The problem of constrained sequencing of a set of jobs on a conveyor system with the objective of minimizing setup cost is investigated in this paper. A setup cost is associated with extra material, labor, or energy required due to the change of attributes in consecutive jobs at processing stations. A finite set of attributes is considered in this research. Sequencing is constrained by the availability of conveyor junctions. The problem is motivated by the paint purge reduction problem at a major U.S. automotive manufacturer. We first model a diverging junction with a sequence-independent setup cost and predefined attributes as an assignment problem and this model is then extended for a more general situation by relaxing the initial assumptions in various ways.