The chain-reentrant shop with the no-wait constraint

We consider a chain reentrant shop problem with m machines, in which a no-wait constraint is imposed. Each job goes through m machines in a fixed order and return back to the first machine for its last operation. We seek to minimize the overall finish time (makespan). We first proof some new NP-hard problems in the case of two machines. For the resolution of the general problem we propose a genetic algorithm with numerical experiments.