Model 15: Production Scheduling over Time
A company has a permit to operate for five seasons. It can manufacture only
during the first four seasons and in the fifth period it is only allowed to
sell any leftover products. It can manufacture two types of products. One
unit of product 1 requires five man-hours in preparatory shop and three
man-hours in finishing shop. Each unit of product 2 requires six man-hours
in preparatory shop and one man-hour in finishing shop. During each season
the company has at most 12,000 man-hours in preparatory and 15,000 man-hours
in the finishing shop (only during the first four seasons). The product
manufactured during some season can be sold anytime from the next season
onward. However, selling requires some marketing effort and it is expected
that 10 and 20 minutes of premium radio marketing time (premium time occur
during high volume listening hours) are required to sell 10 units
of products 1 and 2 per period, respectively. Correspondingly,
25 and 40 minutes of non-premium radio marketing minutes are required to sell 10 units
of products 1 and 2 per period, respectively.
The costs of both premimum and non-premium radio marketing minutes
are given in the table below.
If a unit of product is available for sale during a season, but is not sold in
that season, the manufacturer has to pay carryover charges of $10 per unit to
put it up for sale again in the next season. The selling prices in the
various seasons are given in the table below. How should the company operate
in order to maximize the total profit?
| | | | | Expected Profit per Unit of |
| Season |
Cost per Non-Premium
Radio Minute |
Cost per Premium
Radio Minute |
Maximum Normal
Radio Minutes |
Maximum Premium
Radio Minutes |
Product I |
Product 2 |
| 2 |
$20 |
$80 |
1000 |
200 |
$200 |
$450 |
| 3 |
$40 |
$100 |
800 |
400 |
$250 |
$400 |
| 4 |
$10 |
$55 |
1000 |
200 |
$300 |
$400 |
| 5 |
$25 |
$75 |
900 |
300 |
$150 |
$300 |