I need help please I'm still a rookie
I'm working on optimizing an oil decolorization step using a column with three layers of different adsorbents/decolorizing materials.
My optimization problem has two types of variables:
- Mixture variables: the proportions of the three materials/layers.
- Process variables: contact time, agitation speed, contact surface/area, etc.
I also have two constraints:
- Cost ≤ a maximum acceptable value
- Quality ≥ a minimum acceptable value
My initial idea was to split the optimization into two stages:
Use a mixture design to determine the optimal proportions of the three layers.
Then use Response Surface Methodology (RSM) to optimize the process parameters using those proportions.
However, I'm concerned that optimizing the two stages independently could miss the global optimum, because the optimal process parameters may depend on the mixture proportions, and vice versa.
So my question is: What would be the correct experimental design/statistical approach to optimize both the mixture proportions and the process parameters simultaneously, while applying the cost and quality constraints to the final solution?
Would a combined mixture-process design be appropriate here, or is there a better approach?