The Anchor-Robust Project Scheduling Problem

In project scheduling, the durations of activities are often uncertain. Delays may cause a massive disorganization if a large number of activities must be rescheduled. In “The Anchor-Robust Project Scheduling Problem,” Bendotti, Chrétienne, Fouilhoux, and Pass-Lanneau propose a novel criterion for solution stability in project scheduling under processing times uncertainty. They define anchored jobs as jobs whose starting times can be guaranteed in a baseline schedule. Finding a project schedule with bounded makespan and a max-weight set of anchors is shown to be an NP-hard robust two-stage problem. Taking advantage of the combinatorial structure of project scheduling and budgeted uncertainty, the authors obtain a compact MIP formulation for the problem. Numerical results show that the obtained MIP outperforms standard techniques from the literature. They also showcase the practical interest of anchored jobs in project scheduling. In project scheduling with uncertain processing times, the decision maker often needs to compute a baseline schedule in advance while guaranteeing that some jobs will not be rescheduled later. Standard robust approaches either produce a schedule with a very large makespan or offer no guarantee on starting times of the jobs. The concept of anchor-robustness is introduced as a middle ground between these approaches. A subset of jobs is said to be anchored if the starting times of its jobs in the baseline schedule can be guaranteed. The Anchor-Robust Project Scheduling Problem (AnchRobPSP) is proposed as a robust two-stage problem to find a baseline schedule of bounded makespan and a max-weight subset of anchored jobs. AnchRobPSP is considered for several uncertainty sets, such as box or budgeted uncertainty sets. Dedicated graph models are presented. In particular, the existence of a compact mixed integer programming reformulation for budgeted uncertainty is proven. AnchRobPSP is shown to be NP-hard even for budgeted uncertainty. Polynomial and pseudopolynomial algorithms are devised for box uncertainty and special cases of budgeted uncertainty. According to numerical results, the proposed approaches solve large-scale instances and outperform classical affine decisions rules for AnchRobPSP. Insights on the price of anchor-robustness are given based on computations.