CVRP | Capacitated Vehicle Routing Problem Solution | Machine Learning library

Context: I'm working on a warehouse simulation that supports different floor designs and simulates one or multiple agents that are tasked with order picking. One order can consist of more than one product. The routing for picking products is solved as a capacitated vehicle routing problem (CVRP). This requires a distance matrix between product locations, for which the A* algorithm is used. Currently, distance matrices are generated per order, just before picking on that order is started. Many simulation runs are desired for accurate measures, so computational efficiency is of high importance. For completeness, I included a screenshot of the simulation below, with product locations (dark), an agent (white), products in the current order (blue), and the products being picked in the current route (green/red). Note that the white lines represent the current picking priority, not the exact paths.

Problem: The size of the distance matrix grows quadratically with the number of products per order. Therefore, the time for computing it with A* quickly becomes unacceptable.

Question: I need a method that makes the computation of distance matrices more efficient. This can be either an exact method or a heuristic, as long as not too much accuracy is sacrificed. I am not looking for implementations or specific code snippets, but for ideas and/or methods that are used for similar problems that I can implement myself.

Attempted methods/ideas: Here are some approaches I've considered or tried to implement with no success:

• Distance matrix for the full warehouse: unfeasible, as the number of product locations is simply too large.
• Using Euclidean distance: not good enough. This would assume that products on opposite sides of a warehouse row are close together when in reality an agent would have to take a long detour between the two.
• Using a clustering algorithm to identify areas that are close together and base a distance matrix on clusters instead of individual locations: this would reduce the total matrix size, making it possible to pre-compute it completely. However, this would greatly reduce accuracy and I've yet to find a clustering algorithm that reliably works for this problem with different floor layouts.

Layout examples: White pixels indicate floor cells, black pixels indicate product locations. Products within an order are randomly selected from all possible locations. More floor layouts (any floor layout!) should be supported by the chosen method.

Here is a pasteable array for layout 1 if anyone wants to mess around with it:

I am working on a CVRP and have gotten to the point where I have a list of vehicle fleets, where each fleet is made up of a homogeneous vehicle type, and the amount of goods that should be in each fleet. The corresponding dataframe looks like this:

I am modeling a Time-constrained CVRP. The problem is to minimize the total travel time (not including the package dropping time) subject to vehicle (delivery) capacity and total time spent (per vehicle) constraints. The package dropping time refers to an additional time to be spent at each node, and the total time spent equals to the travel time plus this additional time. I have the below model that works for a single vehicle-type case. I would like to introduce two-vehicle type concept in there, meaning that I have a set of V1 type vehicles and another set of V2 type vehicles. The only difference of the vehicle-types is the per time cost of travel. Let x denote the per time unit cost of travel by V1, and y denote the per time unit travel cost of V2. How can I design the model so that it incorporates this additional aspect?

I have tried to create a CVRPTW solution by combining CVRP and VRPTW from examples provided in the official documentation.

Since the code is big I cannot paste it here, so I am sharing a colab notebook demonstrating a short example reproducing the problem: https://colab.research.google.com/drive/1YN-6kABqGqSkQKxOtWD6YA2ZDlP8RfqD?usp=sharing

The quantities to deliver at each node are [0, 80, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1]

I have 22 vehicles, 21 vehicles with capacity 25 and 1 vehicle with capacity 600. If the vehicles are sorted in ascending order the example with 14 nodes take more than 200 seconds to solve and if they are sorted in descending order the same example gets solved in less than a second.

I am using Google OR Tools for the first time so I don't know if this was expected or not. I have tried adding Guided Local Search also but when I add a time limit to stop it stops without giving a solution.

I created an issue in the repo but it was converted to a Discussion.

https://github.com/google/or-tools/discussions/2554

I have also asked this question in the official mailing list.

https://groups.google.com/g/or-tools-discuss/c/MHoMwkHQuoo

Please help me on my periodic capacitated vehicle routing problem.

Find the same question here on google-groups.

What I am trying to model:

• 1 depot

• multiple customers (let's assume 4)

• multiple days (let's assume 3)

• Multiple vehicle types with price per km and specific capacity

• Every customer has: delivery frequency and demand per delivery

• Every customer has to be assigned to a delivery pattern. Multiple delivery patterns are possible for each frequency. The pattern indicates if a delivery is possible on that day or not. For a frequency of 1 and 3 working days: [[1,0,0],[0,1,0],[0,0,1]], a frequency of 2 [[1,1,0],[1,0,1],[1,1,0]], a frequency of 3: [1,1,1]these are the possible patterns.

The demand of each customer per delivery is the same, for every day a delivery is performed

So we have a set of customers that have to be delivered by one depo. Multiple Vehicle Types are available for the job. The day of service is flexible because only the frequency is fixed to a customer, but there are multiple possibilities to fulfill the demand.

What I did so far:

• I copied every node by the number of working days.

• I restrict the start and end to the depo nodes of each day.

• I multiply the vehicles by the number of days.

• Furthermore, I handle the days as different kinds of cargo. I do assign a capacity of zero to the vehicle when it should not be used on that day.

  ...

I am using the OR-tools code to optimize bus routes with distance and capacity constraints. This is the output that I got:

How does one get googleortools to give back the actual cost of a vrp? This example only returns distance and loads but if I add more cost elements I would like it to show me cheapest outcome. https://developers.google.com/optimization/routing/cvrp

Thanks.

I'm currently using Python and the Google-Or-Tools to solve an VRP problem, that I am not sure how exactly to model. (If someone has a solution with another library/tool, absolutely interested as well)

Problem Statement:

I have basically the classical CVRP problem also described and modelled on the documentation page, but with one addition. So the basic CVRP problem is, I have a depot where cargo is loaded and vehicles start from / end at. Also I have locations where goods are to be delivered to, e.g. they have a demand. Now the addition is, that I not only dropoff goods at the specific locations but also want to pickup goods at the same locations, and eventually dropping them off at the depot again.

Since it is possible for a location to have more goods to pickup than to dropoff, I need to explicitly check this, too ... but I can't find a way so far to do this.

Example: So say I have one Depot node 0 and two location nodes (A,B).

• At location A I need to dropoff 10 units and pickup 11.
• At location B I need to dropoff 10 units and pickup 9.

Now for a vehicle with max capcity 20 the possible solution would be:

• 0 --> B --> A --> 0

First visiting A and then B would not work, since it would violate the capacity constraint in A.

What I've tried:

So to consider the basic dropoff capacity constraint I have the standard

I'm trying to use OR-Tools' Routing Solver to solve a Multi Trip Capacitated VRP. What I need is

• one depot, route starts and ends here.
• one unloading location (different from the depot)
• set time window and demand for each node

So the vehicles should pick up the goods from each node until the capacity is filled. Then go to "unloading location", unload all their weight and keep collecting the demand from nodes until a time limit is reached or all the goods are collected. Then return back to the depot.

CVRP Reload Example seems very close but in my case, at the end of the route vehicles should visit the unloading location before the depot. In other words a vehicle can not go to the depot (starting, ending location) with load.

Example: