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 programme follows directly:

var Flow {SUPPLY_NODES, 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.

In the main discussion of transportation problems, we saw that adding bounds to the flow variables allowed us to easily either bound the transportation of good from a supply node to a demand node or remove an arc from the problem altogether.

We can add bounds to our AMPL formulation by declaring 2 new parameters with defaults:

param Lower {SUPPLY_NODES, DEMAND_NODES} integer default 0; param Upper {SUPPLY_NODES, DEMAND_NODES} integer default Infinity;and adding them to the

`Flow`

variable declaration:
var Flow {i in SUPPLY_NODES, j in DEMAND_NODES} >= Lower[i, j], <= Upper[i, j], integer;

-- MichaelOSullivan - 02 Apr 2008

This topic: OpsRes > WebHome > AMPLGuide > TransportationProblemInAMPL

Topic revision: r3 - 2008-04-02 - MichaelOSullivan

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