In this paper, we will study the permutation flow shop scheduling problem (PFSSP) with sequence independent setup time (SIST). This constraint is the most common encountered in industrial production. In this case, the SIST constraint depends on the technology nature of the machine, as well as the means used to prepare it for the execution of a new job. The purpose of this paper is to develop an artificial intelligence system and to train a neural network model for solving the flow shop scheduling problem. The objective function is to minimize the total completion time, which is known as makespan. The latter is an important task in manufacturing systems. The paper begins by suggesting an exact and four approximate methods: a mixed integer linear programming (MILP), an artificial neural network (ANN), and three efficient heuristics. The first heuristic is based on Johnson’s rule algorithm (ABJR), the second on the Nawaz-Enscore and Ham algorithm (NEH), and the last on the greedy randomized adaptive search procedure algorithm (GRASP). We aim to verify the effectiveness of our resolution algorithms by considering randomly generated instances with n jobs and m machines in the flow shop factory. Our goal is to determine the optimal sequence of n jobs to be scheduled on m machines. The paper moves to the comparison between the studied heuristics. The numerical results demonstrate that the NEH algorithm outperforms the other approximate methods for our considered problem. Indeed, the NEH heuristic performs a success rate of 82.81% and achieves a minimum relative percentage deviation value of 0.0139%. It was observed that ANN method outperforms GRASP and gives sometimes best results than ABJR. The numerical simulations align with our theoretical postulations given by RPD values.