— The group sequence is a well-known proactive-reactive scheduling method that brings sequential flexibility to an initial schedule in order to absorb uncertainties. Hence, group sequence favors the cooperation between human and machine. This method guarantees a minimal quality corresponding to the worst-case. This indicator associated with the best-case schedule provides the decision maker two bounds helping him to choose which operation will be executed first. In this paper, we consider the effect of the group sequence flexibility on the best-case schedule. The experiments made on very well-known instances of the job shop problem, using the makespan objective, brought two new results. The first one is that the best-case schedule of a group sequence is not guaranteed to be an optimal solution for the job shop problem, and the second one is that the more flexibility in a group sequence the better is the quality of the best-case.