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

This topic: OpsRes > WebHome > AMPLGuide > TransportationProblemInAMPL

Topic revision: r2 - 2008-04-02 - MichaelOSullivan

Copyright © 2008-2021 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.

Ideas, requests, problems regarding TWiki? Send feedback

Ideas, requests, problems regarding TWiki? Send feedback