set ORIG; # origins
set DEST; # destinations
set PROD; # products
set orig {PROD} within ORIG;
set dest {PROD} within DEST;
set links {p in PROD} := orig[p] cross dest[p];
param supply {p in PROD, orig[p]} >= 0; # available at origins
param demand {p in PROD, dest[p]} >= 0; # required at destinations
check {p in PROD}:
sum {i in orig[p]} supply[p,i] = sum {j in dest[p]} demand[p,j];
param limit {ORIG,DEST} >= 0;
param cost {p in PROD, links[p]} >= 0; # shipment costs per unit
var Trans {p in PROD, links[p]} >= 0; # units to be shipped
minimize total_cost:
sum {p in PROD, (i,j) in links[p]} cost[p,i,j] * Trans[p,i,j];
subject to Supply {p in PROD, i in orig[p]}:
sum {j in dest[p]} Trans[p,i,j] = supply[p,i];
subject to Demand {p in PROD, j in dest[p]}:
sum {i in orig[p]} Trans[p,i,j] = demand[p,j];
subject to Multi {i in ORIG, j in DEST}:
sum {p in PROD: (i,j) in links[p]} Trans[p,i,j] <= limit[i,j];