Transportation, Transhipment, Integer programming problems
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Problem 35
World foods, Inc., imports food products such as meats, cheeses, and pastries to the United States from warehouses at ports in Hamburg, Marseilles, and Liverpool. Ships from these ports deliver the products to Norfolk, New York, and Savannah, where they are stored in company warehouses before being shipped to distribution centers in Dallas, St. Louis, and Chicago. The products are then distributed to specialty food stores and sold through catalogs. The shipping costs ($/1,000 lb) from the European ports to the U.S. Cities and the available supplies (1,000 lb) at the European ports are provided in the following table:
U.S. City
European Port 4. Norfolk 5. New York 6. Savannah Supply
1. Hamburg $420 $390 $610 55
2. Marseilles 510 590 470 78
3. Liverpool 450 360 480 37
The transportation costs ($/1,000 lb) from each U.S. city of the three distribution centers and the demands (1,000 lb) at the distribution centers are as follows:
Distribution Center
Warehouse 7. Dallas 8. St. Louis 9. Chicago
4. Norfolk $ 75 $ 63 $ 81
5. New York 125 110 95
6. Savannah 68 82 95
60 45 50
Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs.
Problem 22
Max Z = 3x1 + 5x2
Subject to:
7x1 + 12x2 <= 136
3x1 + 5x2 <= 36
x1, x2 >= 0 and integer
Find the optimal solution.
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