# Difference: TransportationProblemInAMPL (1 vs. 2)

#### Revision 22008-04-02 - MichaelOSullivan

Line: 1 to 1

 META TOPICPARENT name="AMPLGuide"

# The Transportation Problem in AMPL

>
>

## AMPL Formulation

The formulation of the transportation problem is AMPL is a straighforward translation of the matehmatical programme for the transportation problem.

The sets and are declared as SUPPLY_NODES and DEMAND_NODES respectively:

set SUPPLY_NODES;
set DEMAND_NODES;


The supply and demand are declared as integer parameters:

param Supply {SUPPLY_NODES} >= 0, integer;
param Demand {DEMAND_NODES} >= 0, integer;


The cost is declared over the SUPPLY_NODES and DEMAND_NODES:

param Cost {SUPPLY_NODES, DEMAND_NODES};


Now, the mathematical proramme follows directly:

var Flow {i in SUPPLY_NODES, j in DEMAND_NODES} >= 0, integer;

minimize TotalCost:
sum {i in SUPPLY_NODES, j in DEMAND_NODES} Cost[i, j] * Flow[i, j];

subject to UseSupply {i in SUPPLY_NODES}:
sum {j in DEMAND_NODES} Flow[i, j] = Supply[i];

subject to MeetDemand {j in DEMAND_NODES}:
sum {i in SUPPLY_NODES} Flow[i, j] = Demand[j];

Note that we assume the transportation is balanced.
-- MichaelOSullivan - 02 Apr 2008
>
>
 META FILEATTACHMENT attachment="latex526e21edb215dffbfdb5ee74dd06358b.png" attr="h" comment="" date="1207132191" name="latex526e21edb215dffbfdb5ee74dd06358b.png" stream="GLOB(0xa44d1b8)" tmpFilename="latex526e21edb215dffbfdb5ee74dd06358b.png" user="MichaelOSullivan" version="1" attachment="latex3c99455acbafe055e535fc129b4dd12e.png" attr="h" comment="" date="1207132191" name="latex3c99455acbafe055e535fc129b4dd12e.png" stream="GLOB(0xa456928)" tmpFilename="latex3c99455acbafe055e535fc129b4dd12e.png" user="MichaelOSullivan" version="1" attachment="latexa518db3a714367f452620a2d18e0d61e.png" attr="h" comment="" date="1207132191" name="latexa518db3a714367f452620a2d18e0d61e.png" stream="GLOB(0xa4568f8)" tmpFilename="latexa518db3a714367f452620a2d18e0d61e.png" user="MichaelOSullivan" version="1" attachment="latex57f16e685545faa46af73ecce6b4eb7c.png" attr="h" comment="" date="1207132191" name="latex57f16e685545faa46af73ecce6b4eb7c.png" stream="GLOB(0xa44d5e4)" tmpFilename="latex57f16e685545faa46af73ecce6b4eb7c.png" user="MichaelOSullivan" version="1" attachment="latex15b62f2a4b15b2f0ea551529e221b54f.png" attr="h" comment="" date="1207132191" name="latex15b62f2a4b15b2f0ea551529e221b54f.png" stream="GLOB(0xa44d950)" tmpFilename="latex15b62f2a4b15b2f0ea551529e221b54f.png" user="MichaelOSullivan" version="1"

Line: 1 to 1