The Journey Through Mathematics and Data: Understanding the Routing Problem

In the world of mathematics, there are few problems as captivating as the routing problem, also known as the "Traveling Salesman Problem" (TSP).

This is not just a puzzle; it's a window into the complexity of logistics.

What is the Traveling Salesman Problem?

At the core of TSP is a seemingly simple question.

"Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?"

This question has led to decades of research, innovative algorithms, and a deeper understanding of computer complexity.

Why is TSP Important?

TSP is more than an academic exercise. It's at the heart of logistics planning, optimising routes for delivery services, and transportation networks. Solving TSP means more efficient routes, reduced fuel consumption, and faster deliveries.

The complexity of TSP lies in its combinatorial nature. As the number of cities increases, the number of possible routes grows exponentially, making it challenging to find the optimal route for larger sets of cities.

Innovative Approaches to TSP

Researchers have developed various solutions to solve TSP:

Machine Learning: These systems can learn from large data sets and identify patterns that humans and traditional algorithms might overlook.

Ant Colony Optimisation (ACO): ACO is inspired by the behavior of ants and how they find the shortest path to food sources. This algorithm simulates a 'colony' of artificial ants exploring routes.

The Link to Last-Mile Logistics

TSP is directly relevant to last-mile logistics – the final step in the delivery chain. At this stage, it's about delivering goods from a distribution center to the end-user as efficiently as possible. By applying TSP algorithms, businesses can optimise routes for delivery, reduce delivery time and costs, and improve customer experience.

Optimisation - A Perpetual Task

There is a "correct" solution to the Traveling Salesman Problem (TSP) in the sense that for a given set of cities and distances between them, there exists a shortest possible route that visits each city once before returning to the starting point.

However, the challenge lies in finding this solution, especially for larger datasets. For a small number of cities, an exact solution can be found relatively easily. Similarly, planning becomes considerably easier when dealing with a smaller number of vehicles.

But as the number of cities increases, it quickly becomes incredibly resource-intensive to find the exact solution due to the exponential increase in the number of possible routes.

Parameters Beyond Route Planning

So, what happens when you additionally have to consider other logistics paramaters, such as:

- Time windows at recipients

- Weight and volume restrictions between products

- Capacity constraints on vehicles

- Driver skills on certain routes

Doesn't this increase the complexity and make it even harder to find the most cost-effective solution?

What is paradoxical is that for a computer, the calculation actually becomes easier to solve. That is the opposite of for a human.

This is because computers, with a more precise and systematically defined set of parameters, can identify the correct solution with impressive precision.

But only 50% of delivery time is spent on the road. The remaining 50% is used for parking, unloading the vehicle, finding the recipient, and registering arrival.

How does a system take this into account? If this question piques your interest, we strongly encourage you to delve into "Time-Consuming Tasks on Delivery Stops"