This paper considers the resource-constrained project scheduling problem with uncertain activity durations. We assume that activity durations lie in a budgeted uncertainty set, and follow a robust two-stage approach, where a decision maker must resolve resource conflicts subject to the problem uncertainty, but can determine activity start times after the uncertain activity durations become known.

We introduce a new reformulation of the second-stage problem, which enables us to derive a compact robust counterpart to the full two-stage adjustable robust optimisation problem. Computational experiments show that this compact robust counterpart can be solved using standard optimisation software significantly faster than the current state-of-the-art algorithm for solving this problem, reaching optimality for almost 50% more instances on the same benchmark set.

本文考虑了活动持续时间不确定的资源受限项目调度问题。我们假设活动持续时间在预算的不确定性集中，并采用可靠的两阶段方法，决策者必须解决问题不确定性下的资源冲突，但可以在不确定活动持续时间已知后确定活动开始时间。

我们引入了第二阶段问题的新公式，这使我们能够导出完整的两阶段可调鲁棒优化问题的紧凑鲁棒对应项。计算实验表明，使用紧凑型坚固耐用的同类产品，可以使用标准优化软件来解决该问题，其速度明显快于解决该问题的最新技术，并在同一基准集上实现了近50％的实例最优。