RevLog SL, the public company in charge of waste collection management in a Spanish region wants to restructure its network of clean points in that region.
The nodes of the graph of the figure represent the municipalities of the region and the arcs to the roads that communicate them. The bold numbers indicate the population of each municipality (in thousands of inhabitants) and the arcs are labeled with the distances between each two municipalities (in italics).
There is a budget to install at most three clean points in three different municipalities to guarantee sufficient coverage.
The question that the RevLog address is asked is where should the different clean points be located in a way that minimizes the average distance traveled per inhabitant from their municipality to the nearest clean point?
Part A: the problem of RevLog
1. What kind of location problem are you raising? Why?
2. Poses the associated linear programming model
3. Implement the model and solve using Python + PuLP
4. Characterize the solution obtained, including the distance traveled by the inhabitants of each municipality to go to the nearest clean point
Part B: other possible developments
5. Construct a graph that represents the average distance traveled by the inhabitants of said region in function of the maximum number of clean points that could be installed.
Shortly there are elections to governor of the region and the inhabitants of the region are very sensitive to the issue of clean points: everyone wants to have one in their city (so as not to take a car in the car) or move as little as possible.
6. The candidate for re-election believes that two more clean points than those provided by RevLog can be built, charged to the public treasury, and consider using the RevLog model to respond to: 6.A. In which municipalities could you promise a clean point of your own?
6.B. What would be the longest displacement that an inhabitant of the region would have to do to access a clean point?
6C. What inhabitants do not promise them that they will have a clean point in their city?
After reflecting on the issue, the candidate believes that issue 6.B. it’s key. Before promising that no inhabitant of the region will have to travel more than 20 km to the nearest clean point, he wants to throw numbers.
7. What are the results that would be obtained with the current RevLog model?
8. What type of location model would be most appropriate to solve this?
– Compressed file (.zip, .7z, etc.) which includes:
• Code (.py)
• Executive report answering the questions posed (.pdf, no more than two pages). o Other file
necessary.
– Copy the Python code used in the Moodle activity to that effect.
– use the Floyd-Warshall algorithm.