Fuzzy project scheduling problem with net present value optimisation under different risk measures
研究了活动工期部分模糊时最大化项目净现值的调度问题，采用VaR和CVaR两种风险度量平衡期望净现值与风险，并开发了两阶段求解方法。
This paper studies the project scheduling with maximising net present value (NPV) of a project when activity durations are partially fuzzy, i.e., the durations of some activities are fuzzy whereas the durations of the rest are deterministic. Naturally, the uncertainties in activity durations may lead to risks in the project management. Ignoring these risks in decision making may result in the inability to achieve project management goals, especially when extreme values of activity durations occur. In this regard, we employ two different risk measures to evaluate the risk of the project’s NPV, including value-at-risk (VaR) and conditional value-at-risk (CVaR). Subsequently, this paper develops two fuzzy programming models with the aim at balancing the expected NPV and the risk of the NPV of the project, namely the expected VaR and expected CVaR models. Two types of two-phase solution approaches are designed simultaneously to efficiently solve the proposed models. Specifically, the analytical procedure of converting the fuzzy models into crisp ones is presented, and then two hybrid intelligent algorithms are successively developed by combining different integration algorithms with a standard heuristic algorithm. Finally, some computational experiments on the data adopted from PSPLIB well demonstrate the effectiveness and efficiency of our treatment.