This paper improves algorithms for an assembly-type flowshop scheduling problem in which each job is to assemble two types of components and makespan is the objective measure. For the assembly, one type of the components is outsourced with job-dependent lead time but the other type is fabricated in-house. When both components for a job are prepared, the assembly operation for the job can be started. This problem had been proved to be NP-Complete, so branch-and-bound (B&B) and heuristic algorithms have already been developed. In this paper, we suggest other dominance rules, lowerbound and heutistic algorithms. Also, we develop a new B&B algorithm using these improved bound and dominance rules. The suggested heuristics and B&B algorithm are compared with existing algorithms on randomly-generated test problems.