Target-based project crashing problem by adaptive distributionally robust optimization

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.