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 ${\cal S}$ and ${\cal D}$ are declared as SUPPLY_NODES and DEMAND_NODES respectively:


The supply $s_i, i \in {\cal S}$ and demand $d_j, j \in {\cal D}$ are declared as integer parameters:

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

The cost $c_{ij}$ is declared over the SUPPLY_NODES and 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

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