In this paper, three different lower bound models of the no-wait flow-shop scheduling problem (NFSSP) with sequence dependent setup times (SDSTs) and release dates (RDs) are proposed to minimize the makespan time criterion, which is a typical NP-hard combinatorial optimization problem. First, a mixed integer programming model for flow shop scheduling problems is proposed. Secondly, some variables and constraints are relaxed based on the model proposed in this paper. Thirdly, in order to improve the lower bound of this model, a Lagrangian relaxation (LR) model for the flow shop scheduling problem is designed and an improved subgradient algorithm is proposed to solve this problem. The algorithm simulation experiment shows the effectiveness of the algorithm proposed by the article about flow shop scheduling problem and can calculate a tight lower bound.