The Traveling Salesperson Problem is a challenge faced every day by logistics for companies. It was heard for the first time in 1832, when a publication called “The Travel Agent” was published in a newspaper in Germany. And he was talking about what must be done to receive orders or reservations and ensure successful results in their business. It was a kind of manual that showed examples of routes to get there in less time.
It not only helps with logistics, but also with distribution. Which is very useful when it comes to having a taxi company or an ally for deliveries. It currently works as an algorithm base and has helped many to organize post-pandemic. Since it helps to choose the best access route to the destination, reducing transfer costs. It sounds simple, but many specialists have spent a great deal of time polishing its operation.
How to solve the TSP?
The TSP has complexity in its calculations, so mathematicians have been involved. As long as it's not an exorbitant number of routes it's totally effective. To be able to make more reservations and return to the place of origin in the shortest possible time. In fact, if a carrier has 10 destinations, it would have around 181,440 possible routes. So the Travel Agent Problem helps filter that congestion.
The Nearest Neighbor method
This mechanism to solve the TSP is known as the KNN algorithm, it is a basic machine learning method. It generates proposals with a very efficient calculation time, used for both classification and regression, used for logistics transport. Basically, it consists of the fact that to reach a certain destination, which would be value K, the journey begins with the destination(s) of K closest samples.
The Brute Force method
This begins with the systematic enumeration of all those possible routes that can be taken. This, in order to solve the Problem of the Traveling Salesperson to find the ones that best suit the needs of the companies. For example, if the idea is to reach the destination in a predetermined time, a brute force algorithm will start enumerating all the routes. Which will facilitate the trip in the time limit.
Branch and Bound method
This method is a somewhat complex algorithm. With the Simplex Method that solves problems with linear programming, you’re not limited in the number of variables. It even provides a greater capacity for sensitivity analysis.
Let's see an example in case the solution obtained is to send 1.54 vehicles to 6.45 cities. New subproblems are defined to provide possible solutions: send 2 vehicles to 6 cities. If it happens that the solutions do not improve the results, the subproblem is discarded.
Is the Traveling Salesperson Problem important in logistics?
The optimization of processes is essential, especially if you are a transport company and you are looking to save time and money. For this, many companies used to use Excel spreadsheets, managing to order the data, but it only works if the destinations are few. However, time is money these days, so very few companies continue to use this system.
If you stop to think about it for a bit, the intuitiveness of the aforementioned tool is minimal. Therefore, the more destinations there are, the higher the possibility of making calculation errors. So the Traveling Salesperson Problem is applied in order to provide a solution to all this.
Route optimization solving the TSP
Route optimization allows the TSP to better define its path before starting the journey. And if you receive the solutions to this problem from a software specially made for route planning, much better. Making transport, delivery and distribution companies increase their income as deliveries increase, without needing more time.
Said software would deliver the proposal to you automatically, thus achieving a better result than if you do this process manually. A custom app like ToolRides can help you by giving you the best routes, thanks to its included map. But for larger merchandise distribution companies, the PlannerPro software is often recommended.
Other areas that have applied TSP
Although we are more interested in its application in distribution and logistics, the TSP has covered different areas. Tourists are the ones who can benefit, since they need to find the best way to go to different points and return to their starting point. Knowing that the more places you can visit taking advantage of your time, the better the stay in the place visited.
Mail delivery can be modeled using TSP, for those deliveries that are very distant from each other. But it can also be applied to any Amazon-type parcel company. School routes were one of the first to apply the TSP, thanks to Merrill Flood, who took an interest in improving these routes to follow.
Improve your organization
It is essential for your company to be organized as much as possible. So the Traveling Salesperson Problem is something we recommend you try as an alternative. You will see how your drivers can be more productive and also save money that can be invested in other areas of the company.