Route Optimization Problem for a Logistics Company The logistics company XpreSS operates with 9 distribution centers strategically located around Nacional level. The company must make daily deliveries of products from these centers of distribution to different destinations. Each connection between two distribution centers has an associated a transportation cost. 1.- Distribution Centers (Nodes): - Arica, Buin, Calama, Dichato, El Quisco, Frutillar, Galvarino, Huasco, Illapel. 2.- Transportation Costs (in monetary units): - Transportation cost from Arica to Buin: $30 - Transportation cost from Arica to Calama: $25 - Transportation cost from Arica to Dichato: $40 - Transportation cost from Buin to Calama: $20 - Transportation cost from Buin to Dichato: $35 - Transportation cost from Buin to El Quisco: $45 - Transportation cost from Calama to Dichato: $15 - Transportation cost from Calama to El Quisco: $30 - Transportation cost from Calama to Frutillar: $50 - Transportation cost from Dichato to El Quisco: $25 - Transportation cost from Dichato to Frutillar: $30 - Transportation cost from Dichato to Galvarino: $40 - Transportation cost from El Quisco to Frutillar: $20 - Transportation cost from El Quisco to Galvarino: $35 - Transportation cost from El Quisco to Huasco: $40 - Transportation cost from Frutillar to Galvarino: $15 - Transportation cost from Frutillar to Huasco: $25 - Transportation cost from Frutillar to Illapel: $30 - Transportation cost from Galvarino to Huasco: $20 - Transportation cost from Galvarino to Illapel: $30 - Transportation cost from Huasco to Illapel: $25 Minimize the total transportation cost by finding optimal routes from each transportation center distribution to others. Each distribution center must be connected to at least one other center (it cannot be isolated). What are the optimal routes that minimize the total transportation cost for each center? of distribution? What is the minimum total transportation cost? # Create a graph g = nx.Graph() # Add edges with weights (transportation costs) g.add_edge('Arica', 'Buin', weight=30) g.add_edge('Arica', 'Calama', weight=25) g.add_edge('Arica', 'Dichato', weight=40) g.add_edge('Buin', 'Calama', weight=20) g.add_edge('Buin', 'Dichato', weight=35) g.add_edge('Buin', 'El Quisco', weight=45) g.add_edge('Calama', 'Dichato', weight=15) g.add_edge('Calama', 'El Quisco', weight=30) g.add_edge('Calama', 'Frutillar', weight=50) g.add_edge('Dichato', 'El Quisco', weight=25) g.add_edge('Dichato', 'Frutillar', weight=30) g.add_edge('Dichato', 'Galvarino', weight=40) g.add_edge('El Quisco', 'Frutillar', weight=20) g.add_edge('El Quisco', 'Galvarino', weight=35) g.add_edge('El Quisco', 'Huasco', weight=40) g.add_edge('Frutillar', 'Galvarino', weight=15) g.add_edge('Frutillar', 'Huasco', weight=25) g.add_edge('Frutillar', 'Illapel', weight=30) g.add_edge('Galvarino', 'Huasco', weight=20) g.add_edge('Galvarino', 'Illapel', weight=30) g.add_edge('Huasco', 'Illapel', weight=25) # Find the minimum spanning tree mst = nx.minimum_spanning_edges(g, data=False) # Print the edges of the minimum spanning tree for edge in mst: print(edge) # Calculate the minimum total transportation cost min_cost = sum(g[u][v]['weight'] for u, v in nx.minimum_spanning_edges(g, data=False)) print('Minimum total transportation cost:', min_cost) The output of the code will be the edges of the minimum spanning tree (the optimal routes) and the minimum total transportation cost. The exact output will depend on the specific weights (transportation costs) given in the problem. The problem is a classic Minimum Spanning Tree problem in Graph Theory, which can be solved using Prim's or Kruskal's algorithm. The Python networkx library provides a function to find the minimum spanning tree of a graph, which can be used to find the optimal routes and the minimum total transportation cost. Represent the problem by using a graph in Python with the networkx library, which Model the network of distribution centers and their connections. Use a route optimization algorithm (such as the Dijkstra algorithm or the Floyd-Warshall) to find the optimal solution.
