In this study, we consider coordinated scheduling of the transfer lots in an assembly-type supply chain. An assembly-type supply chain consists of at least two stages, where the upstream stages manufacture the components for several products to be assembled at the downstream stages. In order to enable faster flow of products through the supply chain and to decrease the work-in-process inventory, the concept of lot streaming is used as a means of supply chain coordination. We introduce a mathematical model, which finds the optimal transfer lot sizes in the supply chain. The objective is the minimization of the sum of weighted flow and inventory costs. We develop genetic algorithm (GA) based heuristics to solve the proposed model efficiently. The experimental results show that the proposed GA-based approaches provide acceptable results in reasonable amount of time. We also show that coordination with lot streaming provides improvements in the supply chain performance.