Transportation Problem 1

Minimize the costs of shipping goods from factories to customers, while not exceeding
the supply available from each factory and meeting the demand of each customer.

Cost of shipping ($ per product)
	Destinations
	Customer 1	Customer 2	Customer 3	Customer 4	Customer 5
Factory 1	$1.75	$2.25	$1.50	$2.00	$1.50
Factory 2	$2.00	$2.50	$2.50	$1.50	$1.00

Number of products shipped
	Customer 1	Customer 2	Customer 3	Customer 4	Customer 5	Total	Capacity
Factory 1	0	0	0	0	0	0	60,000
Factory 2	0	0	0	0	0	0	60,000
Total	0	0	0	0	0
Demand	30,000	23,000	15,000	32,000	16,000

Total cost of shipping		$0


Problem
A company wants to minimize the cost of shipping a product from 2 different factories to 5 different customers.
Each factory has a limited supply and each customer a certain demand. How should the company distribute the
product?

Solution
1) The variables are the number of products to ship from each factory to the customers. These are given the
name Products_shipped in worksheet Transport1.
2) The logical constraint is
	Products_shipped >= 0 via the Assume Non-Negative option
The other two constraints are
	Total_received >= Demand
	Total_shipped <= Capacity
3) The objective is to minimize cost. This is given the name Total_cost.

Remarks
This is a transportation problem in its simplest form. Still, this type of model is widely used to save many
thousands of dollars each year.
In worksheet Transport2 we will consider a 2-level transportation, and in worksheet Transport3 we expand this to
a multi-product, 2-level transportation problem.