We study a project with stochastic activity durations and cash flows; we model the uncertainty using discrete scenarios. The project entails precedence-related activities, each of which incurs a cash flow that may be positive (inflow) or negative (outflow). The problem is to find a scheduling policy that maximizes the expected net present value of the project. A scheduling policy decides the starting time of each activity under every possible realization of the unknown parameters. Ideally, one wants to expedite the inflows (e.g., incoming payments), while delaying the outflows (e.g., costs) as much as possible, without violating the project deadline. In this article, we devise an exact and a heuristic method to define policies within two new classes of scheduling policies. The first policy class generalizes all existing static policies in the literature and further illustrates the importance of intentional activity delays from both a theoretical as well as an empirical point of view. Whereas the literature on project scheduling has mainly focused on static policies, we also propose a second class of dynamic policies. We show that dynamic policies outperform static policies by means of extensive computational experiments.

中文翻译：

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在不确定性下最大化项目的净现值：活动延迟和动态政策

我们研究一个具有随机活动持续时间和现金流的项目；我们使用离散场景对不确定性进行建模。该项目涉及与优先级相关的活动，每项活动都会产生可能为正（流入）或为负（流出）的现金流。问题是找到一个最大化项目预期净现值的调度策略。调度策略决定在未知参数的每种可能实现下每个活动的开始时间。理想情况下，人们希望加快资金流入（例如，收到的付款），同时尽可能延迟流出（例如，成本），而不违反项目期限。在本文中，我们设计了一种精确的启发式方法来定义两类新的调度策略中的策略。第一类政策概括了文献中所有现有的静态政策，并从理论和实证的角度进一步说明了故意活动延迟的重要性。尽管有关项目调度的文献主要集中于静态策略，但我们还提出了第二类动态策略。我们通过大量的计算实验证明动态策略优于静态策略。