What is Multi-depot Heterogeneous Fleet Vehicle Routing Problem (MDHFVRP)? [Key Concepts and Uses]

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What is multi-depot heterogeneous fleet vehicle routing problem

What is Multi-depot Heterogeneous Fleet Vehicle Routing Problem (MDHFVRP)?

The term “Multi-depot Heterogeneous Fleet Vehicle Routing Problem (MDHFVRP)” refers to a situation in which a fleet of vehicles with various capabilities and numerous depots are involved. 

The goal of MDHFVRP is to serve a group of customers with a variety of requests while minimizing the overall distance traveled by vehicles. The limitations on vehicle capacity and the obligation to return vehicles to their respective depots after completing their routes make the problem even more difficult.

In simpler terms, MDHFVRP is a complex routing problem of vehicles that entails determining the most effective routes for a fleet of vehicles while taking into account variables like vehicle capacity, client demand, and the location of depots. 

Key Concepts in MDHFVRP

It’s imperative to know some key concepts to comprehend the MDHFVRP. 

  • Depots: The starting and finishing points of the routes taken by the vehicles are depots. Additionally, they serve as the locations for servicing and maintaining vehicles.
  • Routes:  In the MDHFVRP, a route is a set of stops that a vehicle performs to provide service to clients. 
  • Multiple depots: In the MDHFVRP, there are frequently multiple depots, each of which has its own set of clients and vehicles to serve.
  • Heterogeneous fleet: The MDHFVRP vehicle fleet consists of many vehicle types with a range of capabilities and limitations, including size, weight, and fuel consumption.
  • Time windows: Customers occasionally have certain time limits during which they must be served. This might make the issue even more complicated.
  • Delivery/pickup: Depending on whether the objective is to deliver items to clients or pick up goods from them, the challenge can be further separated into delivery or pickup problems.
  • Constraints: In addition to vehicle capacity and time limits, there may be additional restrictions to take into account, such as limitations on the road network, necessary vehicle maintenance, and customer preferences.

Now that we have a basic idea about what Multi-depot Heterogeneous Fleet Vehicle Routing Problem is, let us find ways to solve this multi-depot vehicle routing problem.

Optimization Techniques to Solve MDHFVRP

Solving MDHFVRP is a complex problem that requires advanced mathematical techniques such as heuristic algorithms or metaheuristics. 

Some of the common techniques used to solve MDHFVRP include:

1. Tabu search

A heuristic search technique with a collection of moves that have already been investigated is put to a tabu list in tabu search to avoid going over them again in the future. By doing this, the algorithm can avoid becoming stuck at a local optimum.

2. Simulated annealing

Simulated annealing is inspired by the annealing process of metals. Starting at a high temperature enables the algorithm to accept less-than-ideal solutions. The algorithm grows more discriminating and begins to converge to the best outcome as the temperature drops.

3. Ant colony optimization

An artificial ant colony is employed in Ant Colony Optimization to scout out initial solutions. The ants communicate with one another by leaving pheromone trails, and they modify their behavior in response to the messages they receive. 

4. Genetic algorithms

To produce new offspring solutions, genetic algorithms employ the concepts of natural selection, crossover, and mutation on a population of candidate solutions. This process is repeated until the algorithm discovers an ideal or nearly ideal answer.

5. Branch and bound

Branch and Bound is an exact algorithm that promises to locate the best answer to the problem. It operates by methodically examining the potential solutions and eliminating any branches that cannot offer better solutions. 

To sum up, these techniques help to attain optimal or nearly ideal solutions that minimize the overall distance covered by the vehicles while providing service to customers.

Uses of Multi-depot Heterogeneous Fleet Vehicle Routing Problem

MDHFVRP has several real-life usages, including:

  • Trash Collection: To streamline the collection procedure in urban areas, trash collection vehicles can be routed to several collection stations. When it comes to waste collection, MDHFVRP can help cut down on the time and expense involved, ease traffic and noise pollution, and enhance the overall cleanliness of the city.
  • Package Delivery: MDHFVRP may assist package delivery businesses in saving time and money, by minimizing the number of delivery vehicles required and the distance traveled, By choosing routes that use the least amount of fuel and emit the fewest emissions, it can also assist lessen the environmental effect.
  • Public Transportation:  MDHFVRP can assist bus firms in public transportation with route optimization to guarantee that passengers have access to dependable, effective, and affordable transportation services. This can lessen traffic on the highways and raise the general quality of life for those who use public transportation.
  • Healthcare Logistics: Medical supply deliveries to hospitals and clinics, such as those of vaccinations or medical equipment, can be made more efficiently using MDHFVRP. This can save wastage and improve patient care by ensuring that healthcare providers have the supplies when and where they need them.

Overall, the MDHFVRP is a useful tool for enhancing transportation and logistics operations since it has a wide range of real-world usages and can be solved using sophisticated mathematical approaches


In conclusion, MDHFVRP is a challenging problem that optimizes a fleet of vehicles’ routes while taking capacity, demand, and depot location into account. It is essential for enhancing productivity and cutting down on trip time, which helps transportation businesses save money and improve customer happiness.

Advanced mathematical methods like heuristic algorithms or metaheuristics are needed to solve MDHFVRP to identify the best paths. However, the choice of technique is influenced by time constraints and task complexity.

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.