In the thin-film transistor liquid crystal display (TFT-LCD) manufacturing, the development of models to determine product mix and capacity allocation for a multi-stage, multi-site, and multi-generation company is very important. As rapid advancement of the electronic-paper display (EPD) technology, it is a trend of the coexistence of heterogeneous products involving LCD and EPD products. In the case we investigated, the TFT-LCD company merged an EPD company and incorporated their electro-phoretic technologies into their company. Notably, the manufacturing processes of the EPD products do not incorporate the process steps of liquid crystal injection and attachment of color filters. Consequently, to minimize the total cost, it is essential to decide the appropriate product mix and capacity allocation with considerations of the resource consumption of LCD and EPD products simultaneously. In this paper, we present mathematical models to determine product mix and capacity allocation, which involve three subsystems for TFT-LCD process with consideration of net demand, inventory level, yield rates, cost, margin, outsourcing allocation, cycle time, and panel conversion rate. To demonstrate the applicability of the proposed models, we present a real-world case taken from a TFT-LCD company located in the Science-Based Industrial Park at Hsinchu, Taiwan and perform sensitivity analysis to investigate the effect on the optimal solution.