multi.mod

multi.mod

set ORIG;   # origins
set DEST;   # destinations
set PROD;   # products

param supply {ORIG,PROD} >= 0;  # amounts available at origins
param demand {DEST,PROD} >= 0;  # amounts required at destinations

   check {p in PROD}:
      sum {i in ORIG} supply[i,p] = sum {j in DEST} demand[j,p];

param limit {ORIG,DEST} >= 0;

param cost {ORIG,DEST,PROD} >= 0;  # shipment costs per unit
var Trans {ORIG,DEST,PROD} >= 0;   # units to be shipped

minimize Total_Cost:
   sum {i in ORIG, j in DEST, p in PROD}
      cost[i,j,p] * Trans[i,j,p];

subject to Supply {i in ORIG, p in PROD}:
   sum {j in DEST} Trans[i,j,p] = supply[i,p];

subject to Demand {j in DEST, p in PROD}:
   sum {i in ORIG} Trans[i,j,p] = demand[j,p];

subject to Multi {i in ORIG, j in DEST}:
   sum {p in PROD} Trans[i,j,p] <= limit[i,j];