set ORIG;   # origins (steel mills)
set DEST;   # destinations (factories)
set PROD;   # products

param rate {ORIG,PROD} > 0;     # tons per hour at origins
param avail {ORIG} >= 0;        # hours available at origins
param demand {DEST,PROD} >= 0;  # tons required at destinations

param make_cost {ORIG,PROD} >= 0;        # manufacturing cost/ton
param trans_cost {ORIG,DEST,PROD} >= 0;  # shipping cost/ton

var Make {ORIG,PROD} >= 0;       # tons produced at origins
var Trans {ORIG,DEST,PROD} >= 0; # tons shipped

minimize total_cost:
   sum {i in ORIG, p in PROD} make_cost[i,p] * Make[i,p] + 
   sum {i in ORIG, j in DEST, p in PROD}
			trans_cost[i,j,p] * Trans[i,j,p];

subject to Time {i in ORIG}:
   sum {p in PROD} (1/rate[i,p]) * Make[i,p] <= avail[i];

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

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