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

Copyright © 2008-2022 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