What is Capacitated Arc Routing Problem (CARP)? [ Challenges and Uses]

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What is capacitated arc routing problem

What is Capacitated Arc Routing Problem (CARP)?

Capacitated Arc Routing Problem (CARP) is a type of routing problem that aims to efficiently provide services to the customers, considering the vehicle capacity and the routing constraints.

In other words, CARP involves planning the routes in a way that minimizes the total distance traveled by the vehicle. This complex problem is generally faced by the transportation and logistics industries, including public transportation, waste collection or disposal, and postal or courier services.

Solving the CARP requires a combination of mathematical algorithms and techniques, including exact algorithms, heuristic algorithms, and metaheuristic algorithms. Further, solving the routing problems in vehicles can have a positive impact on resource utilization, operational costs, and customer satisfaction. 

Key Components of CARP

Capacitated Arc Routing Problem (CARP) mainly includes the below three components:

1. Customers

In CARP, customers are the places that the vehicle is supposed to visit. These places might be people’s homes, places of business, or other interesting places. Every consumer has a unique demand, which is an estimate of the volume of products or services that must be transported to that place. 

2. Vehicles

It is the collection of vehicles that is available to service consumers. Each vehicle has a specified capacity, which denotes the number of maximum products that can be transported. The vehicles might have varying capacities, and some might be more effective than others or have various speed limitations.

3. Constraints

CARP considers two types of constraints: vehicle capacity and routing constraints. Vehicle capacity constraint describes the maximum carrying capacity of the vehicle, whereas the routing restriction is the limitation that each vehicle is supposed to take a specified route to serve the designated consumers.

Now that we are aware of the components of CARP, let us find out how this routing problem can be resolved. 

How is Capacitated Arc Routing Problem Solved?

Even though CARP can be difficult to solve, numerous mathematical algorithms and techniques can be used to find optimal or near-optimal solutions. Here are the commonly used techniques:

  1. Heuristics algorithms are used to address problems through a set of rules or principles. They are frequently employed when an exact solution is impractical or when the size of the problem precludes the use of an exact approach. For example, Clarke & Wright Savings Algorithm, and  Nearest Neighbor Algorithm.
  2. Metaheuristics algorithms are used to find the optimal solution to a problem through a set of rules.  This algorithm is usually utilized when a heuristic algorithm cannot be used plus an exact algorithm is not attainable. For example, Tabu Search and Genetic Algorithm.
  3. Exact algorithms are the one that guarantees the optimal solution to any problem. This algorithm is employed when the problem is manageable and can be resolved in a fair amount of time. For example, Cutting Plane Algorithm, and Branch & Bound Algorithm.

Overall, the selection of an algorithm depends on the particulars of the problem, including its size,  and quantity of the constraints. 

Real-world Challenges of CARP

Although the Capacitated Arc Routing Problem (CARP) has many advantages, there are many real-world challenges, such as:

1. Safety and reliability

Safety and reliability are essential elements in real-world situations. The safety of the drivers and the general public must be guaranteed by the routes produced by CARP algorithms. The system must also be dependable and capable of handling unforeseen circumstances like malfunctions or accidents. To maintain the system’s safety and reliability regular testing and maintenance are necessary.

2. Dealing with uncertainties

Uncertainty is a common feature of real-world surroundings, which can include unforeseen traffic backups, road closures, and weather conditions. Developing reliable and effective routes for vehicles might be challenging due to these concerns. However, these uncertainties can be managed by CARP algorithms and adjust the routes accordingly. 

3. Accurate data

The successful implementation of CARP needs to have accurate and current data. This comprises details about the locations of the customers, the vehicle’s capacity, the trip timings, and the traffic patterns. Accurate data can be hard to find and keep up with, especially in circumstances that change quickly and are dynamic.

4. Resource limitations

Resources like money, time, and labor may be limited when CARP is put into practice. Companies may need to spend money on specialist hardware and software, employ qualified staff, and set aside enough time and money to create and maintain the system. This could be a big problem for tiny enterprises with limited resources.

Despite the difficulties, CARP continues to be a crucial tool for optimizing vehicle routing and enhancing efficiency in numerous industries.

Uses of CARP

Capacitated Arc Routing Problem (CARP) is used in various industries to plan efficient routes for vehicles, minimize costs and maximize performance. Some of the practical applications include:

  • The waste collection and disposal companies use CARP to plan waste collection routes for their vehicles. 
  • CARP can be employed by postal and courier services to map out the most effective routes for their delivery vehicles. 
  • Companies that offer public transportation services use CARP to create effective routes for trains and buses.
  • Online retailers and food delivery services plan routes for their vehicles, ensuring timely and efficient delivery to customers.
  • For fast and effective service to individuals in need, emergency services like ambulance and fire departments use CARP to organize their response routes.
  • CARP can be used to streamline the movement of goods between locations by speeding up delivery and cutting down on transportation costs.

Overall, CARP is a useful tool for any business or organization that has to manage and route vehicles effectively. 


To conclude, the Capacitated Arc Routing Problem (CARP) is a challenging routing problem that requires determining the best route to service a group of clients considering vehicle capacity and routing restrictions. This problem has numerous real-world applications, from waste collection and postal services to public transportation.

CARP is becoming a more crucial tool for businesses and organizations as the demand for effective and affordable transportation solutions rises. Additionally, the possible uses for CARP are nearly endless because of ongoing technological advancements, and it will surely continue to play a significant part in determining the future of transportation logistics.

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