$title Example: Fibonacci example using dynamic sets

option limrow = 0, limcol = 0;

set I / A, B, 1*20 /;
set J(I) /1*20/;

variable x(I), cost;
positive variable x;

equation
	fibonacci(I)
	objective;

* define fibonacci equation only over the set J
fibonacci(J(I))..
	x(I) =e= (x(I-1)+x(I-2));
objective..
	cost =e= sum(I,x(I));

x.fx('A') = 1; x.fx('B') = 1;
model fib /fibonacci, objective/;
solve fib using lp minimizing cost;
display x.l;

* now modify the set J: delete the last two elements.
J('19') = no; J('20') = no;

* after the solve, x('19') and x('20') will be set to their 
* lower bounds of zero, since they are no longer constrained by
* the "fibonacci" constraint. There's no need to change the model -
* by changing J we have changed the definition of the "fibonacci" 
* constraint.

solve fib using lp minimizing cost;
display x.l