Hi @YanivD,
There might be no definitive answer to your question, as both approaches may have benefits and drawbacks. It greatly depends on your goal, the complexity of the model assumed and the experimental budget you have.
As an example, if you want to compare directly and easily these two suppliers, the option to do 2 DoEs is interesting, as you will be able to compare raw values in the experimental space as well as predictions and models parameters. But depending on the mixture model's complexity, this could represent a high experimental cost.
On the other hand, if you want to be able to optimize your mixture depending on the supplier, creating a mixture design with the factor "supplier" might be helpful, as you can take into consideration in the model the interactions between supplier and other mixture factors.
If you want more guidance, you can describe a little more what is your objective, model, constraints... as it may help us figure out which way might be interesting to consider.
I hope this first answer will help you,
Victor GUILLER
L'Oréal Data & Analytics
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)