/* Minimum-cost flow problem */

param N integer, > 0; /* # nodes */

set V := 1..N;

param c{V, V}; /* cost of edge */
param u{V, V}; /* capacity of edge */
param b{V}; /* supply (positive number) or demand (negative number) */

/* decision variables */
var x{V, V}, >= 0;

/* Objective function */
minimize z: sum{i in V} ( sum{j in V} (c[i, j] * x[i, j]) );

s.t. INTERNAL{i in V}:
     sum{j in V} (x[i, j]) - sum{j in V} (x[j, i]) = b[i];

s.t. CAPACITY{i in V, j in V}:
     x[i, j] <= u[i, j];
end;