Vehicle Routing Problem (VRP)
The Vehicle Routing Problem (VRP) is the optimization problem of assigning a set of deliveries to a fleet of vehicles and sequencing the stops to minimize cost while respecting constraints like capacity and time windows.
What is the Vehicle Routing Problem (VRP)?
VRP stands for Vehicle Routing Problem. It generalizes the traveling salesman problem (TSP), which looks for the shortest round trip for one vehicle, to a whole fleet with real-world constraints: vehicle capacity, delivery time windows, driver working hours, vehicle types and more. Dantzig and Ramser first described it in 1959 as the "truck dispatching problem", and it remains one of the most studied problems in operations research.
Most practical problems are a variant. The capacitated VRP (CVRP) limits what each vehicle can carry; the VRP with time windows (VRPTW) adds a pickup or delivery window per stop; the pickup and delivery problem (PDP) pairs each pickup with its delivery on the same vehicle; and multi-depot or mixed-fleet versions let vehicles start from different places or differ in size and equipment.
The VRP is NP-hard: the number of possible solutions explodes with every stop. A single vehicle with ten stops can already visit them in 3,628,800 different orders. Exact methods only work for small instances, so production solvers use heuristics. A construction method such as nearest neighbor or the Clarke–Wright savings algorithm builds a first feasible plan, and local search improves it with moves like 2-opt, relocate and swap, often guided by a metaheuristic such as simulated annealing.
Example: a distributor has 3 vans with a 1,000 kg payload and 45 deliveries, each with a time window. A planner can build a workable plan by hand; a solver respects every window and payload while minimizing total distance, and returns its plan in seconds. Deliveries that cannot fit are reported as unplanned, so the planner can add capacity or relax a window.
Transportial's trip optimization makes the solver a platform setting: PTV OptiFlow, PTV xTour, OSRM for single-vehicle ordering, CloverOpt, or Transportial's own solver, which builds trips with nearest-neighbor construction, improves them with relocate, swap, merge and split moves and polishes each route with 2-opt. The optimizer respects time windows, weight, vehicle type and equipment constraints, can insert legal driving breaks into routes and ETAs, and returns a preview that the planner adjusts before saving.
Frequently asked questions
What does VRP mean in logistics?
VRP stands for Vehicle Routing Problem: deciding which vehicle serves which customers and in what order, so that total distance, time or cost is as low as possible while every vehicle stays within its capacity and every stop within its time window.
What is the difference between TSP and VRP?
The traveling salesman problem (TSP) finds the best order of stops for a single vehicle. The VRP also decides how to divide the stops between several vehicles under capacity and time constraints; once that split is made, each vehicle's route is its own TSP.
How does a VRP solver help logistics planners?
It automatically builds efficient trips — assigning shipments to vehicles and ordering stops — so planners spend less time on manual scheduling and the fleet drives fewer empty or unnecessary miles, all while respecting capacity, time windows, and driving-hour rules.
Can a VRP solver guarantee the best possible plan?
Not for realistic fleet sizes: proving the optimum would take far too long. Practical solvers aim for a very good plan within seconds or minutes and report which stops they could not place, which is what planners need day to day.
See Vehicle Routing Problem (VRP) in a real TMS
Transportial puts these concepts to work in one operational platform — planning, tracking, documents, and finance.