# What is Periodic Vehicle Routing Problem (PVRP)? [Definition and Key Challenges]

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• Last Update: May 23, 2023

## What is Periodic Vehicle Routing Problem (PVRP)?

Periodic Vehicle Routing Problem is an optimization problem that involves finding the most optimal set of routes for a fleet of vehicles to repeatedly serve a set of clients over a specified time period, such as a day or a week.

This type of problem is common for industries that require contacting clients on a regular basis to deliver goods or provide services. For example, waste management, newspaper distribution, and food and beverage delivery.

PVRP is different from other variations of the Vehicle Routing Problem as the vehicles are bound to follow fixed scheduled deliveries rather than flexible deliveries. This is why the problem becomes more challenging and complex to solve because the routes need to be optimized in terms of both distance and time.

## Key Challenges in Solving the Periodic Vehicle Routing Problem

Unlike other forms of the routing problems for vehicles, PVRP has its own challenges. Some of them include:

### 1. Multiple constraints

Finding the best solution for PVRP is challenging because of its several constraints, such as vehicle capacity, time windows, and periodicity.

### 2. Time-consuming computations

It is difficult to compute optimal answers in a reasonable time since the number of PVRP’s solutions grows exponentially with the magnitude of the problem.

### 3. Changing requirements

PVRP is a dynamic problem; client demands, vehicle availability, and road conditions change over time. As a result, solutions must be updated frequently to take into account the most recent developments.

To conclude, the most difficult part of solving the PVRP is juggling the competing needs of route efficiency optimization, time considerations, and complexity reduction.

## Approaches to Solving the Periodic Vehicle Routing Problem

Solving the Periodic Vehicle Routing Problem (PVRP) comes with several approaches, each having its advantages and disadvantages.

• Exact algorithms offer the best results but can be computationally intensive and time-consuming. For example: branch and bound or integer linear programming,
• Metaheuristics offer a more effective and scalable method but may forgo optimality in favor of speed. For example: genetic algorithms or simulated annealing.
• Hybrid approaches are the ones that incorporate components of exact algorithms and metaheuristics intending to establish a balance between speed and accuracy.

These approaches have been successfully applied in several fields, from waste management to healthcare. For example, a study in the Netherlands used a hybrid approach to optimize the routes of home healthcare providers, which led to significant cost savings and improved patient outcomes.

Overall, the choice of approach will be determined by the particulars of the problem as well as the tools available for computation and optimization.

## Benefits of Solving the Periodic Vehicle Routing Problem

Solving the Periodic Vehicle Routing Problem (PVRP) provides several benefits, which include:

• Better efficiency: Businesses can decrease the time and resources required to accomplish deliveries or service visits by optimizing vehicle routes and schedules, thus leading to cost savings and enhanced production.
• Greater adaptability: The periodic vehicle routing systems offer the ability to adjust to shifting demand patterns, traffic conditions, and other variables, thus increasing the agility and reactivity of the companies.
• Improved customer service: Effective routing can lead to faster and more reliable delivery times, increasing customer satisfaction and loyalty.
• Increased safety:  Optimized routes and schedules can improve overall safety and lower liability by reducing the tiredness of drivers and lowering the chance of any type of accident.
• Reduced environmental impact: Periodic vehicle routing systems can aid in lowering carbon emissions and supporting sustainability objectives by reducing the distance traveled and optimizing the usage of fuel.

This is how resolving vehicle routing problems can assist businesses in boosting their revenue, enhancing customer satisfaction, and advancing their sustainability and safety objectives.

## Common Uses of the Periodic Vehicle Routing Problem

Periodic Vehicle Routing Problem (PVRP) has several real-world uses in numerous industries, such as:

1. Transportation and logistics: PVRP is frequently used in logistics and transportation to streamline vehicle delivery routes. It is utilized to ensure that things are transported to their final destinations most practically and economically.
2. Waste management: PVRP is used in the waste management sector to improve waste collection and transportation. This involves planning routes for garbage trucks more effectively so that rubbish is collected from homes and businesses.
3. Healthcare: It is used in the healthcare sector to optimize the routes of ambulances and other emergency vehicles to make sure that patients get quick, effective medical care.
4. Retail and e-commerce:  PVRP is employed to ensure the fulfilment of online orders or store restocking. The optimized delivery routes make sure that clients receive their orders in a timely and effective manner.
5. Field service management: PVRP is utilized to streamline the routes used by service vehicles like maintenance and repair trucks to make sure technicians are sent out to customer locations as quickly as possible.

Some other uses of PVRP include home delivery services, school transportation, postal services, and many more. Hence, by optimizing vehicle utilization and delivery routes businesses can improve their operational efficiency.

## Conclusion

PVRP is a classic vehicle routing problem with several uses in the field of transportation and logistics. It entails figuring out the best routes for delivery drivers to take to serve a group of clients that need regular deliveries or pickups while taking into account restrictions like time windows and vehicle capacity.

The PVRP will continue to be a crucial and relevant topic of research as companies look for methods to improve their processes and cut expenses. Businesses can enhance their bottom line and gain a competitive advantage by better understanding the problem and its characteristics as well as the many options to tackle it.

Author Bio
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.

https://www.upperinc.com/glossary/route-optimization/capacitated-vehicle-routing-problem-cvrp/