The development and assessment of 48 heuristics for the sequence-independent setup time permutation flow shop problem (PFSP-SIST) are presented in this article. This contribution combines four tie-breaking solutions with twelve priority rules for the NEH heuristic fourth and first stage, respectively. Heuristics are evaluated on Ruiz and Allahverdi (2007) benchmark problem instances, that covers small, medium and large-size problems. The popular accelerations of Taillard were used in all tests, which were adapted to the sequence-independent setup time constraint. The aim is to reduce the longest job completion time, which is also referred to as makespan. Computation results show that using different tie-breaking strategies has a greater impact on performance than using different priority rules. The heuristics that presented the best results in relatively low computation time are those that use the FFs tie-breaking strategy procedure to the sequence-independent setup time problem.