The Vehicle Routing Problem (VRP) is all about figuring out the best routes for many vehicles so they spend the least time traveling. You can think of it like having a bunch of Travelling Salesman Problems (TSP) all rolled into one.
You can find real-world VRPs everywhere. Using smart algorithms to solve these can make any vehicle fleet a lot more efficient.
We encounter real-world examples of VRP every day:
Route optimization is commonly mentioned when talking about solving VRP problems in operations research. Both open-source solvers and commercial VRP Routing APIs are available for this. Since finding the perfect solution isn't practical, solvers usually rely on metaheuristic algorithms to quickly find an efficient route. After all, there's no use in finding the best route if it takes days to figure out!
The Vehicle Routing Problem (VRP) is about managing a fleet of vehicles and a set of customer locations or delivery points. The main questions are:
The goal is to cut travel time, but you can also aim to optimize for the shortest route, the fewest number of vehicles, or the lowest total cost.
Any real-life application of the VRP usually comes with specific constraints to meet. These might be vehicle capacity constraints (CVRP), time windows (VRPTW), or other constraints that reflect a particular business scenario.
In this article, we'll cover:
The Vehicle Routing Problem (VRP) seems simple to describe but can be tough to crack. Along with its variations like the Capacitated Vehicle Routing Problem (CVRP) and Vehicle Routing Problem with Time-windows (VRPTW), it stands out as one of the trickiest and most popular optimization puzzles in operations research.
Solving it involves different approaches. These are mainly split into exact methods and approximation methods using metaheuristics. Exact methods are mostly for academic purposes because they struggle with large-scale problems. Plus, in real-life situations, getting the most optimal solution isn't always necessary. Fnding a good enough one can already make a huge difference.
That's why most algorithms for the VRP rely on metaheuristics. They're quick, handy, and adaptable (you can add more rules to the solver easily).
Metaheuristics have many types. Some of the most popular and effective ones for these problems include local search, tabu search, genetic algorithms, and simulated annealing.
When tackling a route problem, you have two options: manual planning or using software. Manual planning involves mapping out routes using Excel and/or relying on Google Maps for routing. Yet, it's better to opt for purpose-built algorithms instead. Humans generally struggle with solving routing and scheduling problems efficiently.
When picking a software approach, you have several options:
The VRP is an optimization problem that merges many Travelling Salesman Problems. The TSP is recognized as NP-hard. So, when you add real-world constraints like time-windows, vehicle capacities, and traffic conditions, the combinatorial optimization problem becomes significantly more complex.
But that's just part of the reason why VRPs are a constant challenge. To understand why Vehicle Routing Problems are so difficult to solve—and why NP-hard problems are particularly tough—we need to first understand a concept called time complexity.
Time complexity refers to how the time taken for computation changes as the size of the problem changes. Let's use some examples to explain:
Imagine you're calculating the total distance of a route with 4 stops. You simply add up the distances between each consecutive stop.
Now, if you add 4 more stops, you need to calculate the total distance for 8 stops. The number of calculations grows linearly with the size of the problem.
This is called a linear problem. As the problem gets bigger, the time needed to solve it also increases linearly.
Now, let’s consider a route optimization scenario with 10 stops. Also, imagine common constraints like delivery time windows and vehicle capacities.
To find the shortest route for your fleet, you'd have to calculate all possible combinations of those 10 stops (while meeting constraints). You'll also have to test each one to find the best solution. The sheer number of combinations is staggering.
With 10 stops, there are over 3.6 million permutations. If we increase to 57 stops, the possible routes skyrocket to 57 quattuorvigintillion, a number with 75 zeroes!
This is known as an exponential problem. As the size grows, the time to find the best solution increases exponentially. It becomes incredibly complex, making it practically impossible for a human to calculate without assistance.
Interestingly, humans are naturally good at solving Vehicle Routing Problems. Yet, we struggle to handle it on a large scale and find it difficult to factor in many constraints. It quickly becomes too complicated.
Without extra constraints, we want our routes to resemble loops, or many loops if there is more than one driver. These loops should have minimal overlap, much like the petals of a flower.
A deeper understanding of the Vehicle Routing Problem highlights the complexity of finding a solution. This is why computers, algorithms, and route planning software are essential.
Each routing situation is unique, but with eLogii, you can flexibly configure your real-world constraints and choose your objective function. You can do this whether it’s minimizing travel time, shortest distance, or the fewest number of vehicles.
When you optimize routes for time, you're solving the Vehicle Routing Problem by finding the quickest way to complete all deliveries. This is especially useful if you pay your drivers an hourly wage. Namely, labor costs typically make up the largest part of delivery expenses. By creating solutions that cut the total duration, you can significantly cut down on costs.
Or, you can optimize routes for the shortest distance. This approach solves the VRP by finding the route that covers the least number of miles. It reduces or eliminates any idle time for your drivers. This is particularly beneficial if you pay your drivers based on mileage. By focusing on distance, you can lower costs while still optimizing your routes.
Assigning the appropriate drivers to specific stops offers significant advantages. In some cases, vehicles have specific capacities. Or, drivers have constraints such as availability during certain times of the day if they operate in shifts. Consider the scenario of Bear's Blooms.
For example, consider a company that delivers flowers to customers weekly. They need to segment their delivery schedule by region and distribute it throughout the week.
Thus, they must determine:
Considering these factors when planning delivery routes can be quite complex to handle manually.
Each morning, an hour is dedicated to planning routes, a task that would take twice as long without eLogii. For example, a company can start by uploading a CSV of orders to eLogii. Routes can then be organized by postal code. Delivery days are assigned to customers based on their postal code, and they are informed in advance of their expected delivery day. It is indeed a straightforward process.
If you perform a rapid Google search on the Vehicle Routing Problem, you're likely to encounter several scientific articles. You might also run into TED Talk-style presentations delving into its complexities. This is because the Vehicle Routing Problem continues to be a focal point of research for data scientists and engineers.
Currently, addressing the Vehicle Routing Problem typically involves employing algorithms. This is done to approximate the closest workable solution based on time or distance. Often, these algorithms don't aim to fully "solve" the problem. Instead, they strive to approach a solution within a reasonable computational timeframe.
As a result, not all algorithms are created equal. Some deliberately take longer to process to provide a more optimal solution. Others prioritize quicker processing times, offering a solution that may be sub-optimal but still quite effective.
Ultimately, it hinges on what your team prioritizes the most.
eLogii offers intelligent route optimization, streamlined customer communications, and efficient order execution for distribution and field service businesses worldwide. You can effortlessly plan across an unlimited date range, directly from the dashboard or through our API. eLogii stands out as the sole end-to-end solution in the market, catering to distribution or field service businesses of any size, regardless of location. Our Routing Engine API accounts for the following delivery constraints:
If your business handles home deliveries or deals with a Vehicle Routing Problem, chances are we've encountered your situation before. It might be time to consider using vehicle routing software.
For a deeper look at how eLogii addresses the Vehicle Routing Problem, and to gain a better understanding of the issue as a whole, you can learn more here.