Proc Optmodel SAS Maintaining Defined Separation within Group - optimization

Question

I am relatively new to proc optmodel and have been struggling with syntax/structure. I was able to get help once before and am stuck again.
Here is my dataset:
data have;
input NAME $ TEAM $ LEAD GRADE XXX MIN MAX YYY RATE;
cards;
HAL A 1 1 50 45 55 100 1.1
SAL A 0 2 55 0 9999 200 1
KIM A 0 3 70 0 9999 50 1.4
JIM B 1 2 100 90 110 300 .95
GIO B 0 3 120 0 9999 50 1
CAL B 0 4 130 0 9999 20 .9
TOM C 1 1 2 1 5 20 .7
SUE C 0 3 5 0 9999 10 .5
VAL D 1 7 20 15 25 100 .6
WHO D 0 4 10 0 9999 10 .9
;
run;
Here are the specifics:
1. Only the "team lead" has any meaningful constraints.
2. However, the other members of the team will be adjusted accordingly. The value of XXX will be ten percent lower or higher relative to the difference in grade from the team lead. So, if HAL's NEW_XXX is 50 (stays same), then SAL will be 10% higher than HAL's (2 is 1 unit greater than 1) which is 55. KIM's NEW_XXX is 60, since this is twenty percent higher than HAL (3 is 2 units greater than 1. SImilarly, WHO's NEW_XXX will be 30% lower than VAL's.
Does that make sense?
Below is what I have so far, which is the skeleton from a similar project.
proc optmodel;
*set variables and inputs;
set<string>NAME;
string TEAM{NAME};
number LEAD{NAME};
number GRADE{NAME};
number XXX{NAME};
number MIN{NAME};
number MAX{NAME};
number YYY{NAME};
number RATE{NAME};
set TEAMS = setof{i in NAME} TEAM[i];
set NAMEperTEAM{gi in TEAMS} = {i in NAME: TEAM[i] = gi};
var NEW_XXX{i in NAME}>=MIN[i]<=MAX[i];
*read data into procedure;
read data have into
NAME=[NAME]
TEAM
LEAD
GRADE
XXX
MIN
MAX
YYY
RATE;
*state function to optimize;
max metric=sum{gi in TEAMS}
sum{i in NAMEperTEAM[gi]}
(NEW_XXX[i])*(1-(NEW_XXX[i]-XXX[i])*RATE[i]/XXX[i])*YYY[i];
expand;
solve;
*write output dataset;
create data results
from [NAME]={NAME}
TEAM
LEAD
GRADE
XXX
NEW_XXX
MIN
MAX
RATE
YYY;
*write results to window;
print NEW_XXX metric;
quit;

Answer 1

If I understand this correctly, you need set the non-team leads NEW_XXX variable in an equality constraint. That leaves only the team lead NEW_XXX variables free for the optimization.
Let me know if this is what you are trying to accomplish.
Here's how I did it:
proc optmodel;
*set variables and inputs;
set<string> NAME;
string TEAM{NAME};
number LEAD{NAME};
number GRADE{NAME};
number XXX{NAME};
number MIN{NAME};
number MAX{NAME};
number YYY{NAME};
number RATE{NAME};
*read data into procedure;
read data have into
NAME=[NAME]
TEAM
LEAD
GRADE
XXX
MIN
MAX
YYY
RATE;
set TEAMS = setof{i in NAME} TEAM[i];
set NAMEperTEAM{gi in TEAMS} = {i in NAME: TEAM[i] = gi};
/*Helper array that gives me the team leader for each team*/
str LEADS{TEAMS};
for {i in NAME: LEAD[i] = 1} do;
LEADS[TEAM[i]] = i;
end;
var NEW_XXX{i in NAME} init XXX[i] >=MIN[i]<=MAX[i];
*state function to optimize;
max metric=sum{gi in TEAMS}(
sum{i in NAMEperTEAM[gi]} (
(NEW_XXX[i])*(1-(NEW_XXX[i]-XXX[i])*RATE[i]/XXX[i])*YYY[i]
)
);
/*Constrain the non-lead members*/
con NonLeads{i in NAME: LEAD[i] = 0}: NEW_XXX[i] = (1 + (GRADE[i] - GRADE[LEADS[TEAM[i]]]) * 0.1) * NEW_XXX[LEADS[TEAM[i]]] ;
expand;
solve;
*write output dataset;
create data results
from [NAME]={NAME}
TEAM
LEAD
GRADE
XXX
NEW_XXX
MIN
MAX
RATE
YYY;
*write results to window;
print new_xxx metric;
quit;