The Math Problem That Saves Companies Millions in Fuel

The Traveling Salesman Problem (TSP): a salesman needs to visit a set of cities and return home while traveling the shortest possible distance.

It sounds straightforward: calculate every possible route, pick the shortest. But the number of possibilities grows factorially. For just 10 stops, there are over 3.6 million possible routes (10!). That's not "simple" at all. It's a famously hard optimization problem.

From One Salesman to a Fleet

Now imagine not one salesman but a fleet of vehicles. That's the Vehicle Routing Problem (VRP): how to assign stops across multiple drivers while minimizing total distance, time, or cost.

If you tried to calculate every possible assignment, the math blows up even faster. That's why real-world VRP solvers don't brute-force it. Instead, they rely on heuristics and clever algorithms (branch and bound, local search, metaheuristics) that find solutions very close to optimal in a fraction of the time and compute.

Why It Matters

The payoff is significant. Research and industry results consistently show 10–30% reductions in miles driven when fleets move from manual routing to optimized routes.

That translates directly into:

• Lower fuel costs
• Less driver time on the road
• Reduced emissions

For a fleet of any meaningful size, those percentages turn into millions of dollars a year, and a real dent in the carbon footprint of moving goods.