Resource leveling is a variant of resource-constrained project scheduling in which a non-regular objective function, the resource availability cost, is to be minimized. We present a branch-and-price approach together with a new heuristic to solve the more general turnaround scheduling problem. Besides precedence and resource constraints, also availability periods and multiple modes per job have to be taken into account. Time-indexed mixed integer programming formulations for similar problems quite often fail already on instances with only 30 jobs, depending on the network complexity and the total freedom of arranging jobs. A reason is the typically very weak linear programming relaxation. In particular for larger instances, our approach gives tighter bounds, enabling us to optimally solve instances with 50 multi-mode jobs.
TU Berlin, Institut für Mathematik, Preprint 2010/04