In the general flow shop model, it is assumed that the buffers have unlimited capacity. However, in many real flow shop environments, the buffers have zero capacity that the related problem is known as the blocking flow shop scheduling problem (BFSP). In recent years, the BFSP has attracted much attention among researchers. But most of the studies are done for makespan criteria and studies about the other criteria are scarce. In this study we developed some exact and inexact methods for solving the BFSP with total completion time criteria. To the best of our knowledge, no exact method has been presented for the considered problem, so far. So first, we proposed two mixed binary integer programming models, one based on departure time of the jobs from each machine and another based on idle and blocking times of the jobs on each machine. After this, for presenting a more powerful exact method for the considered problem, we suggested a branch and bound algorithm. The suggested lower bounds have been developed based on the considered problem characteristics and its graph for a specific sequence. Also, the proposed procedures enjoy novel ideas and increase the branch and bound strength very much. The proposed branch and bound algorithm succeeded in solving 17 instances of the first two groups of Taillard benchmark instances, considering 3600 second time limit. After developing the mentioned exact methods, we proposed an improved iterated greedy (IG) algorithm for obtaining efficient solutions for the large sized problems. This algorithm showed much more efficiency than the only last proposed metaheuristic. Finally, we tried to present some new rules for the two machine case of the considered problem. So, first we showed how to obtain the optimal solution of two special cases of this problem. Then, we proposed a branch and bound algorithm for solving the mentioned problem. For this algorithm, we developed a heuristic using IG algorithm idea for obtaining an initial upper bound. We also developed one new efficient lower bound and three procedures for fathoming the nodes. The suggested branch and bound succeeded in solving 75% of the problems up to 30 jobs, considering 3600 time limit.