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What is the Travelling Salesperson Problem (TSP)?

Breaking down the Travelling Salesperson Problem (TSP), a classic optimization issue in computer science that involves finding the shortest possible route through a set of locations.

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The Travelling Salesperson Problem (TSP), or sometimes known as the Travelling Salesman Problem, is the challenge of determining the quickest path for your delivery drivers, field sales representatives, and service reps given a list of specific locations.

Let’s look at an example to better grasp the issue: A salesman wants to sell his products in a few different places. He is familiar with the names of the locations as well as the distances between them.

What is the quickest route for the salesman to take to visit each place only once before returning to the starting point?

The problem you just read is the well-known problem of the travelling salesperson.

The TSP is an old problem in computer science that has ramifications in complexity theory and the P versus NP dilemma. It is an extension of the Hamiltonian Circuit Problem.

The Travelling Salesperson Problem and the Vehicle Routing Problem (VRP) are also generalizations of TSP.

Below, we go over the Travelling Salesperson Problem in great depth.

Table of Contents

  • About the Travelling Salesperson Problem
  • Why is it so difficult to solve the Travelling Salesperson Problem?
  • Applications for the Travelling Salesperson Problem
  • Challenges faced by Travelling Salespeople
  • How to Solve the Travelling Salesperson Problem by Using a Route Planner
  • Final Thoughts on the Travelling Salesperson Problem

About the Travelling Salesperson Problem

Even though the travelling salesman problem (TSP) was first proposed in 1930, it remains one of the most researched combinatorial optimization problems today.

Richard Karp established in 1972 that the Hamiltonian cycle problem, a class of combinatorial optimization problems, was NP-complete.

This suggests that the TSP was NP-hard, and that determining the optimum route becomes exponentially more difficult as additional destinations are added to the issue.

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

This is due to the fact that scientists compute not only the most efficient approach, but also the one that works.

This algorithm employs the brute-force method, which entails calculating every possible solution and then selecting the best one. To put it another way, look for every possible twist and turn the salesman might take.

Since the early 1990s, computer scientists have been able to determine the ideal solution to this problem for thousands of cities, despite the fact that computing challenges rise with each additional city added to the itinerary.

Many towns and cities in a US state, for example, could be included in the delivery region of a large logistics provider.

It would save a lot of time and money to figure out the shortest route between all of the stops the vehicle needs to make on a daily basis.

Why is it so difficult to solve the Travelling Salesperson Problem?

The TSP is simple to state in theory, and it can be solved by checking all round-trip routes to identify the shortest one.

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

With ten cities, more than 300,000 round-trip permutations and combinations are possible.

With 15 cities, there might be more than 87 billion different paths.

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

While scientists progressed with specific cases, there was no effective travelling salesman problem solver accessible.

It’s likely that a one-size-fits-all algorithm isn’t even possible.

Applications for the Travelling Salesperson Problem

The TSP is still used in a variety of industries. The TSP’s efficient solutions have been used to astronomy, computer science, and even vehicle navigation.

The travelling salesperson problem can also be used to determine how a laser should move when boring points into a PCB.

TSP ideas are used by astronomers to calculate the movement of a telescope for the shortest distance between stars in a constellation.

TSP can also be used for internet planning, agribusiness, microchip manufacturing, and computer-generated art.

Challenges faced by Travelling Salespeople

Almost every salesman thinks about how to make the most of their day when they get up.

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

Salespeople’s schedules aren’t usually set in stone. Salespeople are frequently forced to retrace and take longer routes to reach customer locations as a result of this flaw.

Missed appointments and opportunities come from this lack of route planning.

In addition to the route issues that plagued yesteryear’s salesperson, today’s salesperson encounters traffic congestion, last-minute customer requests, and strict delivery window timings.

Try this: If you thought the TSP from the mathematics puzzle was challenging, consider these questions:

  • What if you had to plan routes for more than one salesperson?
  • What if you had a sales staff on your side?
  • What if you had to divide and conquer the visits with your team?
  • What if salespeople had varied appointment slots and your goal was to maintain their routes as short, quick, and efficient as possible?

Think about the following scenario: If your company has 100 customer addresses and eight salesmen, there could be over a million possible route permutations.

It will take days, if not months, to run a rudimentary algorithm that weighs every conceivable combination and selects the best one.

That’s a real-world problem, and that’s where route optimization comes in.

The goal of a route optimizer is to determine the quickest, shortest, and most fuel-efficient route between two points.

How to Solve the Travelling Salesperson Problem by Using a Route Planner

Route planning will inevitably become too complex to manage with pen and paper or common technologies like Google Maps or Waze as your delivery business grows. If route planning is done manually, sticking to schedules may be difficult, if not impossible.

Without route planning software, you won’t be able to manually factor in variables like customer time windows and weather conditions, and you’ll end up spending a lot of time arranging routes.

Unexpected circumstances, such as road congestion or construction, might make keeping your field reps on schedule and meeting consumers on time difficult. You also risk boosting your operating costs, which would most likely come in the form of wasted gasoline and salaries as a result of the lengthier driving time.

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

In a matter of minutes, a trustworthy route optimization program like EasyRoutes will help you decrease driving time and fuel consumption by determining the most effective route for your team.

It’s a tool that effectively addresses the difficult Travelling Salesperson Problem of determining the most efficient path to a location. The Travelling Salesperson Problem has no human answer; finding the most efficient path is physically impossible, but it is conceivable to find a highly efficient route or one that is more efficient than humans could ever be by using advanced routing software.

A route planner will assist in ensuring on-time customer encounters, cost savings, and the safety of field workers. This is because we all have a tendency to drive quickly in order to “make up” for lost time, which increases the danger of an accident.

A route optimizer will also cut down on your field service personnel’ driving time, allowing them to spend more time with clients and improving your bottom line.

Final Thoughts on the Travelling Salesperson Problem

If you look around, there will be many more TSP-like situations with people and vehicles dealing with erroneous routes and delays.

  • The couriers who are delivering packages to your place of business.
  • The delivery team is sending you fresh groceries the same day you placed your purchase.
  • The school buses that always arrive on schedule and pick up and drop off your children at the same time each day.

For decades, scientists have been attempting to solve challenges like TSP. Complex algorithms via easy-to-use route planner apps are the closest we’ve come.

About Roundtrip

Roundtrip's mission is to equip every business with the software tools they need to deliver products to their customers in a delightful way. Thousands of worldwide choose EasyRoutes to power their local deliveries across dozens of product categories, from meal kits and groceries to coffee, cupcakes, kibble, and so much more. Our easy-to-use route planning and delivery optimization app is certified Built for Shopify, a two-time Shopify staff pick, and the top rated local delivery app on the Shopify App Store.

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