Lagrangian relaxation and column generation-based lower bounds for the Pm,hj1‖∑wiCiPm,hj1‖∑wiCi scheduling problem

We consider an identical parallel-machine scheduling problem to minimize the sum of weighted completion times of jobs. However, instead of allowing machines to be continuously available as it is generally assumed, we consider that each machine is subject to a deterministic and finite maintenance period. This condition increases the problem complexity. We provide for the problem an adapted heuristic, lower bounds based on Lagrangian relaxation and column generation methods. Computational study shows satisfactory results.