| 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. | ||||||||
