Modelling and Solving the Vehicle Routing Problem (VRP)

Project for the "Decision Making of Constraint Programming" course, University of Bologna (2020/2021)

Assignment

Modelling and solving the vehicle routing problem in MiniZinc (using the MiniZinc IDE or the Python API) with Gecode.

• Given:
  • a setof customers, each with a:
    • demand (e.g.,the quantity required);
    • location;
  • a fleet of vehicles, each with a capacity, determine:
  • the vehicle serving to each customer;
  • the route of each vehicle,
• so as to minimize the total cost:
  • e.g., total distance, total distance + number of vehicles.
• assuming that each vehicle departs from and returns to the depot.

Given Data

• n customers: N = {1,.., n}
• n customer demands: D = {d1,.., n}
• m vehicles (and routes): V = {1,.., m}
• m vehicle capacities: C = {c1,…, cm}
• n+1 locations: L = {l1, l2,…, ln, ln+1}
  • Each customer i is represented as a pair of x and y coordinates.
  • The final location is that of the depot.

We Also Need

• Distance between every Ii and Ij.
  • Calculate using the coordinates.
  • Multiply by 1000 and round it.
• Total visits = n+2m
• Z = {1,.., n, n+1,.., n+m, n+m+1,.., n+2m}

Developers

• Cotugno Giosuè
• Pruscini Davide

Setup

To execute the script, Python must be installed(download), and some external libraries must be downloaded and installed using the pip (or pip3) package manager:

pip install -r requirements.txt

It is also need to have installed MiniZinc (download): it is important to have MiniZinc usable from teminal. To do that you have to add the path of the MiniZinc installation folder to the PATH environment variable (here).

Usage

python preprocessing.py dzn_path [-o OUTPUT] [[-s] -m MODEL] [-l LIMIT] [-or {customers, demands, distances}] [-p]

Below are some examples, to learn more about all the avaible parameters refer to the help.

python preprocessing.py -h

Examples

1. Preprocessing only, the default output file is named tmp.dzn

python preprocessing.py prXX.dzn

2. Preprocessing and searching for solutions with the specified model, a time limit of 300s is set

python preprocessing.py prXX.dzn -sm vrp.mzn -l 300

3. Preprocessing and searching for solutions with the specified model, setting a time limit of 300s, sorting the dataset by nearest customer and finally plot the routes for each vehicle

python preprocessing.py prXX.dzn -sm vrp.mzn -l 300 -or customers -p