Flow shop scheduling problems with queue time constraints abound in many types of industries. The waiting times between consecutive steps in flow shop production with queue time constraints cannot exceed a given interval. Typically, managers use mixed integer linear programming (MILP) to schedule the process starting times of jobs in a queue. However, as the number of jobs in the system increases, the MILP-based model cannot return an optimal solution within a reasonable time because of its combinatorial nature. This paper proposes a mixed integer programming with Lagrangian relaxation (MIPLAR) method to solve the time-indexed MILP model with a separable structure for the production scheduling problem with queue time constraints. Lagrangian relaxation techniques are used to decompose the problem into job-level subproblems, which are solved by dynamic programming. The subgradient method is used to solve the Lagrangian dual problem. A 4.6-month simulation study demonstrates that the proposed MIPLAR method improves the scrap count by a percentage range from 32.1% to 83.7% across the studied 16 scenarios compared to the first-in-first-out (FIFO) rule while maintaining the same range of the throughput.