  The concept of anchored solutions is proposed as a new robust optimization
approach to the Resource-Constrained Project Scheduling Problem (RCPSP) under
processing times uncertainty. The Anchor-Robust RCPSP is defined, to compute a
baseline schedule with bounded makespan, sequencing decisions, and a max-size
subset of jobs with guaranteed starting times, called anchored set. It is shown
that the Adjustable-Robust RCPSP from the literature fits within the framework
of anchored solutions. The Anchor-Robust RCPSP and the Adjustable-Robust RCPSP
can benefit from each other to find both a worst-case makespan and a baseline
schedule with an anchored set. A dedicated graph model for anchored solutions
is proposed for budgeted uncertainty. Compact MIP reformulations are derived
for both the Adjustable-Robust RCPSP and the Anchor-Robust RCPSP. Dedicated
heuristics are designed based on the graph model. For both problems, the
efficiency of the proposed MIP reformulations and heuristic approaches is
assessed through numerical experiments on benchmark instances.
