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;   # maximum shipments on routes
param minload >= 0;             # minimum nonzero shipment
param maxserve integer > 0;     # maximum destinations served

param vcost {ORIG,DEST,PROD} >= 0; # variable shipment cost on routes
var Trans {ORIG,DEST,PROD} >= 0;   # units to be shipped

param fcost {ORIG,DEST} >= 0;      # fixed cost for using a route
var Use {ORIG,DEST} binary;        # = 1 only for routes used

minimize Total_Cost:
   sum {i in ORIG, j in DEST, p in PROD} vcost[i,j,p] * Trans[i,j,p]
 + sum {i in ORIG, j in DEST} fcost[i,j] * Use[i,j];

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

subject to Max_Serve {i in ORIG}:
   sum {j in DEST} Use[i,j] <= maxserve;

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] * Use[i,j];

subject to Min_Ship {i in ORIG, j in DEST}:
   sum {p in PROD} Trans[i,j,p] >= minload * Use[i,j];