What is the Travelling Salesman Problem (TSP)?

The Travelling Salesman Problem (TSP) is the difficulty of calculating the fastest path for your delivery drivers, field sales people, and service personnel given a list of specified destinations.

Consider the following scenario to better understand the problem: A salesperson wants to sell his goods in a variety of locations. He knows the names of the places as well as their distances from one another.

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What is the fastest route for the salesman to travel so that he only has to visit each location once before returning to his starting point?

The question you just read is the well-known Travelling Salesman Problem. The TSP is an old computer science issue with repercussions in complexity theory and the P vs. NP debate. The Hamiltonian Circuit Problem is an expansion of this problem.

TSP generalizations include the Travelling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP). Let’s dig in.

Table of Contents

• About the Travelling Salesman Problem
• Why is it so hard to solve the Travelling Salesman Problem?
• Applications for the Travelling Salesman Problem
• Challenges faced by Travelling Salesmen
• How a Route Planner can Solve the Travelling Salesman Problem
• Final Thoughts on the Travelling Salesman Problem

About the Travelling Salesman Problem

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The traveling salesman problem (TSP) was first proposed in 1930 and is still one of the most studied combinatorial optimization problems today.

In 1972, Richard Karp proved that the Hamiltonian cycle problem, which is a type of combinatorial optimization problem, is NP-complete.

This indicates that the TSP was NP-hard, and that choosing the best route becomes exponentially more complex as the number of destinations increases.

For example, there are three possible routes if there are four cities; but, if there are six cities, there are 360 possible paths.

This is because scientists compute not just the most efficient but also the most effective technique.

The brute-force method is used in this technique, which involves calculating all possible solutions and then selecting the best one. To put it another way, be on the lookout for any potential salesmen detours.

Despite the fact that computing obstacles increase with each additional destination added to the itinerary, computer scientists have been able to identify the best solution to this problem for thousands of locations since the early 1990s.

Many towns and cities in a US state, for example, could be included in a large logistics provider’s delivery territory.

Figuring out the shortest route between all of the stops the car must make on a daily basis would save a lot of time and money.

Why is it so hard to solve the Travelling Salesman Problem?

In theory, the TSP is easy to state, and it can be solved by comparing all round-trip routes to find the shortest one.

However, when the number of cities grows, the number of round-trips required exceeds even the most powerful computers’ capabilities.

More than 300,000 round-trip permutations and combinations are available with ten cities.

There could be almost 87 billion possible ways in 15 cities.

In the early days of computers, computer scientists hoped that someone would come up with a better algorithm or strategy for solving the travelling salesman problem in a reasonable amount of time.

While scientists worked on specific cases, there was no effective problem solver in the form of a traveling salesman.

A one-size-fits-all algorithm is unlikely to be possible.

Applications of the Travelling Salesman Problem

The TSP is still in use across a wide range of sectors. Astronomy, computer science, and even car navigation have all benefited from the TSP’s efficient solutions.

The traveling salesperson problem can also be used to figure out how to move a laser when boring points into a PCB.

Astronomers employ TSP ideas to figure out how to move a telescope to get the smallest distance between stars in a constellation.

TSP can be used for internet planning, agribusiness, microchip production, and computer-generated art, among other things.

Challenges faced by Travelling Salesmen

When almost every salesperson wakes up, they consider how to make the most of their day.

They have a lot of scheduled appointments as well as a lot of last-minute ones with their customers.

The timetables of salespeople are rarely set in stone. As a result of this problem, salespeople are frequently compelled to retrace their steps and take longer routes to reach customers.

This lack of route planning results in missed appointments and opportunities.

Today’s salesperson faces traffic congestion, last-minute customer requests, and strict delivery window timings, in addition to the route challenges that plagued yesterday’s salesman.

Consider the following: Consider these questions if you felt the TSP from the math puzzle was difficult:

• What if you had to map out routes for multiple salespeople?
• What if you had a sales team working for you?
• What if you had to divide and conquer your team’s visits?
• What if your salespeople had a variety of appointment slots and you wanted to keep their routes as short, swift, and efficient as possible?

Consider the following situation: There might be over a million different route variations if your organization has 100 customer addresses and eight salespeople.

Running a simple algorithm that weighs every possible combination and finds the best one will take days, if not months.

This is a real-world issue, and route optimization can help with it.

A route optimizer‘s purpose is to find the fastest, shortest, and most fuel-efficient path between two points.

How a Route Planner can Solve the Travelling Salesman Problem

As your delivery service grows, route planning will inevitably become too difficult to manage with pen and paper or common technology like Google Maps or Waze. Sticking to timelines can be difficult, if not impossible, if route planning is done manually.

You won’t be able to manually factor in variables like customer time windows and weather conditions if you don’t use route planning software, and you’ll end up wasting a lot of time organizing routes.

Unexpected situations, such as traffic or construction, may make it difficult to keep your field agents on schedule and meet customers on time. As a result of the longer travelling time, you risk increasing your operating costs, which would most likely come in the form of wasted gasoline and salary.

Additionally, if your salespeople or delivery drivers are late for meetings, your clients will have a terrible first impression.

A reliable route optimization application like EasyRoutes can help you reduce driving time and fuel consumption in minutes by identifying the most efficient route for your team.

It’s a tool that solves the challenging Travelling Salesman Problem of figuring out the most efficient route to a location. The Travelling Salesman Problem has no human solution; finding the most efficient path is physically impossible, but utilizing modern routing software, it is possible to find a very efficient route or one that is more efficient than humans could ever be.

A route planner can help ensure on-time client contacts, cost savings, and field worker safety. This is due to the fact that we all have a predisposition to drive hastily to “make up” for lost time, which raises the risk of an accident.

A route optimizer will help save driving time for your field service workers, allowing them to spend more time with customers and enhancing your bottom line.

Final Thoughts on the Travelling Salesman Problem

There will be many more TSP-like situations with people and vehicles dealing with incorrect routes and delays if you look around.

• The couriers who deliver packages to your company’s location.
• The delivery staff will deliver fresh products on the same day that you place your order.
• The school buses that arrive on time every day and pick up and drop off your children at the same time.

Scientists have been seeking to solve problems like TSP for decades. We’ve gotten as close as we can with complex algorithms and easy-to-use route planner tools.

Learn more about EasyRoutes or install the EasyRoutes local delivery app on the Shopify App Store to start solving your own TSP today!