/* Maximum Flow Problem */

param N integer, > 0; /* # nodes */
param s integer, > 0; /* ID source */
param t integer, > 0; /* ID terminal */

set V := 1..N;
set E within {V, V};

param u{E}; /* capacity of edge */

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

/* Objective function */
maximize z: sum{j in V} (x[s, j]);

s.t. INTERNAL{i in V: i != s && i != t}:
     sum{j in V} (x[i, j]) - sum{j in V} (x[j, i]) = 0;

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