Prefabrication or off-site construction is a growing trend contributing to productivity improvements. It motivates specialty contractors and suppliers to operate multiple fabrication shops close to market regions, where a shop can produce and delivery prefabricated components in a timely fashion and at a minimal cost. Few quantitative models are available to assist companies with scheduling and allocation questions. This research utilizes optimization to answer these questions supporting the production planning in prefabrication supply chains. The paper presents an optimization model that seeks minimal cost while considering job demands and shop capacities. Computational results suggest that the model generates a lower-cost production schedule than the early due date (EDD) method. It also indicates that varying due dates cause changes in total cost. Moreover, this research supports decision-makers by analyzing the impacts of changing shop capacities regarding available machines. It provides further insight into construction supply chain management with multiple shops.