The Conversion of a Transshipment Problem to a Transportation Model

The problem from the first level (Table 7.11) can be converted to a classic transportation model under following steps

1) The points where you can ship into and out of, occur in the converted transportation problem twice – first as a ”Transshipment (or Transit) Points” and second as a standard demand points. The transshipment points are situated on both sides of the model (as supply points and as demand points) Their capacity must sufficient for transport realization – must be grater or equal to the sum of destination demands (red cells in the following table).

2) The capacity slack (unused capacity) of a transshipment point is defined as an amount of transported material within a single transshipment point. The cost of such transport will be zero (orange cell). The unused capacity will be nonnegative.

3)  The cost of transport on non-existing or non-allowed roads will be set very high (we call them penalty cost) because the amount of material transported on such routs must be zero in the optimal solution (gray cells).