In the resource levelling problem (RLP) under uncertainty, existing studies focus on obtaining an open-loop activity list that is not updated during project execution. In project management practice, it is also necessary to address more situations, such as activity overlaps and resource breakdowns. In this paper, we extend the uncertain RLP by proposing a resource levelling problem with multiple uncertainties (RLP-MU) that simultaneously considers uncertainties in activity durations, activity overlaps and resource availabilities. We formulate the RLP-MU as a Markov decision process model. Aimed at levelling resource usage by dynamically scheduling activities at each decision point based on the observed information, we develop a hybrid open–closed-loop approximate dynamic programming algorithm (HOC-ADP). In the HOC-ADP, we devise a closed-loop rollout policy to approximate the cost-to-go function and use the concept of the average project to avoid time-consuming simulation. A greedy-decoding-based estimation of distributed algorithm is also devised to construct an open-loop policy that is embedded in the HOC-ADP to further improve it. We additionally develop a simulation algorithm to evaluate the resource levelling performance of the HOC-ADP. Computational experiments on a benchmark dataset consisting of 540 problem instances are conducted to analyze the performance of the HOC-ADP, and the impact of various factors on resource levelling are investigated. The comparison experimental results indicate that our HOC-ADP outperforms the state-of-the-art meta-heuristics.

在不确定性下的资源均衡问题（RLP）中，现有研究侧重于获取在项目执行期间不更新的开环活动列表。在项目管理实践中，还需要解决更多的情况，例如活动重叠和资源分解。在本文中，我们通过提出具有多重不确定性的资源均衡问题 (RLP-MU) 来扩展不确定 RLP，该问题同时考虑活动持续时间、活动重叠和资源可用性的不确定性。我们将 RLP-MU 制定为马尔可夫决策过程模型。为了通过基于观察到的信息在每个决策点动态调度活动来均衡资源使用，我们开发了一种混合开闭环近似动态规划算法 (HOC-ADP)。在 HOC-ADP 中，我们设计了一个闭环推出策略来近似成本函数，并使用平均项目的概念来避免耗时的模拟。还设计了一种基于贪婪解码的分布式算法估计，以构建嵌入 HOC-ADP 中的开环策略，以进一步改进它。我们还开发了一种模拟算法来评估 HOC-ADP 的资源均衡性能。在由 540 个问题实例组成的基准数据集上进行了计算实验，以分析 HOC-ADP 的性能，并研究了各种因素对资源均衡的影响。比较实验结果表明，我们的 HOC-ADP 优于最先进的元启发式算法。