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.