Mixture problem - linear programming

Heinrich

Dear All, I have a question concerning linear programming in JMP. The problem how I can set up a model for finding the optimum mixture with a constrain. I have let say 5 materials (A, B, C, D, E) for selection and each material has 2 properties. (p1, p2). So I have A(p1,p2), B(p1,p2), … My goal is to find the best mixture (a.A +b.B + c.C + d.D +e.E ) where (a, b, c, d, e) are the amounts of the given materials to match my wanted 2 properties (wp1, wp2). The constraint is now that I only want to use 2 materials for the mixture, or maximum 3 materials. It’s quite easy to solve this problem with Oracle Crystal Ball in Excel via Monte Carlo method, but I couldn’t set up this in JMP. Thank you Heinrich.

cwillden

I have an idea.  Create formula column that counts the number of active componenents for each mixture.  I did one for the Yarn Elongation sample data like this:

If( :Name( "ethylene (x1)" ) == 0,
	0,
	1
) + If( :Name( "styrene (x2)" ) == 0,
	0,
	1
) + If( :Name( "propylene (x3)" ) == 0,
	0,
	1
)

Then, do the optimization in Graph > Profiler.  Include the prediction formula from your model and the formula column you just created in the "Y, Prediction Formula" input.  Set the desirabilities for your functions from the Optimization and Desirability menu.  For the Yarn Elongation data, I  set a desirability function to target 1 active component like this:

In the end, I was able to get this result from the optimization with the constraint of no more than 1 active component:

I attached the data set I used to illustrate with scripts to reproduce these results.

Yarn Elongation.jmp