set CITIES;
set LINKS within CITIES cross CITIES;
set PRODS;
param supply {CITIES,PRODS} >= 0; # amounts available at cities
param demand {CITIES,PRODS} >= 0; # amounts required at cities
check {p in PRODS}:
sum {i in CITIES} supply[i,p] = sum {j in CITIES} demand[j,p];
param cost {LINKS,PRODS} >= 0; # shipment costs per ton
param capacity {LINKS,PRODS} >= 0; # max tons shipped/product
param cap_joint {LINKS} >= 0; # max total tons shipped/link
minimize Total_Cost;
node Balance {k in CITIES, p in PRODS}:
net_in = demand[k,p] - supply[k,p];
subject to Multi {(i,j) in LINKS}:
to_come <= cap_joint[i,j];
arc Ship {(i,j) in LINKS, p in PRODS} >= 0, <= capacity[i,j,p],
from Balance[i,p], to Balance[j,p],
coeff Multi[i,j] 1.0,
obj Total_Cost cost[i,j,p];