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

var Ship {(i,j) in LINKS} >= 0, <= capacity[i,j]; 
                              # packages to be shipped

minimize Total_Cost:
   sum {(i,j) in LINKS} cost[i,j] * Ship[i,j];

subject to Balance {k in CITIES}:
   supply[k] + sum {(i,k) in LINKS} Ship[i,k] 
      = demand[k] + sum {(k,j) in LINKS} Ship[k,j];