Model for seemingly easy problem

General
1

Dear Community,
i am a newbie in gams and announced here only since yesterday. I want to enhance the game Domination and therefore create a model for a seemingly easy problem: i have several countries c(i), who provide armies in number of p(i) and i want to move them to several destiny countries d(j) whereby the countries c are possibly neighbours only from one or more of the dest countries d. I want to assign the armies in such a way, that the destiny countries are preferably equal strong afterwards, which can be formulated as the absolute of the sum of differences between them is to be minimized.
My model is very tiny for test purposes with 3 dest countries an 2 source countries from which ‘nw’ is neighbour of ‘al’ and ‘gl’.
My model:

set
    c   countries    /nw, wa  /
    d destcountries / al, gl, ca /;
Alias (c,cc);
Alias (d,dd);

Table  w
                     al gl ca armies2
                 nw   1  1       3
                 wa         1    5
            armies1   4  2  1
                            ;
scalar armiestotal;
armiestotal = sum(c, w(c,'armies2')) + sum(d, w('armies1',d));
display armiestotal;

variable g(d)
       x(c,d)
       z       assigned armies in dest
;
integer Variable g,x;

Equations
       cost        define objective function
       supply(c)   observe army limit at country c
       supply2     observe limit of totalarmies
       demand      observe armies demand in all dest countries
;

supply(c) ..   sum(d,w(c,d)*x(c,d))  =e=  w(c, 'armies2') ;

demand .. sum(d, g(d)) =e= armiestotal ;

supply2 ..  sum((c,d), w(c,d)*x(c,d)) =e= armiestotal - sum(d, g(d));

cost.. z  =e=  sum(d, sum(dd$(ord(dd) > ord(d)), abs(g(d) - g(dd))));

Model atest /cost, supply, demand, supply2/ ; option limrow=0, limcol=0;
Solve atest using minlp minimizing z ;

Because of the abs function, i have to use in the cost function, i am forced not to use the lp solver but the minlp solver. But the result is not the best solution. Gams rsponds: “The relaxed NLP is infeasible”. The best solution would be to move all armies from ‘nw’ to ‘gl’.

Does somebody have any hints?

2

This code does not run due to some formatting issues. Please paste multiline code into triple backticks (```). The backticks are also inserted automatically when clicking the preformatted text (</>) icon. Thanks!

3

Hi Fred, thank you for your answer. In my post, the code is obviously malformed, but in gams it works, so it is not malformed, as fas as i understand. If i am wrong: which section of the code should be pasted into triple backticks?

4

@Micha All code snippets should be surrounded with three backticks at the beginning and three backticks at the end to improve the readability of your code snippets.

For example, without the backticks, a code snippet looks as follows:

Set a / a1…a3 /;
Set b / a1…a3 /;

but with backticks, it looks like as follows:

Set a / a1..a3 /;
Set b / a1..a3 /;

I did the necessary changes for your code snippet.