How do I use summation with limited area? Topic is solved

[duringyear]

Hi there.

I'm dealing with gams syntax, But having trouble with it.

I'd like to use summation function as below.

sum(T, Y(T,D)) = Bd * Cd
but T is from Sd to Sd + Bd -1
where Sd and Bd is paramete.

How can I deal with it?





FYI, explanatory data will be given as below.
1) Formulation

2) GAMS coding

Set
T 'time balocks' /1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12/
D 'demands' /d1, d2, d3/;


Parameter
cars(D) 'How many cars it needs' /d1 3, d2 4, d3 5/
earl(D) 'When is the earliest departure time' /d1 1, d2 3, d3 5/
late(D) 'When is the latest departure time' /d1 3, d2 5, d3 6/
betw(D) 'How long it will occupy' /d1 3, d2 4, d3 2/;

Integer variables
start(D);

Scalar
v 'cars available' /10/;

Binary Variables
x(T,D);

Positive variables
Y(T,D) 'Binary x(T,D) and card(D)';
Y.up(T,D) = cars(D) * x.up(T,D);

Positive variables
mean;

Free variable
obj;

Equations
meanf, objf, demandff, capa, asrA, asrB, asrC, BR;
meanf..
mean =e= sum((T,D), Y(T,D)) / card(t);

objf(t)..
obj =e= sqr(mean - sum(D, Y(T,D))) ;

capa(t)..
sum(D, Y(T,D)) =l= v;

asrA(D)..
start(D) =g= earl(D);

asrB(D)..
start(D) =l= late(D);

asrC(D,T)$(start(D) <= T <= start(D)+betw(D)-1)..
sum(T, Y(T,D)) =e= betw(D)*cars(D);


Model Carpoor /all/;

Solve Carpoor minimizing obj using minlp;






Thank you in advance!

[abhosekar]

Instead of using $ condition on the equation, you can use if condition with the summation.
sum(T$(T ge SD and T le Sd + Bd -1), Y(T,D)) = Bd * Cd

further, since your asrC(D,T), you may have to use alias (t, tt) and use tt inside the summation.

Hope this helps!
- Atharv

[duringyear]

Thank you for your help!