Standard recommender systems usually rely only on past user ratings as well as optional profiles of customers and products. In e-commerce settings, however, a more complete understanding of the corresponding bi-directional impact between the demands of customers and the supply capabilities of providers can be the key to success. This motivates us to design a recommendation model that explicitly reflects the supply and demand chains. We propose a Multi-relational Coupled Tensor and Matrix Factorization model, which jointly models user ratings as well as supply chain relationships for product recommendation. In addition, our model can predict the links between suppliers and manufacturers. We design an algorithm based on the Alternating Direction Method of Multipliers (ADMM) technique. Experiments on real-world datasets find that the proposed model outperforms traditional methods.