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.