set CITIES;
set LINKS within (CITIES cross CITIES);

param supply {CITIES} >= 0;   # amounts available at cities
param demand {CITIES} >= 0;   # amounts required at cities

   check: sum {i in CITIES} supply[i] = sum {j in CITIES} demand[j];

param cost {LINKS} >= 0;      # shipment costs/1000 packages
param capacity {LINKS} >= 0;  # max packages that can be shipped

minimize Total_Cost;

node Balance {k in CITIES}: net_in = demand[k] - supply[k];

arc Ship {(i,j) in LINKS} >= 0, <= capacity[i,j],
   from Balance[i], to Balance[j], obj Total_Cost cost[i,j];