The two-machine flow shop problem was shown to be NP-hard when the objective is to minimize total (mean) completion time instead of makespan even for the case where setup times are neglected. This means that it is highly unlikely to find a polynomial algorithm to solve the problem. Therefore, researchers concentrated on developing branch-and-bound or heuristic algorithms. Ali Allahverdi, 1998 obtained the optimal solutions for minimizing mean flow time in a two-machine flow shop with Sequence-independent set up times by using three heuristic algorithms. In this project we addressed the same problem of Ali Allahverdi, based in his model a simulation model was built and validated using Witness software. Experiments were conducted for different number of jobs and different dispatching rules for jobs sequence. The setup-time also varied along the experiments. The effectiveness of the rules used was also measured by two other performance measures beside the mean flow time; they are WIP and machine utilization. The results were analysed and discussed and it concluded that all the performance measures were affected by number of jobs and change of set-up time for all rules used. It found that SPT rule generally performs best in terms of minimizing flow time, minimizing average number of jobs in the system and maximize machine utilization
