The problem appears to have been caused by the orders and positioned I had placed the buildings in, in comparison to the coal mine. This appears to be down to the route that the agents carrying the materials in choose to travel when leaving the Coal Mine.
In the original route, the coal power plant was at the end of the blue route on a backstreet, while it is now located on the yellow route, before the trading port;
When the agents carrying coal leave the coal mine, they always seem to take the easiest route, which in this instance results in them not crossing over the road, thus they always turn right towards the smelting plant.
Each stop along the way has a specific level amount of coal they can store;
- The Smelting Plant has storage for 10 tons of coal
- The Trade Port has storage for 100 tons of coal
- The Coal Mine has storage for 20 tons of coal
Before the agents will start delivering elsewhere, each of these storages need to fill up to maximum, which means the Coal Power Plant wasn't getting coal in the original instance because the output of the Coal Mine wasn't sufficient enough to fill up the storage capacities of all of the buildings before it.