Project control that aims to track the project performance and to expedite relevant tasks when necessary has become the main aspect to ensure a successful scheduling outcome. We consider a project crashing problem with task completion due date. To cope with uncertainties lie in the duration time of tasks, we can crash the task with outsourced capacities, which should be reserved during the project planning stage. The total cost, including both capacity reservation cost and crashing cost, should be no more than the project budget. Since meeting with the task due date is a natural target, we focus on minimizing the overall task delay risk and model the objective using the target-based measure of minimizing delay risk index (DRI). We establish an adaptive distributionally robust optimization (ADRO) model for the project crashing problem and translate it into an equivalent mixed integer programming model. We compare the performance of our model against the stochastic approach and the expected makespan minimization model. Our model shows more efficiency and robustness with only mean and support information.

旨在跟踪项目绩效并在必要时加快相关任务的项目控制已成为确保成功调度结果的主要方面。我们考虑到任务完成截止日期导致项目崩溃的问题。为了解决任务的持续时间带来的不确定性，我们可以使用外包的能力来使任务崩溃，这应该在项目计划阶段保留。总成本，包括容量保留成本和崩溃成本，都不应超过项目预算。由于满足任务到期日是很自然的目标，因此我们专注于最大程度地降低总体任务延迟风险，并使用基于目标的最小化延迟风险指数（DRI）的措施对目标进行建模。我们针对项目崩溃问题建立了自适应分布鲁棒优化（ADRO）模型，并将其转换为等效的混合整数规划模型。我们将模型的性能与随机方法和预期的最小跨度最小化模型进行了比较。我们的模型仅借助均值和支持信息即可显示出更高的效率和稳健性。