There are multiple options, much depends on what you want to achieve (Are you going to choose one supplier over the other?, Do you want each supplier to improve their yields independently/simultaneously? How good are your supplier relationships? What is yield and how is it measured? Is this a batch process? If so do you understand within batch and batch to batch variation? etc.). There is not enough information provided to provide specific advice, but here are my initial thoughts:
1. Sampling. Perform a component of variation study with components of measurement system, within supplier and between supplier at a minimum (you could also include within batch and between batch). This has the advantage of assessing the measurement system, consistency within supplier and differences between suppliers. In this case the SPD and TMP are nested within supplier. Perhaps before you start experimentation.
2. It seems unlikely there are only 2 factors affecting yield. What about variation in raw materials, ambient conditions, duration of agitation, duration at temperature, etc.? Perhaps run separate screening experiments with each supplier and then iterate.
3. Run nested experiments where the levels for the factors are nested within supplier. This would not allow for assessing interactions between suppliers, but who cares? I'm not sure you can manage an interaction between suppliers and x's other than optimizing them independently (see option 2).
"All models are wrong, some are useful" G.E.P. Box
