The Transportation problem is simpler than the Transshipment problem because there are no intermediate warehouse nodes. There exists m supply stations si, each capable of producing sup(si) units of a commodity. There are n demand stations tj, each demanding dem(tj) units of the commodity. There is a fixed per-unit cost d(i, j)≥0 associated with transporting a unit over the edge (i, j). The goal is to determine the flow f(i, j) of units from supply stations si to demand stations tj that minimizes the overall transportation cost, TSC, which can be concisely defined as:
|Total Shipping Cost (TSC) = Σ i Σ j d(i, j)*f(i, j)|
The solution must also satisfy both the total demand for each demand station tj and the supply capabilities for supply stations si.
We convert the Transportation problem instance into a Transshipment problem instance with no intermediate warehouse nodes.