What Is the Multi-Depot Vehicle Routing Problem? [+How to Solve It]

This article is a super in-depth guide to the Multi-Depot Vehicle Routing Problem.

If you own and operate a delivery or field service than you know how hard it is to route multiple vehicles to and from multiple depots and customer locations.

That's why in this article, we explain exactly:

• What is the Multi-Depot Vehicle Problem
• Why it's so difficult to solve
• How it's solved (and how you can do it too)
• And why you should consider doing it.

So if you want to learn the answers to these questions, and discover a proven way to navigate the complexities of this logistical issue, read on.

Let’s start.

What Is the Multi-Depot Vehicle Routing Problem?

Multi-Depot Vehicle Routing Problem (MDVRP) is a logistics problem that involves finding the most efficient route to transport goods between multiple different pickup and delivery locations.

The problem is challenging to solve because it takes into account numerous stops, vehicles, and constraints including time windows, vehicle capacities, and driver schedules.

Key Terms Related to the Multi-Depot Vehicle Routing Problem

Before you get a handle on the Multi-Depot Vehicle Routing Problem, you should be familiar with a few terms. Here’s what you need to know to get started:

• Depot: A facility where vans, trucks, and other vehicles come to pick up or drop off goods. This can mean a warehouse, storage facility, retail store, kitchen, service headquarter, fulfillment center, and many other locations where you store goods for transportation.
  
  
• Vehicle: A method of transportation that’s used for moving goods from one depot to another (in this context). This can mean cars, vans, trucks, but also bikes, motorcycles, and other vehicles.
  
  
• Customer: A person, business, or organization that receives goods or services.
  
  
• Routing: The process of planning the most efficient route for a vehicle to travel between two or more depot or customer locations. Efficiency is determined by the distance, time, money, fuel, and other factors spent to complete a route.
  
  
• Scheduling: The process of determining the time when items will be picked up from a depot or customer, dropped off to a depot or customer, or services provided at the customer’s location.

Restrictions That Can Affect MDVRP Level of Complexity

On its own, the Multi-Depot Vehicle Routing Problem already has a high degree of complexity: Mapping routes for multiple vehicles, multiple depots, multiple tasks, and multiple routes. 

But this isn’t the end.

Due to the demands of modern delivery and field service operations, planners add new restrictions to routes. Which increases their efficiency. But makes the MDVRP even more complicated to solve.

These restrictions encompass a wide range of considerations that impact every aspect of the routing process, from depot selection to delivery scheduling.

Here are all of the restrictions that you may encounter:

• Depot Location: The physical site of a depot influences routing efficiency, as vehicles must travel to and from these locations to begin and end their routes. This impacts overall logistics complexity.
  
  
• Pickup/Dropoff Location: The specific addresses where goods are picked up and delivered determine the sequence and efficiency of routes, considering factors like proximity and traffic conditions.
  
  
• Time Windows: Time windows specify the allowable times for pickups and deliveries. Adhering to these constraints ensures timely service and customer satisfaction while minimizing delays and penalties.
  
  
• Driver Schedules: Driver schedules dictate when and for how long they can operate vehicles. Optimizing routes must align with these schedules to avoid overtime, ensuring compliance with labor regulations.
  
  
• Vehicle Capacity: The maximum load a vehicle can carry affects the number and size of goods that can be transported in one trip, directly influencing route planning and efficiency.
  
  
• Vehicle Load Limit: This constraint ensures vehicles do not exceed their designed load capacity, preventing potential damage to the vehicle and ensuring safe transportation.
  
  
• Vehicle Capabilities: Vehicles differ in capabilities such as size, special equipment, or fuel type, impacting which tasks they can undertake effectively and efficiently.
  
  
• Vehicle Speed: The speed at which vehicles can travel affects route planning by influencing travel times between locations, directly impacting delivery schedules and overall efficiency.
  
  
• Zones: Dividing the operational area into zones determines which vehicles and drivers are eligible to service specific areas, optimizing logistics by assigning tasks based on proximity and efficiency.
  
