In implementing carbon emission trading schemes (ETSs), the cost of carbon embedded in raw materials further complicates supplier selection and order allocation. Firms have to make decisions by comprehensively considering the cost and the important intangible performance of suppliers. This paper uses an analytic network process–integer programming (ANP–IP) model based on a multiple-criteria decision-making (MCDM) approach to solve the above issues by first evaluating and then optimizing them. The carbon embedded in components, which can be used to reflect the carbon competitiveness of a supplier, is integrated into the ANP–IP model. In addition, an international large-scale electronic equipment manufacturer in China is used to validate the model. Different scenarios involving different carbon prices are designed to analyze whether China’s current ETS drives firms to choose more low-carbon suppliers. The results show that current carbon constraints are not stringent enough to drive firms to select low-carbon suppliers. A more stringent ETS with a higher carbon price could facilitate the creation of a low-carbon supply chain. The analysis of the firm’s total cost and of the total cost composition indicates that the impact of a more stringent ETS on the firm results mainly from indirect costs instead of direct costs. The indirect cost is caused by the suppliers’ transfer of part of the low-carbon investment in the product, and arises from buying carbon permits with high carbon prices. Implications revealed by the model analysis are discussed to provide guidance to suppliers regarding the balance between soft competitiveness and low-carbon production capability and to provide guidance to the firm on how to cooperate with suppliers to achieve a mutually beneficial situation.