Job precedence can often be seen in various manufacturing process scenarios. For instance, in the context of flow shop scheduling, certain jobs must be processed before a specific job may be executed. Formally, this scenario is known as precedence constraint, which influences the optimal job sequence. Because of this practical significance, in this study, a two-machine flow shop scheduling problem in which transportation times, breakdown time, and weighted jobs are considered. In addition to that, an ordered precedence constraint is considered that ensures a successor job cannot start on any machine before its predecessor job has been done on all machines. This is the first study that deals with flow shop scheduling problems with transportation times, breakdown time, job weights, and precedence constraints altogether, to the best of the author’s knowledge. To solve this problem, a simple and efficient solution methodology is developed that assures optimal or near-optimal solutions effectively. The developed algorithm is tested on various test instances and results are reported, which will be useful for future comparative studies.