We address the two-stage assembly scheduling problem where there are m machines at the first stage and n assembly machines at the second stage under lot sizing environment. Lot streaming (lot sizing) means breaking a lot into some sublots, where each sublot is transferred to the next machine for continuing operations. This problem can be considered as a production system model consisting of production stage and assembly stage. If different production operations are done in parallel machines independently, then the manufactured parts transferred to the next stage are assembled with purchased parts at n machines according to the operation process chart to produce the final products. Here, work-in-process inventories, work shifts, and sequencedependent setup times are also considered as three important presumptions in order to make the problem more realistic. The objective is to minimize the sum of weighted completion times of products in each shift in order to furnish better machine utilization for the next shifts. In recent years, much effort has been made to develop good heuristics and search techniques. We propose a genetic algorithm and simulated annealing to compute the best sequence and scheduling for a two-stage assembly hybrid flow shop problem. Our numerical results demonstrate the effectiveness of the presented model and the proposed solution approach.