Constrained Optimization with constraints on Sum of Columns conditional on selection of Rows

[thepushkarsingh]

Hi 

For a simplified case, let's assume, I have following data:

id	cost	profit_in_case1	profit_in_case2
A	-1	10	11
B	-0.6	10	5
C	-0.75	10	10.5
D	-0.75	10.5	10

And I have to maximize my profit with decisions,so if I just see the profits as individual rows, I'll have decisions like - 

A - case2, B - case1, C - case2, D-case1.

But I have constraints like, I can only avail costs up to 1.5, so I can't choose A-case2 and B-case1 or A-case2 and C-case2(D-case1), instead I have to choose : C-case2 and D-case1. The final decision for maximum profit will look like:

decision_Cost	decision_profit_case1	decision_profit_case2
1	0	0
1	0	0
0	0	1
0	1	0

This way, we have minimized cost (Total = 1.33) and maximized profit (Total = 21) in the constraints that we can chose only one of the decisions to be 1 and total cost doesn't breach the boundary of 1.5.

My original problem has other constraints as well, but if I can get a solution to this one in PROC IML or PROC OPTMODEL, I think I can build from there. Any help is deeply appreciated. I am using SAS 9.4.

[Ksharp · Accepted solution]

PROC IML 's Genetic Algorithm can do it.

But better use SAS/OR , so post it at OR forum. @RobPratt is there.

[thepushkarsingh]

Hi @Ksharp, can you please help me with the solution in PROC IML? We need a dynamic solution as no one is sure how many constraints, how many columns will be there. There may be many constraints added in each period and I want the code to be reuseable. Kindly suggest.

[Ksharp]

As far as I know, SAS/OR is the best choice . If you are using GA ,that would cost you lots of time. Doesn't @RobPratt  answer your Q, or he is just in busy time .

[thepushkarsingh]

Thanks @Ksharp, @RobPratt answered the question and the solution is great. Many thanks to both of you.