The formulation of the transshipment problem in AMPL we present here is a straightforward translation of the alternative mathematical programme for the transshipment problem. We will build the file `transshipment.mod`.

The set is declared as `NODES`

:

set NODES;

The net demand is declared as an **integer** parameter (note there is no `>= 0`):

param NetDemand {NODES} integer, default 0;Setting the default

`NetDemand`

to be 0 means that no values need to be entered for transshipment nodes.
Note that the set `NODES`

and the parameter `NetDemand`

can be easily created from `SUPPLY_NODES`

, `DEMAND_NODES`

, `Supply`

, etc, e.g.,:

set SUPPLY_NODES; set DEMAND_NODES; set TRANSSHIPMENT_NODES; set NODES := SUPPLY_NODES union TRANSSHIPMENT_NODES union DEMAND_NODES; param Supply {SUPPLY_NODES} >= 0, integer; param Demand {DEMAND_NODES} >= 0, integer; param NetDemand {n in NODES} integer := if n in SUPPLY_NODES then -Supply[n] else if n in DEMAND_NODES then Demand[n]; # else 0 by defaultNote that no default value is needed for

`NetDemand`

as it is explicitly defined for all nodes.
The set `ARCS`

is defined between pairs of nodes and costs and bounds are also defined:

set ARCS within NODES cross NODES; param Cost {ARCS}; param Lower {ARCS} >= 0, integer, default 0; param Upper {(i, j) in ARCS} >= Lower[i, j], integer, default Infinity;

Now, the mathematical programme follows directly:

var Flow {(i, j) in ARCS} >= Lower[i, j], <= Upper[i, j], integer; minimize TotalCost: sum {(i, j) in ARCS} Cost[i, j] * Flow[i, j]; subject to ConserveFlow {j in NODES}: sum {(i, j) in ARCS} Flow[i, j] - sum {(j, k) in ARCS} Flow[j, k] >= NetDemand[j];

-- MichaelOSullivan - 06 Oct 2014

I | Attachment | History | Action | Size | Date | Who | Comment |
---|---|---|---|---|---|---|---|

mod | transshipment.mod | r5 r4 r3 r2 r1 | manage | 1.5 K | 2008-04-28 - 02:21 | MichaelOSullivan |

This topic: OpsRes > WebHome > NetworkOptimisation > TransshipmentProblem > TransshipmentProblemInAMPL

Topic revision: r8 - 2019-11-11 - MichaelOSullivan

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