Problem: The National Tire Company (NTC) manufactures only one type of tire and wants to plan its production and inventory levels for the next five months. Company policy is to schedule all of its overtime production during one month. The following table provides the relevant data for each month, where the inventory-level requirements refer to the level at the end of each month.
Other relevant information is as follows:
- NTC estimates that it costs $1 to hold one tire in inventory from one month to the next.
- NTC currently has an inventory level of 4,000 tires.
- NTC wants to meet its demand with no backorders; that is, all demand must be met no later than the month in which it occurs.
Q1. Construct a network diagram to represent the NTC scenario. Using the diagram, build a spreadsheet model for the production and inventory plan.
Q2. What is the minimum total cost, including production and invetory costs, for the five-months period (ignoring the cost of the initial inventory)? What production levels minimize total cost?
| month |
unit demand |
production cost |
maximum production level |
minimum production level |
maximum inventory level |
minimum inventory level |
| 1 |
12000 |
$11.00 |
18,000 |
6,000 |
10,000 |
2,000 |
| 2 |
18000 |
$11.00 |
18,000 |
6,000 |
10,000 |
2,000 |
| 3 |
24000 |
$11.50 |
30,000 |
6,000 |
15,000 |
2,000 |
| 4 |
20000 |
$11.00 |
18,000 |
6,000 |
10,000 |
2,000 |
| 5 |
22000 |
$11.00 |
18,000 |
6,000 |
10,000 |
2,000 |