Vehicle Routing Problem (VRP)

The VRP (Vehicle Routing Problem) is the formal name for the problem of deciding how a fleet of vehicles covers a set of destinations at the lowest possible cost. Instead of one truck and one route, it splits many stops among several vehicles, each with its own limits, and looks for the cheapest combination of assignments and sequences. It is a classic of operations research and the mathematical model behind all routing software.

The VRP is a generalization of the traveling salesman problem (finding the shortest route that visits every city once). The difference is that it does not work with a single vehicle or ignore real-world constraints: each vehicle's capacity, delivery time windows, the driver's shift and traffic. Modeling those constraints well is exactly the territory of the route optimization that Trazzo handles in the last mile.

As a pure optimization problem, the VRP has no single obvious answer: among all the possible ways to build the route sheets, one is the most efficient, and finding it is the challenge.

Why it is a hard problem

The difficulty of the VRP is not understanding it, but solving it. The number of possible combinations grows explosively with every new stop: with just a few dozen destinations it is already impossible to try them all, even with the fastest computer. That is why real operations do not look for the perfect solution but for a very good one in a reasonable time, using heuristic algorithms that explore the solution space intelligently without covering all of it.

This is why the mathematical complexity lives inside the software engine and not in the planner's head. The company does not need to solve equations: it provides the real constraints of its operation, loaded correctly, and the engine returns the routes.

The most common variants

The pure VRP almost never shows up in real operations: what gets solved is always some variant with constraints. The main ones are:

• CVRP (capacitated): each vehicle has a weight or volume limit it cannot exceed. It is the most basic and almost universal constraint.
• VRPTW (with time windows): each customer must be served within a time range. Arriving outside the window triggers a penalty or simply a failed delivery.
• Multi-depot VRP: the fleet leaves from several distribution centers, not just one, so you also have to decide where it makes sense to leave from.
• VRP with pickups and deliveries: the same route combines deliveries and pickups, typical of reverse logistics or delivery with returns.

Why it matters to a company in Latin America

In cities such as Mexico City, Bogotá or Buenos Aires, the VRP is not an academic exercise: it is the difference between a fleet that improvises and one that delivers. Transportation is usually one of the heaviest costs in the supply chain, and much of that cost is decided before the truck starts, in how the route sheets are built. Modeling the problem with the real constraints (capacity, receiving windows, city traffic) lets you spread the work evenly and add stops without adding vehicles. When those constraints are loaded poorly or "for show", the plan looks neat on screen but is impossible on the street.

How it differs from related terms

Four concepts often get mixed up, and it helps to separate them:

• The VRP is the mathematical problem, the formal model.
• Route optimization is the practical application and the software that solves it.
• Dynamic routing is an extension that re-solves the VRP in real time when the day changes, for example a new order or a truck that breaks down.
• The TMS is the transportation management system that may include a VRP engine but covers much more: documentation, costs and tracking.

In practice

A beverage distributor in Bogotá delivers to 200 points of sale with eight trucks. Without solving the VRP, the supervisor builds routes from inherited fixed zones, and on Mondays, the peak day, some drivers finish at 7 p.m. while others are back by noon. By modeling the problem with each store's receiving windows (many do not receive goods from noon to 2 p.m.), each truck's capacity and traffic, the route sheets are rebalanced: the work is spread evenly and the same fleet covers more stops without stretching the workday.

Common mistakes

• Confusing it with the traveling salesman problem: the VRP has several vehicles and constraints, not a single route.
• Loading unrealistic constraints: windows or capacities "for show" that inflate the cost and make the plan hard to believe.
• Chasing the perfect exact solution: for real operations, a very good one in minutes is worth more than the optimal one in hours.
• Ignoring geocoding: if the points are in the wrong place, even the best VRP solution fails on the street.