Relaxation of the no-idle constraint in the flow-shop problem

The max / / C idle no F − problem is solved by a branch and bound algorithm, or a mixed integer programming solver. This problem is known to be NP-hard. The noidle flow-shop configuration, where machines work continuously without idle intervals is an interesting manufacturing environment in many industries. The idle characteristic is a very strong constraint and it affects seriously the value of makespan ( max C ). Under some circumstances we can authorise some idle periods. But, we should choose the best location that maximises the degradation of the max C and the order on which an idle will be inserted.