Traveling Salesman Problem (TSP) and the Role of AI in Solving it

Travelling Salesman Problem: It's more than cost-efficiency

Updated: Apr 19, 2022

Traveling is a prerequisite for all salespersons. Since the Covid-19 pandemic, businesses are seriously working on expanding their customer base with a strong e-commerce presence. But for the growth and expansion of any business, traveling is a must. 

When salespersons begin their day, they aim to make the most of it through their business travels. Every salesperson deals with scheduled and last-minute appointments with their customers. Their timetables are rarely fixed.

Because of this, salespersons are forced to take longer routes to reach their customers. By taking longer routes, they miss crucial appointments and valuable business opportunities. This algorithmic challenge that salespersons face while traveling to multiple customer locations is famously known as the Traveling Salesman Problem.

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What is Traveling Salesman Problem (TSP)? 

What is Traveling Salesman Problem?

The solution to the Traveling Salesman Problem (TSP) is in finding the shortest possible route to several cities/destinations and returning to where you started. TSP is a complex issue given the numerous delivery-based constraints like traffic, last-minute customer requests, and strict delivery window timings. 

Solving the TSP challenge can make supply chains efficient and cut down logistics costs. In short, TSP is an easy problem to define, but a difficult one to solve. 

Example: Imagine that there are three possible routes to complete deliveries in six cities. In six cities there may be 360 possible routes. You should not only find the most efficient path but the one that works. You have to work out every possible route and pick the best one. 

The computational difficulty increases or multiplies as you add cities to the itinerary. Since the early 90s, people have been trying to solve this problem. 

There are several industries that counter the Traveling Salesman Problem. Here are some of them:

  • Astronomy
  • Computer science
  • Car navigation
  • Agri-business
  • Airline crew scheduling
  • Computer-generated art
  • Internet planning
  • Logistics planning and scheduling
  • Microchip production

Why is the Traveling Salesman Problem crucial to solve?

The Traveling Salesman Problem is a serious challenge for the logistics and supply chain industry. With multiple vehicles, more cities and multiple sales professionals, TSP gets tougher to crack. Not solving the TSP makes it difficult for sales professionals to efficiently reach their customers, and lead to a fall in business revenues.

Solving traveling salesman problems benefit businesses in numerous ways:

  • Saves fuel and reduces the hours traveled by the sales and field professionals 
  • Minimizes the distance traveled, thereby reducing the carbon footprint considerably
  • Timely meetings with clients and on-time delivery of goods 
  • Elevate last-mile customer experience for delivery and field service businesses

Why is Traveling Salesman Problem challenging to solve? 

Why is Travelling Salesman Problem challenging to solve?

It is easier to solve TSP in theory because you have to find the shortest route for every trip within a city. But it becomes difficult to solve TSP manually as the number of cities increases. The permutations and combinations for 10 cities are multifold. 

Adding five more cities can multiply these permutations and combinations. Hence, it may take months to solve this problem.

It’s impossible to find an algorithm that solves every single TSP problem. There are also some constraints that make TSP more challenging to solve:

  • No automated records of scheduled and last-minute business appointments 
  • Traffic congestion
  • Sudden change of routes 
  • Increasing number of last-minute business appointments 
  • Stricter customer time windows 
  • Rising operational fleet costs

All these constraints give a clear insight that TSP is a real-world problem. It is impossible to solve this challenge with even the best of your manual efforts. Thus, it is necessary to harness the power of technology to manage the TSP problem efficiently.

How does Artificial Intelligence technology help in solving the Traveling Salesman Problem? 

Solving the Travelling Salesman Problem using AI

Modern enterprises want to attract customers by providing superior service. A customer that interacts with an enterprise for a business opportunity wants the business to value their needs. 

Most customers make business decisions based on how salespeople from an enterprise respond to their requirements. The crucial aspect that they look out for in a salesperson is whether they are able to be on time for business appointments. A salesperson that travels to multiple locations should ensure they attend business appointments on time.

The Traveling Salesman Problem makes it way more difficult for salespersons to make their business appointments on time and reach their sales targets. With a lot of complexities involved in routes traveled, it is necessary for them to employ the right technology to counter them. Artificial Intelligence (AI) plays an active role in helping businesses counter route inefficiencies and solve TSP.

