Your model might use variables, objective and constraints
from *multicommodity network flow* models and *blending and
pooling* problems (look these up on Google!).

Modelling network flow can be carried out by flow conservation equations (see the Shortest Path Formulation in Giacomo Nannicini's presentation). If more materials are using the same network (which is your case), we speak of multicommodity flows. Something else that might be relevant is the pooling problem, which we also studied in class (see exercise 7.3 in the exercise book and slides 15-17 in the NLP slides).