Solving equations iteratively (faster) in GAMS

Problems with modeling
Post Reply
jonathanl91
User
User
Posts: 5
Joined: 4 months ago

Solving equations iteratively (faster) in GAMS

Post by jonathanl91 » 1 month ago

I am doing a Gravity model in GAMS to estimate the trade between countries. That is, I want to do the following equation:

Image

Where A_i^m and B_j^m are unknown. They are calculated in the following way:

Image

That is, they should be solved iteratively. I am doing that in GAMS using loops.

Consider the following data:

Code: Select all

   set I "Iteration"       / I01 * I100 /
        C "Commodity"       / C01 /
        A "Export country"  / USA,Japan,Germany /
        D "Import country"  / USA,Japan,Germany /
        T "Time"            / 2018,2019 /;
        
    parameters
        tc(A,D,C) "Transport distance in 1.000 km (intranational distance is set to 1000000)"
        /    USA     .USA        .C01 1000000
             USA     .Japan      .C01 10.14
             USA     .Germany    .C01 7.85
             Japan   .Japan      .C01 1000000
             Japan   .USA        .C01 10.14
             Japan   .Germany    .C01 9.04
             Germany .Germany    .C01 1000000
             Germany .USA        .C01 7.85
             Germany .Japan      .C01 10.14 /
        
        x(A,C,T) "Export"
        /    USA        .C01    .2018   5000
             USA        .C01    .2019   6000
             Japan      .C01    .2018   2000
             Japan      .C01    .2019   2500
             Germany    .C01    .2018   3000
             Germany    .C01    .2019   3500 /
             
        y(D,C,T) "Import"
        /    USA        .C01    .2018   4000
             USA        .C01    .2019   5000
             Japan      .C01    .2018   3000
             Japan      .C01    .2019   3500
             Germany    .C01    .2018   3000
             Germany    .C01    .2019   3500 /
        fc(A,D,C) "Function of transport distance";
             
    fc(A,D,C) = exp(tc(A,D,C)*(-1));
    loop((A,D)$(ord(A)=ord(D)),
        fc(A,D,C) = 0;
    ;)
Then I am solving A_i^m and B_j^m and calculating x_{ij}^m (called "Trade" in the code below) in the following way:

Code: Select all

    parameters Av(A,C,I),Bv(D,C,I),AvT(A,C),BvT(D,C),trade(A,D,C,T);
    
    loop(T,
        loop(C,
            Av(A,C,"I01") = 1;
            loop(I$(I.pos>1 and I.pos<100),
                Bv(D,C,I) = 1 / (sum(A,fc(A,D,C) * Av(A,C,I-1) * x(A,C,T)));
                Av(A,C,I) = 1 / (sum(D,fc(A,D,C) * Bv(D,C,I) * y(D,C,T)));
                AvT(A,C) = Av(A,C,I);
                BvT(D,C) = Bv(D,C,I); 
            );
            Av(A,C,"I01") = AvT(A,C);
            Bv(D,C,"I01") = BvT(D,C);
        );
        trade(A,D,C,T) = Av(A,C,"I01")*Bv(D,C,"I01")*x(A,C,T)*y(D,C,T)*fc(A,D,C);
    );
However, my problem it takes me very long time if I have do to for at lot of years, commoditity and countries. Therefore, can anyone tell me if there is a faster way of doing it compared to the method above. Can I somehow optimize my loop or something like that?

Post Reply