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. | ||||||||