A branch-price-and-cut algorithm for multi-mode resource leveling

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 an exact branch-price-and-cut approach together with a new heuristic to optimally or near-optimally solve the more general turnaround scheduling problem. In addition to precedence and resource constraints, also resource 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.