The software, produced by Paragon Software Group, uses sophisticated algorithms to determine optimum routes combining the shortest distance without duplication for the company's delivery vehicles.
The firm - which delivers 27,000 product lines to 6,500 customers using 600 vehicles from 19 depots - previously had to rely on a manually-generated fixed-route plans to organise its deliveries.
The new system enables logistics staff to input quantities of goods, destination addresses, numbers of vehicles available, and driver hours available within the regulations to generate the most efficient routing plan.
The software calculates drivers' hours, mileages and overall delivery costs.
Steve Anderson, organisation manager at AAH, said, "The software has enabled us to effectively re-evaluate our transport operation with minimum fuss.
"We are seeing huge cost savings and expect them to increase as we roll it out to additional sites," he said. "We are also getting better customer service - we can now guarantee delivery times to the nearest 15 minutes."
Large cost savings are possible by applying processing power to logistics problems.
The industry has traditionally faced the conundrum of how to make the best use of fixed capacity efficiently where large numbers of vehicles are empty at any given time.
Routing and scheduling to determine the shortest route between a number of points magnified by the number of vehicles and destinations is a complex problem and, until recently, only the largest organisations possessed enough computing power to calculate it.