We consider a scheduling problem in which N products are processed on M identical parallel machines. Each product comprises two components. Because the components of a product are processed in a fixed order, one is conveniently called as first-component and the other is as second-component. First-components are fabricated in batches, each of which is initiated with a set-up. As for second-components, they are manufactured individually. Two components of a product are restrictedly processed on the same machine. A product is completed when both its two components have been completed and are available. We propose two heuristics to build up near-optimal schedules with respect to minimizing the total completion time of products. The performances of both heuristics are compared with a lower bound. Especially, within the experimental range, one heuristic not only dominates over the other all the time but also is much more timesaving.
