Parallel assembly lines are special flow type production systems where two or more neighbouring assembly lines are balanced together. In some industries such as automobile and household appliances industries, neighbouring lines are frequently used. In parallel assembly lines, a setup can be defined as a set of activities to perform a task, such as movements, selecting a new assembly tool and/or taking a position in order to using the most suitable installation procedure. Setups in a workstation on the same line may occur in two ways; forward setup and backward setup. And also, a setup in a workstation on two neighbouring lines may occur. In this study, this is named as line-switching setups. In this paper, the problem of balancing and scheduling tasks in parallel assembly lines with sequence-dependent setup times (PALBPS) is introduced and characterised. A binary linear mathematical programming (BLP) model and a simulated annealing (SA) algorithm are proposed to model and solve the PALBPS. A computational study is performed in order to test the proposed SA algorithm. The computational results show that the proposed algorithm is very effective and successful for the PALBPS.