合问题.从实践上,随着我国高新产业的发展,具有超前性与特殊性的研究与发展(RD)、信息科技与信息系统(IT/IS)等新兴项目的投资日益受到重视.相较于传统项目,这类项目的高度不确定性使得探究项目组合选择问题的鲁棒优化理论日益迫切.故而本文的研究具有明显的理论价值和现实意义.

Robust optimization for project portfolio selection problem with divisibility under information uncertainty

In project portfolio selection problem, the uncertainty of parameters can bring high risk to decision making. Thus, it has a great realistic significance to build an appropriate robust optimization model and provide companies with a robust solution, which is able to handle the uncertainty of the parameters. This paper first analyzes the characteristics of the mathematical model of divisible project portfolio selection problem when parameters are certain. Furthermore, the concept of uncertainty set is introduced. Then we provide decision makers with a method which enables them determine the size of uncertainty set based on their preference. A new robust optimization model based on uncertainty set is then formulated, which enables decision makers make a trade-off between robustness and optimality. A robust solution, which is feasible and optimal even in the worst-case of the determined uncertainty set is provided. Finally, we use GAMS/BARON to conduct a numerical example and highlight the capability and characteristics of the proposed model. From the theoretical perspective, this paper first extends the robust optimization theory to the divisible project portfolio selection problem. In view of the problem that the existing robust optimization theory can only handle the project portfolio selection problem with finite feasible solutions, this paper provides a new robust optimization method, which is able to handle the divisible project portfolio selection problem with infinite feasible solutions. From the practical perspective, with the rapid development of high and new technology industries, the investment of newly-developing projects, such as R&D projects and IT/IS projects, has been attached increasing importance. This kind of projects make it become increasingly urgent to explore the new robust optimization theory for project portfolio selection problem owing to their high uncertainty. Thus, this paper has good practical significance for companies to prevent investment risk.