AI combines human intuition with complex mathematics in real-time. It analyzes a massive amount of data clearly and quickly. It mainly helps a modern enterprise to make operational, strategic and tactical decisions.

Here’s how AI solved TSP in many modern enterprises. 

Makes optimized decisions for each vehicle and route

With increasing business appointments, it would be difficult for enterprise businesses to control operational fleet costs. It is highly challenging to manage crucial business appointments without the help of technology, especially when the business handles multiple vehicles and multiple salespersons.

AI technology helps operation managers in a business to prepare and assign optimal sales schedules for their workforce. By taking into account vicinity, vehicle capacity, customer time window, skills of sales professionals, driver skills and so on, it generates optimal appointment schedules. These optimal schedules help the businesses strictly adhere to the Service Line of Agreement (SLA)

Read:     The Definitive Guide to Logistics Route Optimization

Saves fuel and labor costs

The average fuel cost per mile fell from $0.433 in 2018 to $0.308 in 2020. – An Analysis of the Operational Costs of Trucking: 2021 Update 

Since the outbreak of the Covid-19 pandemic, the fuel cost tumbled to record levels. As we started moving towards a post-pandemic stage globally, the fuel costs started rising steadily. The Ukraine-Russia war in 2022 and its trade shocks have resulted in skyrocketing fuel prices, making fuel the larger part of operational costs for carriers.

The increasing number of appointments on a daily basis for salespersons makes it difficult for businesses to minimize fuel costs.

Employing the right technology like AI will help salespersons complete the maximum number of customer appointments by traveling a minimal distance. Its optimally allocated route plans reduce the traveling time and help businesses avoid wastage of fuel and labor costs.

Recognize the right addresses

When you are in a rush to complete your sales visits, unclear addresses can induce delays. If the driver is going to ride in an unfamiliar area, delays will increase. These delays can even cause missed appointments.

By using an AI application like route optimization software, enterprise businesses can avoid delays caused due to incorrect addresses. Its competent geocoding capabilities convert unclear or incomplete text addresses into geographical coordinates, thereby reducing the chances of reaching wrong customer locations.

Reduces cost per mile

The average cost per mile of trucks reduced from $1.821 in 2018 to $1.646 in 2020. – An Analysis of the Operational Costs of Trucking: 2021 Update, American Transport Research Institute 

The average cost per mile for trucks has reduced due to a fall in demand resulting from the COVID-19 pandemic. But the rising fuel costs and the world moving towards a post-pandemic period may increase the average cost per mile for trucks.

Modern enterprise businesses want salespersons to reach their targets without increasing operational fleet costs. In order to attain their sales targets, they should attend more business appointments. Salespersons need assistance from technology like AI to counter this situation.

AI technology with its algorithms factors business goals and delivery constraints to come up with efficient routes. Its optimal route recommendations enable salespersons to take the cost-minimizing route, thereby attending a maximum number of business appointments in a day and minimizing cost per mile. 

Improves productivity 

Deadhead miles represented 20.6 percent of miles among all carriers. – An Analysis of the Operational Costs of Trucking: 2021 Update, American Transport Research Institute.

What happens when salespersons attend business appointments in locations where they may not have many opportunities? It results in deadhead or empty miles. Empty miles kill the productivity of the fleet, and drive up operational costs considerably. 

AI technology coupled with data insights helps modern enterprise businesses analyze their past performance of sales appointments. It helps them identify business opportunities that incur huge costs and work out new ways to counter them. Based on historical data, it assists stakeholders of a business to rightsize their fleet requirements and direct them to locations where higher demand is expected. The past data records and predictive capabilities of AI help them implement strategies that improve productivity of their sales professionals.


With modern enterprise businesses struggling from incorrect routes and delays, it has become highly-crucial to solve TSP situations. Scientists have been working on solving the TSP problem for decades. But the modern AI-backed routing software has gone closer towards solving traveling salesman problems with their complex algorithms and enhanced route planning capabilities.

Locus routing software is the best-in-class tool that has helped many enterprise businesses solve their traveling salesman problems. Its algorithms help sales professionals generate the most efficient schedules for any complicated routes without any manual interference. By employing its AI capabilities, you can increase the number of appointments with your customers by traveling a minimal distance, thereby making sales visits more optimal.

To build the most efficient routes for your sales schedules and counter TSP effectively, try a demo with Locus now!

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