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];