In this article, a production–assembly scheduling problem is presented in three steps. In the first step, the production operation is performed by dedicated parallel machines; in the second step, the assembly operation is performed by the same parallel machines, and in the third step, the post-assembly operation is performed by one machine, and these three steps exist in parallel factories. This problem is NP hard and cannot be solved in a reasonable time by mathematical models. Therefore, a mixed integer linear programming algorithm is presented for small-sized problems, and a new metaheuristic algorithm is presented for large-sized problems, by combining quantum-behaved particle swarm optimization (QPSO), shortest processing time (SPT) and dominance rules, which is called the hybrid QPSOSPT dominance rules (HQSD) algorithm. Accurate parameter adjustment was achieved by analysis of variance. The HQSD algorithm was shown to obtain better results than the other algorithms.
