transp3.mod

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transp3.mod

set ORIG;   # origins
set DEST;   # destinations

set LINKS within {ORIG,DEST};

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

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

param cost {LINKS} >= 0;   # shipment costs per unit
var Trans {LINKS} >= 0;    # units to be shipped

minimize Total_Cost:
   sum {(i,j) in LINKS} cost[i,j] * Trans[i,j];

subject to Supply {i in ORIG}:
   sum {(i,j) in LINKS} Trans[i,j] = supply[i];

subject to Demand {j in DEST}:
   sum {(i,j) in LINKS} Trans[i,j] = demand[j];