The VRP (Vehicle Routing Problem) is the mathematical problem of assigning a set of stops to a fleet and ordering them so as to minimise total cost (kilometres, time, vehicles), while respecting constraints such as capacity and time windows. It’s the model behind route optimization.
Why it’s hard
The VRP is “NP-hard”: the number of possible combinations grows explosively with the stops, making it impossible to try them all. With just a few dozen deliveries the solutions are already astronomical — which is why you need an algorithm, not a spreadsheet.
The variants
There are many VRP variants depending on real-world constraints: time windows (VRPTW), capacity (CVRP), multiple depots, pickups and deliveries, heterogeneous fleet. Modern software — often with artificial intelligence — solves complex variants in seconds. On the practical value, see route optimization ROI.
FAQ
Why isn’t a spreadsheet enough to solve the VRP?
Because the combinatorics are too large: even with a few dozen stops the possible solutions exceed any manual calculation. You need an algorithmic solver.
Are the VRP and the TSP the same thing?
No. The TSP (Travelling Salesman Problem) concerns a single vehicle visiting all stops; the VRP generalises to multiple vehicles with constraints, and is therefore more complex.