Introduction to the vehicle routing problem
A vehicle routing problem is a generalisation of the famous commuter problem, which consists of finding the shortest route through a series of cities, departing from a city and ending in the same city.
As its name suggests, it is a problem with very practical applications in the optimisation of vehicle routes, such as in the case of delivery and collection of goods by truck.
The typical problem to be solved consists of a depot from which vehicles depart and a number of customers or points on the map to which goods must be delivered.
Solving the problem, therefore, consists of assigning routes to the available trucks that meet the needs of the customers, minimising the number of resources used and the length of the routes.
A VRP problem is nothing more than a mathematical model that approximates the real needs of, for example, a distribution company. As such, there are several variations on the base problem, which introduce more detail.
Capacities can be added to vehicles creating the type of problem known as a CVRP or capacitated vehicle routing problem. Another typical constraint that can be added and that is of great importance in the real world is time windows, which indicate times between when trucks can make deliveries and destinations can receive them. Additionally and to make the model more complete, the concepts of delivery and pick-up can also be included instead of just the former, making different demands exist at each of the points along the route.
Key pieces to solving the vehicle routing problem: mathematical solvers
A solver or mathematical solver is software that allows both modelling the problem mathematically and solving it. The objective of using this type of tool is to find good solutions in feasible times in the real world.
Specifically, this vehicle routing problem is usually posed as a combinatorial optimisation problem solved by the use of heuristics and metaheuristics. Solvers allow the problem to be specified and solved following one of these options or a combination of both.
Each solver has different execution times and results for the same problem, and the vehicle routing problem is no exception. This is one of the characteristics to take into account when choosing a mathematical solver, in addition to the cost of acquiring the licence to use these tools. At decide4AI we work with different mathematical solvers such as Gurobi, CPLEX, LocalSolver, FICO® Xpress Solver or More Optimal.
In this article, we would like to focus on the More Optimal platform, which enables the development of first-class customised supply chain planning solutions. The platform is hosted in the cloud and can be used directly from the web browser. It offers powerful algorithmic building blocks that come out of the box and are fully integrated into the platform, and useful customisable visualisations such as maps, 3D visuals, Gantt charts and other graphics that can be easily configured.
Applying a tool such as More Optimal allows you to optimise the use of both material and human resources, improve operational margins by maximising profits and minimising costs, increase efficiency and productivity, and improve service levels. Providing real business value and constituting a competitive advantage.
If you want to know more about More Optimal, the mathematical solvers or the vehicle routing problem, contact us without obligation.
We can help you analyse your case and see the potential of applying this powerful technology in your daily operations.