This paper presents a 0-1 Mixed Integer Programming Model and a heuristic approach based on restricted enumeration and machine grouping for solving k-stage Hybrid Flexible Flow Shop Problems with Sequence-Dependent Setup Times (HFFS_SDST) with Cmax. As presented in this paper in detail, recent reviews show that there is less research on flowshop with SDST than on regular flowshops, although Permutation Flow Shop (PFS) problems is extensively considered in the literature. Mathematical model presented in this work can solve the problems with five stages, eight machines, and six jobs in an acceptable time and this size is relatively bigger than of the ones previously have been solved by mathematical models for defined problems. The heuristic algorithm, based on sub-flow shops via forming machine groups in different clusters, is suggested to give good solutions for large-size problems and can to reach the optimal or near-optimal solutions for some instances and the computational time of the algorithm is shorter than solution time of the mathematical model as expected. In terms of proposed heuristic, to the best of our knowledge, this type of grouping algorithm to form flow shops in the machine environment is not introduced before and provides more efficient solutions by restricting the enumerations. There are no test problems for the problem under consideration. Therefore, real manufacturing environment instances are used. Computational results show that the proposed model and the heuristic algorithm are superior to the current scheduling approach in the company. The heuristic approach also provides a userfriendly environment and efficient scheduling.