Minimize the costs of shipping 3 different goods from factories to warehouses and customers, and | |||||||
warehouses to customers, while not exceeding the supply available from each factory or | |||||||
the capacity of each warehouse, and meeting the demand from each customer. | |||||||
Cost of shipping ($ per product) | |||||||
Destinations | |||||||
Warehouse 1 | Warehouse 2 | Warehouse 3 | Warehouse 4 | ||||
Factory 1 | Product 1 | $0.50 | $0.50 | $1.00 | $0.20 | ||
Product 2 | $1.00 | $0.75 | $1.25 | $1.25 | |||
Product 3 | $0.75 | $1.25 | $1.00 | $0.80 | |||
Factory 2 | Product 1 | $1.50 | $0.30 | $0.50 | $0.20 | ||
Product 2 | $1.25 | $0.80 | $1.00 | $0.75 | |||
Product 3 | $1.40 | $0.90 | $0.95 | $1.10 | |||
Customer 1 | Customer 2 | Customer 3 | Customer 4 | Customer 5 | |||
Factory 1 | Product 1 | $2.75 | $3.50 | $2.50 | $3.00 | $2.50 | |
Product 2 | $2.50 | $3.00 | $2.00 | $2.75 | $2.60 | ||
Product 3 | $2.90 | $3.00 | $2.25 | $2.80 | $2.35 | ||
Factory 2 | Product 1 | $3.00 | $3.50 | $3.50 | $2.50 | $2.00 | |
Product 2 | $2.25 | $2.95 | $2.20 | $2.50 | $2.10 | ||
Product 3 | $2.45 | $2.75 | $2.35 | $2.85 | $2.45 | ||
Customer 1 | Customer 2 | Customer 3 | Customer 4 | Customer 5 | |||
Warehouse 1 | Product 1 | $1.50 | $0.80 | $0.50 | $1.50 | $3.00 | |
Product 2 | $1.00 | $0.90 | $1.20 | $1.30 | $2.10 | ||
Product 3 | $1.25 | $0.70 | $1.10 | $0.80 | $1.60 | ||
Warehouse 2 | Product 1 | $1.00 | $0.50 | $0.50 | $1.00 | $0.50 | |
Product 2 | $1.25 | $1.00 | $1.00 | $0.90 | $1.50 | ||
Product 3 | $1.10 | $1.10 | $0.90 | $1.40 | $1.75 | ||
Warehouse 3 | Product 1 | $1.00 | $1.50 | $2.00 | $2.00 | $0.50 | |
Product 2 | $0.90 | $1.35 | $1.45 | $1.80 | $1.00 | ||
Product 3 | $1.25 | $1.20 | $1.75 | $1.70 | $0.85 | ||
Warehouse 4 | Product 1 | $2.50 | $1.50 | $0.60 | $1.50 | $0.50 | |
Product 2 | $1.75 | $1.30 | $0.70 | $1.25 | $1.10 | ||
Product 3 | $1.50 | $1.10 | $1.50 | $1.10 | $0.90 | ||
Number of products shipped | |||||||
Warehouse 1 | Warehouse 2 | Warehouse 3 | Warehouse 4 | Total | |||
Factory 1 | Product 1 | 0 | 0 | 0 | 0 | 0 | |
Product 2 | 0 | 0 | 0 | 0 | 0 | ||
Product 3 | 0 | 0 | 0 | 0 | 0 | ||
Factory 2 | Product 1 | 0 | 0 | 0 | 0 | 0 | |
Product 2 | 0 | 0 | 0 | 0 | 0 | ||
Product 3 | 0 | 0 | 0 | 0 | 0 | ||
Total | Product 1 | 0 | 0 | 0 | 0 | ||
Product 2 | 0 | 0 | 0 | 0 | |||
Product 3 | 0 | 0 | 0 | 0 | |||
Capacity | Product 1 | 35,000 | 20,000 | 30,000 | 15,000 | ||
Product 2 | 30,000 | 25,000 | 15,000 | 24,000 | |||
Product 3 | 20,000 | 20,000 | 25,000 | 20,000 | |||
Customer 1 | Customer 2 | Customer 3 | Customer 4 | Customer 5 | Total | ||
Factory 1 | Product 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Product 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
Product 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
Factory 2 | Product 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Product 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
Product 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
Capacity | |||||||
Total products shipped out of factory 1 | Product 1 | 0 | 90,000 | ||||
Product 2 | 0 | 100,000 | |||||
Product 3 | 0 | 80,000 | |||||
Total products shipped out of factory 2 | Product 1 | 0 | 75,000 | ||||
Product 2 | 0 | 65,000 | |||||
Product 3 | 0 | 90,000 | |||||
Customer 1 | Customer 2 | Customer 3 | Customer 4 | Customer 5 | Total | ||
Warehouse 1 | Product 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Product 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
Product 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
Warehouse 2 | Product 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Product 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
Product 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
Warehouse 3 | Product 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Product 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
Product 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
Warehouse 4 | Product 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Product 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
Product 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
Total | Product 1 | 0 | 0 | 0 | 0 | 0 | |
Product 2 | 0 | 0 | 0 | 0 | 0 | ||
Product 3 | 0 | 0 | 0 | 0 | 0 | ||
Demands | Product 1 | 30,000 | 23,000 | 15,000 | 32,000 | 16,000 | |
Product 2 | 20,000 | 15,000 | 22,000 | 12,000 | 18,000 | ||
Product 3 | 25,000 | 22,000 | 16,000 | 20,000 | 25,000 | ||
Total cost of shipping | $0 | ||||||
Problem | |||||||
This model builds on model Transport2. Again, a company wants to minimize cost of shipping, but this time | |||||||
there are 3 products to distribute. How should the company distribute the products? | |||||||
Solution | |||||||
The solution to the problem is identical to the one in Transport2. Notice that we have used the 'Insert Name | |||||||
Define' command to extend the model to a multiproduct problem. This way the variables and constraints are | |||||||
still the same as in Transport2. | |||||||
Remarks | |||||||
Notice that this model delivers the same result as three separate models for the three products. There will be | |||||||
times however, that there are constraints that apply to more than one product. In that case it would not be | |||||||
desirable to have three different models and maybe even impossible. For an extension of this model, where the | |||||||
number of products made in the factories depends on the demand and distribution rather than being constant, | |||||||
see the worksheet Prodtran in this workbook. | |||||||