Simple Optimization Analysis

[grodman]

Hello - 

I'm producing an analysis in which I have to find the different combination of sample pools that will result in the most total subjects to available to study.  However, there are rules which govern how many subsets from each group I may take.  

For example... using the sample data below, I need to find the 5 combinations that will result in the most total people.  However, each combination must consist of hte following:

• 1 subset from group A
• 2 subsets from group B
• 1 subset from group C

Is there a quick procedure/method to find this?

Note - in my real dataset, there are hundreds of subsets within each group.

Thanks!

data samples;
input group $ people;
datalines;
A 61
A 32
A 30
B 35
B 21
B 11
B 12
B 70
B 52
B 48
B 65
B 57
B 51
C 18
C 56
C 28
C 45
;;;;
run;

[PGStats]

Simply take the n highest from each group?

data samples;
input group $ people;
subset = _n_; /* unique subset number */
datalines;
A 61
A 32
A 30
B 35
B 21
B 11
B 12
B 70
B 52
B 48
B 65
B 57
B 51
C 18
C 56
C 28
C 45
;

data alloc;
input group $ subsets;
datalines;
A 1
B 2
C 1
;

proc sort data=samples; by group descending people;

data want;
merge alloc samples; by group;
if first.group then order = 0;
order + 1;
if order <= subsets then output;
drop order subsets;
run;

proc print data=want noobs; run;