multmip1.mod
Sample model from the AMPL book
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 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 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];