Difference: TransportationProblemInAMPL (2 vs. 3)

Revision 32008-04-02 - MichaelOSullivan

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META TOPICPARENT name="AMPLGuide"

The Transportation Problem in AMPL

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 param Cost {SUPPLY_NODES, DEMAND_NODES};
Changed:
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Now, the mathematical proramme follows directly:
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Now, the mathematical programme follows directly:
 

Changed:
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var Flow {i in SUPPLY_NODES, j in DEMAND_NODES} >= 0, integer;
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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];
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  Note that we assume the transportation is balanced.
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Adding Bounds

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;

Balancing Transportation Problems

  -- MichaelOSullivan - 02 Apr 2008
 
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