Proc Optmodel - Minimize Mean Absolute Error with two variables

[dsklein12]

Piggy backing off my last post titled, "Proc Optmodel - Minimize Mean Absolute Error". I'm adding another constant to smooth for trend, but need to add in another equation. In the below code, I have two implicit variables, b and forecast, that are used to optimize a and y. When I run the code, I get the follow error: "The symbol 'forecast' is unknown. This occurs on the "impvar b" step. How do I make the two implicit variable equations compatible with each other since they need to be equating simultaneously? Thank you.

data _null_;
if 0 then set example_data2 nobs=n;
call symputx('nrows',n);
stop;
run;
%put &nrows.;

proc optmodel;
set <str,num> MASTER_DATES;
set MASTER = setof {<i,t> in MASTER_DATES}i;
set NROW = setof {<i,t> in MASTER_DATES}t;

num performance {MASTER_DATES};
num month {MASTER_DATES};

read data example_data2 into MASTER_DATES=[master_nbr nrow] performance month;

var a >=0 <=1;
var y >=0 <=1;

impvar b{<i,t> in MASTER_DATES} =
if <i,t-1> in MASTER_DATES then ((forecast[i,t] - forecast[i,t-1])* y) + ((1 - y) * b[i,t-1])
else (performance[i,t+(&nrows.-1)] - performance[i,t]) / (&nrows. - 1);

impvar forecast{<i,t> in MASTER_DATES} =
if <i,t-1> in MASTER_DATES then (performance[i,t]*a) + ((1 - a) * (forecast[i,t-1] + b[i,t-1]))
else performance[i,t];

impvar sae{<i,t> in MASTER_DATES} = abs(performance[i,t] - forecast[i,t]);

impvar ape{<i,t> in MASTER_DATES} =
if <i,t-1> in MASTER_DATES then abs(sae[i,t] / performance[i,t])
else 0;

min mae = (sum {<i,t> in MASTER_DATES} sae[i,t]) / (&nrows. -1);

solve;
print a y;

create data optmodel_outdata2 from a y mae;
create data optmodel_outdata from [master_nbr nrow] performance month b forecast sae ape;
quit;

[RobPratt · Accepted solution]

Because you cannot have circular references between implicit variables, you should instead use explicit variables and constraints in this case, as follows: 

var b{MASTER_DATES};

var forecast{MASTER_DATES};

con b_con{<i,t> in MASTER_DATES}: b[i,t] =
   if <i,t-1> in MASTER_DATES then ((forecast[i,t] - forecast[i,t-1])* y) + ((1 - y) * b[i,t-1])
   else (performance[i,t+(&nrows.-1)] - performance[i,t]) / (&nrows. - 1);
   
con forecast_con{<i,t> in MASTER_DATES}: forecast[i,t] =
   if <i,t-1> in MASTER_DATES then (performance[i,t]*a) + ((1 - a) * (forecast[i,t-1] + b[i,t-1]))
   else performance[i,t];

[dsklein12]

Thanks, Rob. This works great!