Summary form only given. In a flow-shop organisation, all jobs follow the same route (machine sequence) and each job has exactly one operation on each machine. A permutation flow-shop is a flow-shop where all machines process the jobs in the same sequence. An important class of these scheduling problems is constrained by the no-idle production environment, where the machines work continuously without any interruption from the start of the first job processing to the last job completion. We present the F/no-idle/c problem and the different proposed heuristics and exact method. Experiments about a branch and bound algorithm are presented.