Question: The Audiofile Company produces boomboxes. However, management has decided to subcontract out the production of the speakers needed for the boomboxes. Three vendors are available to supply the speakers. Their price for each shipment of 1,000 speakers is shown below.
| Vendor |
Price |
| 1 |
$22,500 |
| 2 |
$22,700 |
| 3 |
$22,300 |
In addition, each vendor would charge a shipping cost. Each shipment would go to one of the company's two warehouses. Each vendor has its own formula for calculating this shipping cost based on the mileage to the warehouse. These formulas and the mileage data are shown below.
| Vendor |
Charge per shipment |
| 1 |
$300+0.40/mile |
| 2 |
$200+0.50/mile |
| 3 |
$500+0.20/mile |
| Vendor |
Warehouse 1 |
Warehouse 2 |
| 1 |
1,600 miles |
400 miles |
| 2 |
500 miles |
600 miles |
| 3 |
2,000 miles |
1,000 miles |
Whenever one of the company's two factories needs a shipment of speakers to assemble into the boomboxes, the company hires a trucker to bring the shipment in from one of the warehouses. The cost per shipment is given in the next column, along with the number of shipments needed per month at each factory.
|
Unit Shipping Cost |
Unit Shipping Cost |
|
Factory 1 |
Factory 2 |
| Warehouse 1 |
$200 |
$700 |
| Warehouse 2 |
$400 |
$500 |
| Monthly demand |
10 |
6 |
Each vendor is able to supply as many as 10 shipments per month. However, because of shipping limitations, each vendor is able to send a maximum of only 6 shipments per month to each warehouse. Similarly, each warehouse is able to send a maximum of only 6 shipments per month to each factory. Management now wants to develop a plan for each month regarding how many shipments (if any) to order from each vendor, how many of those shipments should go to each warehouse, and then how many shipments each warehouse should send to each factory. The objective is to minimize the sum of the purchase costs (including the shipping charge) and the shipping costs from the warehouses to the factories.
(a) Draw a network that depicts the company's supply network. Identify the supply nodes, transshipment nodes, and demand nodes in this network.
(b) Formulate an optimization model to solve this problem. (Set-up only the objective function and the Constrains do not solve)