A salesman, a Chinese postman, and AI to optimize delivery routes

Route optimization in logistics has historically been a complex challenge due to the vast number of variables involved in the process. Factors such as traffic, delivery time windows, the distance between drop-off points, and vehicle capacity have all made the search for efficient solutions considerably difficult.

Traditionally, these challenges were tackled through heuristic approaches and business rules built from experience at first, and later with specialized software grounded in mathematical optimization algorithms.

Route planning complexity has been mathematically modeled through classic problems such as the Travelling Salesman Problem (TSP) and the Chinese Postman Problem (CPP).

Mathematical models in logistics

The Travelling Salesman Problem and the Chinese Postman Problem emerged from graph theory and combinatorial optimization in the mid-20th century. Both have since served as foundational models for the development of advanced algorithms applied to logistics and distribution. These problems describe common scenarios in transportation, mobility, and logistics planning.

• The Travelling Salesman Problem seeks the most efficient route to visit a set of points and return to the starting location, ensuring the path is optimal in terms of time, distance, and cost.
  
  —It's used in planning and optimizing deliveries across dispersed locations, including courier services, transport routes, or even manufacturing for production planning.
• The Chinese Postman Problem focuses on efficiently covering every street or segment of a network while minimizing total travel distance to save time and operational costs.
  
  —It's applied in sectors where uniform coverage is essential, such as postal delivery, waste collection, infrastructure maintenance, urban cleaning fleet management, mail distribution, or surveillance and patrolling.

With the rise of e-commerce and the need for faster, more efficient, and more sustainable logistics systems, AI has become a key tool for tackling both mathematical problems.

Advanced AI solutions for logistics optimization

While traditional algorithms can produce valid solutions to both TSP and CPP, their application at scale often becomes inefficient. The complexity of these problems tends to grow rapidly—often exponentially—as the number of variables increases.

This is where AI introduces advanced approaches that yield far more practical approximations in a fraction of the time:

• Deep learning: By leveraging neural networks trained on large volumes of historical data, AI identifies patterns and improves decision-making, effectively learning and accumulating courier practical knowledge.
• Reinforcement learning: This allows AI systems to explore multiple combinations and fine-tune their strategies through trial and error, improving route efficiency with each iteration.

By using these advanced techniques, AI can identify optimal routes quickly and with greater flexibility, adapting in real-time to dynamic variables like traffic conditions, weather changes, or fluctuating demand.

Integrating AI into logistics enhances operational efficiency and redefines distribution planning and execution.

AI’s impact on logistics beyond deliveries

Beyond route optimization and better delivery planning, AI transforms logistics across multiple layers. Its influence extends to demand forecasting, predictive maintenance, and process automation, enabling a logistics sector that is more agile, accurate, and sustainable:

• Demand forecasting: AI analyzes sales data, events, weather, and mobility trends to anticipate demand and allocate storage and delivery resources accordingly. It synthesizes data from a wide range of sources, including real-time population movement, tourism, and events, offering more precise and responsive forecasts.
• Warehouse optimization: Algorithms organize product layouts more effectively, reducing processing times and boosting operational throughput.
• Predictive maintenance: IoT sensors paired with AI detect early signs of equipment failure or wear in vehicles and machines, minimizing costs, unplanned downtime, and disruptions.
• Automation and computer vision: Technologies like smart glasses and camera systems streamline goods handling and improve warehouse safety protocols.
• Sustainability: Reducing unnecessary routes and optimizing energy usage lower logistics sector environmental impact. Given that logistics accounts for 30% of EU's final energy consumption, AI plays a critical role in minimizing travel and maximizing resource efficiency.

Success Story: Smart Steps in Infra Brasil

In logistics, understanding mobility is crucial to streamlining distribution and improving operational performance. Analyzing the movement of people, vehicles, and goods enables companies to quickly adapt to changing conditions and anticipate market demands.

At Telefónica Tech, we worked with Brazilian logistics firm Infra SA to optimize their transport network using our Smart Steps platform. By analyzing mobility data, Infra SA reduced operational costs and CO₂ emissions, significantly improving logistics efficiency and sustainability.

This case illustrates how integrating AI and Big Data solutions can meaningfully transform logistics management, unlocking economic, operational, and environmental benefits. Learn more →

Conclusion

AI has become a powerful tool for solving complex logistical problems. While it may not always find mathematically perfect solutions to Travelling Salesman's or Chinese Postman's problems, it delivers efficient and adaptable routing strategies. Its influence reaches far beyond route planning, including demand prediction, warehouse automation, and the sector's overall sustainability.

The future of logistics will be shaped by AI's continued evolution, with increasingly sophisticated models capable of integrating real-time data and optimizing ever-more complex transport networks.

In a world where productivity, efficiency, and sustainability are no longer optional but imperative, AI is already transforming how goods move across the supply chain—from manufacturing and inter-process transitions to last-mile delivery.