Route Optimization Problem for a Logistics Company
The logistics company XpreSS operates with 9 distribution centers strategically located around
Nacional level. The company must make daily deliveries of products from these centers of
distribution to different destinations. Each connection between two distribution centers has an associated
a transportation cost.
1.- Distribution Centers (Nodes):
- Arica, Buin, Calama, Dichato, El Quisco, Frutillar, Galvarino, Huasco, Illapel.
2.- Transportation Costs (in monetary units):
- Transportation cost from Arica to Buin: $30
- Transportation cost from Arica to Calama: $25
- Transportation cost from Arica to Dichato: $40
- Transportation cost from Buin to Calama: $20
- Transportation cost from Buin to Dichato: $35
- Transportation cost from Buin to El Quisco: $45
- Transportation cost from Calama to Dichato: $15
- Transportation cost from Calama to El Quisco: $30
- Transportation cost from Calama to Frutillar: $50
- Transportation cost from Dichato to El Quisco: $25
- Transportation cost from Dichato to Frutillar: $30
- Transportation cost from Dichato to Galvarino: $40
- Transportation cost from El Quisco to Frutillar: $20
- Transportation cost from El Quisco to Galvarino: $35
- Transportation cost from El Quisco to Huasco: $40
- Transportation cost from Frutillar to Galvarino: $15
- Transportation cost from Frutillar to Huasco: $25
- Transportation cost from Frutillar to Illapel: $30
- Transportation cost from Galvarino to Huasco: $20
- Transportation cost from Galvarino to Illapel: $30
- Transportation cost from Huasco to Illapel: $25
Minimize the total transportation cost by finding optimal routes from each transportation center
distribution to others.
Each distribution center must be connected to at least one other center (it cannot be
isolated).
What are the optimal routes that minimize the total transportation cost for each center?
of distribution?
What is the minimum total transportation cost?
# Create a graph
g = nx.Graph()
# Add edges with weights (transportation costs)
g.add_edge('Arica', 'Buin', weight=30)
g.add_edge('Arica', 'Calama', weight=25)
g.add_edge('Arica', 'Dichato', weight=40)
g.add_edge('Buin', 'Calama', weight=20)
g.add_edge('Buin', 'Dichato', weight=35)
g.add_edge('Buin', 'El Quisco', weight=45)
g.add_edge('Calama', 'Dichato', weight=15)
g.add_edge('Calama', 'El Quisco', weight=30)
g.add_edge('Calama', 'Frutillar', weight=50)
g.add_edge('Dichato', 'El Quisco', weight=25)
g.add_edge('Dichato', 'Frutillar', weight=30)
g.add_edge('Dichato', 'Galvarino', weight=40)
g.add_edge('El Quisco', 'Frutillar', weight=20)
g.add_edge('El Quisco', 'Galvarino', weight=35)
g.add_edge('El Quisco', 'Huasco', weight=40)
g.add_edge('Frutillar', 'Galvarino', weight=15)
g.add_edge('Frutillar', 'Huasco', weight=25)
g.add_edge('Frutillar', 'Illapel', weight=30)
g.add_edge('Galvarino', 'Huasco', weight=20)
g.add_edge('Galvarino', 'Illapel', weight=30)
g.add_edge('Huasco', 'Illapel', weight=25)
# Find the minimum spanning tree
mst = nx.minimum_spanning_edges(g, data=False)
# Print the edges of the minimum spanning tree
for edge in mst:
print(edge)
# Calculate the minimum total transportation cost
min_cost = sum(g[u][v]['weight'] for u, v in nx.minimum_spanning_edges(g, data=False))
print('Minimum total transportation cost:', min_cost)
The output of the code will be the edges of the minimum spanning tree (the optimal routes) and the minimum total transportation cost. The exact output will depend on the specific weights (transportation costs) given in the problem.
The problem is a classic Minimum Spanning Tree problem in Graph Theory, which can be solved using Prim's or Kruskal's
Represent the problem by using a graph in Python with the networkx library, which
Model the network of distribution centers and their connections.
Use a route optimization algorithm (such as the Dijkstra algorithm or the
Floyd-Warshall) to find the optimal solution.
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