Bounds for multiprocessor flow shops

We consider a generalization of the flow shop scheduling problem in which, at each production stage, a set of identical machines is available. As finding a schedule of minimum makespan is NP-hard, we set out to find good upper and lower bounds. Good schedules are found by local search techniques, whereas lower bounds are based on relaxation of the capacities of all machines sets except one. The resulting head-body-tail problem is again hard to solve to optimality, but several lower bounds on its optimum solution value have been derived and implemented in a branch-and bound algorithm. We present an experimental comparison of the various upper and lower bounds for the multiprocessor flow shop.