  
• Route Duration: Setting a maximum time limit for routes ensures drivers operate within predefined schedules, balancing efficiency with timely delivery requirements.
  
  
• Route Distance: Limiting the distance between stops optimizes fuel efficiency and reduces vehicle wear and tear, ensuring cost-effective and sustainable logistics operations.
  
  
• Travel Time: Accounting for travel time between stops ensures realistic route planning, considering factors like traffic conditions and road closures that affect delivery schedules.
  
  
• Stop Priority: Prioritizing stops ensures critical deliveries are made on time, optimizing customer satisfaction and operational efficiency by managing task urgency effectively.
  
  
• Stop Order: Optimizing the sequence of stops minimizes travel distances and time, maximizing vehicle productivity and reducing operational costs in multi-stop delivery scenarios.

Challenges of Solving the Multi-Depot Vehicle Routing Problem

It's crucial to acknowledge the inherent challenges that come with the Multi-Depot Vehicle Routing Problem. But knowing what they are is half the battle in the first place.

Here are the most common challenges when it comes to solving MDVRP:

1. Vehicle Routing

Vehicle routing is the core challenge of MDVRP. But it doesn’t just involve planning a route from point A to point B to point C… No!

Instead, the main issue involves planning and optimizing routes while considering factors like vehicle capacity constraints, pickup and dropoff time windows, and delivery locations. 

With so many factors to consider, it’s almost impossible to generate complex routing solutions manually.

In fact, it requires high computational intensity due to its NP-hard nature (nondeterministic polynomial time). 

That’s why modern route optimization software relies on various optimization methods and heuristics. Including methods like genetic algorithms, tabu search, and ant colony optimization.

This is a proven way to tackle this challenge.

2. Task Assignment

Assigning tasks to vehicles in the most efficient way is another HUGE hurdle to solve the Multi-Depot Vehicle Routing Problem.

Basically:

It adds another level of complexity because of the additional factors that you have to consider.

These may include: task locations, task priority, task order, task time windows, and the field service or delivery zones that tasks belong to.

Solving it utilizes another set of optimization methods such as genetic algorithms, simulated annealing, and branch-and-bound algorithms.

3. Depot Location and Allocation

Vehicle route efficiency depends on the number, locations, and allocation of depots. 

That’s why it’s super important to optimize depot locations to plan better routes. 

In the same way, it’s also key to distribute vehicles and other resources to depots effectively. 

These challenges are resolved using methods such as genetic algorithms, simulated annealing, and tabu search.

4. Dynamic Nature of the Problem

MDVRP is inherently dynamic due to changing pickup and delivery locations and associated constraints over time.

This dynamic nature poses challenges in maintaining an optimal solution continuously.

Approaches such as SaaS route optimization and real-time scheduling can address this challenge effectively.

5. Real-World Constraints

External factors such as congestion, road conditions, and weather force practical constraints on MDVRP. That can significantly impacting system efficiency.

Adding these constraints to the problem means you'll have to account for them when coming up with a solution.

That's why methods using techniques like mixed-integer linear programming, constraint programming, and metaheuristic algorithms are essential for generating effective solutions.

How Is the Multi-Depot Vehicle Routing Problem Solved?

To ensure efficient operations, careful planning and optimization is essential for solving the Multi-Depot Vehicle Routing Problem. 

Here are several methods and algorithms that have been developed to tackle the problem:

• Genetic Algorithm: This method applies evolving principles to find optimal solutions. For example, the gardening industry uses this method to streamline landscaping professional scheduling and routing. Just like one of our clients: Crocus.
  
  
• Ant Colony Optimization: This method is inspired by how ants find the shortest path to food sources. This method has been applied, for instance, in optimizing ambulance routing for multi-depot emergency medical services. It’s one of the ways the NHS cuts manual work by 90% in the UK with eLogii.
  
  
• Tabu Search: Tabu Search is also widely used in a wide array of industries. This method employs new criteria to avoid revisiting previous solutions. For example, it has been utilized in e-commerce to enhance the routing and scheduling of delivery vehicles. Ananas have used this to build their last-mile delivery from the ground up.

