SAS - Selecting optimal quantities - sas

Question

I'm trying to solve a problem in SAS where I have quantities of customers across a range of groups, and the quantities I select need to be as even across the different categories as possible. This will be easier to explain with a small table, which is a simplification of a much larger problem I'm trying to solve.
Here is the table:
Customer Category | Revenue band | Churn Band | # Customers
A 1 1 4895
A 1 2 383
A 1 3 222
A 2 1 28
A 2 2 2828
A 2 3 232
B 1 1 4454
B 1 2 545
B 1 3 454
B 2 1 4534
B 2 2 434
B 2 3 454
Suppose I need to select 3000 customers from category A, and 3000 customers from category B. From the second category, within each A and B, I need to select an equal amount from 1 and 2. If possible, I need to select a proportional amount across each 1, 2, and 3 subcategories. Is there an elegant solution to this problem? I'm relatively new to SAS and so far I've investigated OPTMODEL, but the examples are either too simple or too advanced to be much use to me yet.
Edit: I've thought about using survey select. I can use this to select equal sizes across the Revenue Bands 1, 2, and 3. However where I'm lacking customers in the individual churn bands, surveyselect may not select the maximum number of customers available where those numbers are low, and I'm back to manually selecting customers.

Answer 1

There are still some ambiguities in the problem statement, but I hope that the PROC OPTMODEL code below is a good start for you. I tried to add examples of many different features, so that you can toy around with the model and hopefully get closer to what you actually need.
Of the many things you could optimize, I am minimizing the maximum violation from your "If possible" goal, e.g.:
min MaxMismatch = MaxChurnMismatch;
I was able to model your constraints as a Linear Program, which means that it should scale very well. You probably have other constraints you did not mention, but that would probably beyond the scope of this site.
With the data you posted, you can see from the output of the print statements that the optimal penalty corresponds to choosing 1500 customers from A,1,1, where the ideal would be 1736. This is more expensive than ignoring the customers from several groups:
[1] ChooseByCat
A 3000
B 3000
[1] [2] [3] Choose IdealProportion
A 1 1 1500 1736.670
A 1 2 0 135.882
A 1 3 0 78.762
A 2 1 28 9.934
A 2 2 1240 1003.330
A 2 3 232 82.310
B 1 1 1500 1580.210
B 1 2 0 193.358
B 1 3 0 161.072
B 2 1 1500 1608.593
B 2 2 0 153.976
B 2 3 0 161.072
Proportion MaxChurnMisMatch
0.35478 236.67
That is probably not the ideal solution, but figuring how to model exactly your requirements would not be as useful for this site. You can contact me offline if that is relevant.
I've added quotes from your problem statement as comments in the code below.
Have fun!
data custCounts;
input cat $ rev churn n;
datalines;
A 1 1 4895
A 1 2 383
A 1 3 222
A 2 1 28
A 2 2 2828
A 2 3 232
B 1 1 4454
B 1 2 545
B 1 3 454
B 2 1 4534
B 2 2 434
B 2 3 454
;
proc optmodel printlevel = 0;
set CATxREVxCHURN init {} inter {<'A',1,1>};
set CAT = setof{<c,r,ch> in CATxREVxCHURN} c;
num n{CATxREVxCHURN};
read data custCounts into CATxREVxCHURN=[cat rev churn] n;
put n[*]=;
var Choose{<c,r,ch> in CATxREVxCHURN} >= 0 <= n[c,r,ch]
, MaxChurnMisMatch >= 0, Proportion >= 0 <= 1
;
/* From OP:
Suppose I need to select 3000 customers from category A,
and 3000 customers from category B. */
num goal = 3000;
/* See "implicit slice" for the parenthesis notation, i.e. (c) below. */
impvar ChooseByCat{c in CAT} =
sum{<(c),r,ch> in CATxREVxCHURN} Choose[c,r,ch];
con MatchCatGoal{c in CAT}:
ChooseByCat[c] = goal;
/* From OP:
From the second category, within each A and B,
I need to select an equal amount from 1 and 2 */
con MatchRevenueGroupsWithinCat{c in CAT}:
sum{<(c),(1),ch> in CATxREVxCHURN} Choose[c,1,ch]
= sum{<(c),(2),ch> in CATxREVxCHURN} Choose[c,2,ch]
;
/* From OP:
If possible, I need to select a proportional amount
across each 1, 2, and 3 subcategories. */
con MatchBandProportion{<c,r,ch> in CATxREVxCHURN, sign in / 1 -1 /}:
MaxChurnMismatch >= sign * ( Choose[c,r,ch] - Proportion * n[c,r,ch] );
min MaxMismatch = MaxChurnMismatch;
solve;
print ChooseByCat;
impvar IdealProportion{<c,r,ch> in CATxREVxCHURN} = Proportion * n[c,r,ch];
print Choose IdealProportion;
print Proportion MaxChurnMismatch;
quit;