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];