Each of these methods has its own advantages and limitations.

So it’s crucial to compare and contrast these approaches to determine the most suitable one for a specific multi-depot pickup and delivery scenario.

Is It Possible to Do Multi-Depot Vehicle Routing in 2024?

Yes! Absolutely.

In fact, we’ve already shown you that the Multi-Depot Vehicle Routing Problem is solved.

And the methods used in solving it have been applied into the development of technology that makes it possible to route multiple vehicles to and from multiple depots automatically.

Chief among them:

Route Optimization Software.

This tool integrates a variety of routing algorithms to automate multi-depot vehicle routing. 

At the same time, it enables you to choose the constraints and operational requirements that you want to apply to your vehicle routes and schedules.

The result:

You can easily plan, optimize and dispatch routes to drivers that are efficient and aligned with your business goals.

This is what we had in mind when developing eLogii:

A comprehensive solution designed to simplify vehicle routing, especially in scenarios involving multiple depots.

eLogii Makes It Easy to Route Vehicles When You Have Multiple Depots

eLogii is one of the most powerful route optimization solutions available on the market at the moment. Our software stands out as a premier solution is its configurability and wide range of advanced features and capabilities. 

This high level of customization is what allows you to shape the software to match your operational needs, regardless of their size or complexity.That includes the way you route vehicles to and from multiple depot locations. 

For our users, this is especially useful, since you are the one in control: 

You set and order the optimization parameters, which instructs the software to generate routes according to the degree of efficiency you want to achieve. Be it streamlining your operations, cutting costs or planning time, raising driver performance or vehicle capacity, field service or delivery effectiveness, and more.

Besides this our solution has a range of benefits that are tailored to meet the complex demands of solving the Multi-Depot Vehicle Routing Problem in day-to-day scenarios. Including:

• Unlimited Depots: eLogii doesn’t have a limit on the number of depot locations you can set up into the system. This is perfect for multi-depot planning. It also means you can scale operations as you grow or as the demand for your goods or services increases.
  
  
• Unlimited Vehicles: eLogii also doesn’t have a limit on the number of vehicles (or drivers) you can create. This is the second part that determines the effectiveness of routing software to solve the MDVRP. And we don’t want to impose limits on it.
  
  
• Multiple Constraints: There are 25 unique constraints you can set in the system. Our software will follow each constraint and generate fully optimized routes according to your preferences and order of importance. (Includes all restrictions mentioned in the article.)
  
  
• Multiple Route Optimization Modes: Our solution has three optimization modes: Single-Segment Optimization, Cost-Based Optimization, and Cluster Optimization. All three determine the system’s behavior; how it generates routes, delegates tasks, and area of operation that increases in efficiency.
  
  
• Centralized Multi-Depot Planning: With eLogii, depot and route planning is centralized on a single, user-friendly platform. This approach ensures consistency and efficiency across all depots, streamlining operations and maximizing use of your resources.
  
  
• Connecting Depots to Zones and Drivers: eLogii simplifies the process of connecting depots to specific zones and drivers. This helps you to manage, coordinate, and execute tasks seamlessly across all three levels, even when they overlap.
  
  
• Total Visibility Over Last Mile Operations: You gain complete visibility over all last-mile operations, from depot to doorstep. Real-time tracking capabilities enable you to monitor driver and vehicle movements, track delivery completion, and dynamically respond to any changes at a depot level.
  
  
• API Integration with Other Systems: eLogii seamlessly integrates with your existing systems, such as ERP, CRM, and OMS via our routing API. This ensures smooth data exchange and workflow integration, eliminating the need for manual operations and enhancing overall route planning and delivery efficiency.
  
  
• Real-Time Route Tracking and Analytics: eLogii has real-time data tracking and analytics tools. These enable you to make data-driven decisions and optimize depots and resources according to historical and real-time metrics. These include: delivery times, vehicle utilization, and route efficiency, and more.

Want to see how all of this works in action? Click on the banner to book a demo call: