Ben-Gurion University of the Negev Jacob Blaustein Institutes for ...

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more sophisticated model that allows a better description of real life situation: the
transshipment model.
Though, the transportation model is not realistic for the following reasons:
1. the network is designed with no consideration for the geomorphologic
aspect of the study area. Therefore, the arcs of connection that were
sketched in the model may be completely unfeasible in a real life
situation;
2. each source is directly connected to each and every destination with a
dedicated arc.
3. destinations are not connected between each other.
These may be the reasons of very probable unwanted redundancies of arcs resulting in
the calculation of unpractical solutions. Therefore the transportation model does not
provide realistic solutions for this study in terms of any practical field application. The
transportation model is used as a stepping stone for the transshipment model
3.3 The Transshipment Model
The standard transportation model assumes that the direct route between a source and a
destination is the only possible connection between supply and demand of water.
An alternative procedure to the use of regular transportation model is the so called
transshipment model. This model has the additional feature of considering the
transportation from sources to destination to be allowed to pass through intermediate
nodes before ultimately reaching their designated destination.
An example will be used to describe the mathematical method applied for the solution
of the problem. Figure 8 represents a lay-out of a transshipment scheme where the
supply amount at the two sources, node 1 and 2, are A1 and A2. The water demand at
destination 5, 6, and 7 are B5, B6, and B7. Water is transported to destination nodes 5,
6, and 7 through intermediate nodes 3 and 4.; and water can be transported from a
destination to another destination, for instance from node 5 to node 6. In terms of
connection nodes 1 and 2 are characterized by outgoing arcs only, whereas node 7 is
characterized by incoming arcs only. All the remaining nodes have both incoming and
outgoing arcs. In the nodes 3 and 4 water is not consumed so that all the input is equal