In this paper we present SS-GNEH, a simulation-based algorithm for the Permutation Flowshop Sequencing Problem (PFSP). Given a PFSP instance, the SSGNEH algorithm incorporates a randomness criterion to the classical NEH heuristic and starts an iterative process in order to obtain a set of alternative solutions, each of which outperforms the NEH algorithm. Thus, a random but oriented local search of the space of solutions is performed, and a list of "good alternative solutions" is obtained. We can then consider several desired properties per solution other than maximum time employed, such as balanced idle times among machines, number of completed jobs at a given target time, etc. This allows the decision-maker to consider multiple solution characteristics other than just those defined by the aprioristic objective function. Therefore, our methodology provides flexibility during the sequence selection process, which may help to improve the scheduling process. Several tests have been performed to discuss the effectiveness of this approach. The results obtained so far are promising enough to encourage further developments on the algorithm and its applications in real-life scenarios