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In project scheduling under processing times uncertainty, the Anchor-RobustProject Scheduling Problem is to find a baseline schedule of bounded makespanand a max-weight subset of jobs whose starting times are guaranteed. Theproblem was proven NP-hard even for budgeted uncertainty. In the present workwe design mixed-integer programming (MIP) formulations that are valid for avariety of uncertainty sets encompassing budgeted uncertainty. A new dominanceamong solutions is proposed, resulting into an MIP formulation. We furtherstudy the combinatorial structure of the problem. Non-trivial polynomial casesunder budgeted uncertainty are exhibited, where the dominance-based formulationyields a polyhedral characterization of integer solutions. In more generalcases, the dominance-based formulation is shown to be tighter than allpreviously known formulations. In numerical experiments we investigate how theformulation performs on instances around the polynomial cases, for bothbudgeted uncertainty sets and more elaborate uncertainty sets involving severalbudgets.

Dominance-based linear formulation for the Anchor-Robust Project Scheduling Problem