What is Arc Routing Problem (ARP)? [Types and Importance]

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What is arc routing problem

What is Arc Routing Problem (ARP)?

The Arc Routing Problem (ARP) is a type of routing problem that includes finding the ideal routes for a fleet of vehicles to serve a group of clients. In this problem, the roads or arcs that connect the consumers are taken into account.

ARP wants to keep the distance to minimum that vehicles travel while providing services to customers. Organizations can save time, cut costs, and increase overall efficiency by addressing the Arc Routing Problem. Further, they can also get the benefits like quicker delivery times, less fuel prices, and higher customer satisfaction.

Overall, ARP is a significant issue in the optimization area with numerous real-world applications including trash collection, school bus route planning, package and newspaper delivery, security guard patrolling, and snow plowing.

Importance of Arc Routing Problem

The importance of the routing problem for vehicles lies in its ability to identify the most effective routes to travel to serve a group of consumers. Going ahead, let us learn about the importance of ARP in detail:

  • Arc Routing Problem can promote efficient transportation by optimizing the travel routes hence cutting down on trip time and fuel costs.
  • As a part of waste management, it is being used by municipalities to plan and optimize routes for garbage collection. 
  • By minimizing trip distances and fuel consumption, Arc Routing Problems can help to increase sustainability by lowering the carbon footprint of waste management and transportation activities.
  • Organizations can save money and boost their bottom line by optimizing routes, cutting down on travel time, and lowering fuel expenses.

After discussing the importance of the Arc Routing Problem, let’s take a closer look at different types of routing problems that fall under ARP. 

Types of Arc Routing Problem

There are various types of Arc Routing Problems, each with different traits and restrictions. Some of them are: 

1. Capacitated Arc Routing Problem (CARP)

CARP is a type of Arc Routing Problem that aims to service every customer while keeping in mind the limited capacity of the vehicles. This problem can be generally seen in garbage pickup, mail delivery, and food delivery processes. 

2. Split Delivery Vehicle Routing Problem (SDVRP)

SDVRP is a variation of ARP that allows vehicles to make numerous deliveries along their routes, either to the same client or to various customers. This issue occurs when a customer may need repeated delivery of various goods or when their overall demand surpasses the carrying capacity of a single truck. 

3. Pickup and Delivery Problem with Time Windows (PDPTW)

The goal of this problem is to serve every client within their time windows while limiting the overall distance traveled. Numerous situations, including those involving public transportation, the routing of school buses, and airport shuttle services, present this issue.

By comprehending different types of Arc Routing Problems and their unique limitations, we can create more efficient optimization algorithms and solutions for several real-life applications. 

How to Solve the Arc Routing Problem?

Numerous optimization strategies can be used to resolve the challenging Arc Routing Problem. Below are some of the common techniques for solving Arc Routing Problems:

  • Exact algorithms: These are algorithms that ensure the best solution to the issue will be found. They might not be useful for huge issue instances and can be computationally expensive. 

    The branch and cut approach, which uses a combination of branch and bound and linear programming techniques to achieve the ideal solution, is one illustration of an exact algorithm for the Arc Routing Problem.

  • Heuristics: Heuristics are algorithms that can solve problems fast and effectively, but they may not always lead to the best solution. For complex problems where exact techniques are impractical, heuristics might be helpful. 

    The nearest neighbor algorithm, which starts at a depot and chooses the closest client to visit next until all customers have been served, is an illustration of a heuristic for the Arc Routing Problem.

  • Metaheuristics: Metaheuristics are advanced algorithms that can be utilized to direct your search for a suitable answer. Finding effective solutions to difficult issues, like the Arc Routing Problem, can benefit from using metaheuristics. 

    The tabu search method is one instance of a metaheuristic for the Arc Routing Problem that effectively explores the solution space and identifies excellent solutions by combining neighborhood search with tabu list algorithms.

Overall, the selection of an algorithm will be influenced by the particular issue instance and the trade-off between computing speed and solution quality.


To sum up, the Arc Routing Problem (ARP) is a challenging issue especially in the logistics and transportation sector. But, the main issue is finding the most effective way to satisfy the requirements of the clients. For companies that depend on logistics and transportation, finding a solution to this issue can help in significant cost savings and increased productivity. 

It is impossible to overestimate the significance of the ARP because it is essential to many real-world applications. Businesses and organizations can make more educated decisions that can result in more productive and cost-effective logistics and transportation operations by comprehending the Arc Routing Problem and its numerous facets.

Author Bio
Rakesh Patel
Rakesh Patel

Rakesh Patel, author of two defining books on reverse geotagging, is a trusted authority in routing and logistics. His innovative solutions at Upper Route Planner have simplified logistics for businesses across the board. A thought leader in the field, Rakesh's insights are shaping the future of modern-day logistics, making him your go-to expert for all things route optimization. Read more.