The Possibility of Solving the “Traveling Salesman Problem” in Business

Solving the Traveling Salesman Problem in Business

The term “traveling salesman problem” seems very far from modern problems related to the efficiency of numerous types of movements and relocations. But the paradox lies in the fact that it was thanks to this problem that various navigators appeared in the modern world and effective decision-making systems were born.

In simple terms, the traveling salesman problem (TSP), in fact, is the choice of the most efficient solution from the set of existing ones to achieve a certain goal. With regard to our topic of movements and relocations, when somebody plans a course between different locations, the TSP is intended to identify the most appropriate route of all possible.

In this case, it is necessary to take into account some mandatory features, which we will discuss below briefly. This should help you find the traveling salesman problem solver.

A bit of history

A bit of history

Before introducing you to the various ways of solving the TSP, we want to take you back to the 19th century and remember what this outdated word “traveling salesman” means. A traveling salesman or, in modern terms, a sales representative, offered various goods for purchase in different inhabited localities.

His goal was to interest as many people as possible in goods, for which he visited most of the houses in the settlements. The traveling salesman had to overcome this entire route as quickly as possible and then return to the starting point. Therefore, in the classical version, the salesman's task was: to choose the shortest path between settlements, without returning there again, and return home. Of course, it was necessary to go all this way as quickly as possible.

It`s a familiar target for many people now too. In today's world, any planner of optimal routes sets the same goal every time. At first glance, it seems that it will not be difficult to cope with such a task. Especially if you have computers. However, let's not rejoice in advance. We have to recall that the number of locations involved in the route can be two-digit and sometimes more numbers.

But turns out that the presence of more than 66 locations will already require several billion years of operation from the computer. Why is that? – you ask – is it really so difficult even for the computer to estimate the distances between locations?

Conditions for solving TSP

Conditions for solving TSP

Of course, when we create certain routes, we mean distance as a dominant factor. And if the goal was just to leave point A and get to point B, regardless of any other requirements, then the TSP solution would be elementary and would not require much time and effort. But the problem is that, more often than not, distance is only part of several route features.

An equally important parameter is the time to overcome this distance. And these two components – distance and time – are not equivalent. That is, a short road may require more time to overcome than long one. The causes can be different – reverse traffic, drawbridges, one-way traffic, etc.

Another factor that complicates the calculations may be certain restrictions associated with the route. For example, the number of visits to the same location (no more than once / twice, etc.). And if additional factors are added to the route planning, the absence of which will lead to the futility of the trip, then the task becomes much more complicated. For example, before visiting a certain location, you need to take with you the required documents in a company whose location does not fit into the optimal travel trajectory.

So, analyzing this example, we can come to the conclusion that in different situations for different purposes with different amounts of initial facts, it is necessary to choose different methods for solving the TSP. There are several such methods. Most of them belong to the so-called academic methods and are poorly suited for real practice by real logistics and transport companies.

After all, the task of any business is not just an effective solution to the problem, but an effective solution in the shortest possible time to achieve the greatest efficiency.

Therefore, in contrast to academic methods, companies use approaches based on the use of the API interface. And among a considerable number of services with API solutions, the API distance matrix (DMA) is ​​​​the best option. Firstly, the work of this service covers almost all known roads in the world.

Secondly, the calculations take into account the real situation along the roads of the requested route. And of course, the fact of the almost instantaneous response of the DMA to the sent request is also important. All this contributes not only to the solution of the TSP, as such, but also helps utilizers to carry out and improve their business, reducing overhead costs and increasing their revenue.

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