Model 28: Production Planning
A company manufactures a product, the demand for which varies from month to
month. The raw material and labor availability exhibit seasonal variations.
During the months 10, 11, 12, 1, 2, 3 the company can hire at most enough
labor to produce 1200 and 600 tons per month during regular time and
overtime, respectively. In months 4, 5, 6, 7, 8, 9 these labor capacities
are 800 and 500 tons, respectively. The product manufactured during a month
can be sold anytime during the next month or later. Storage costs are
$1.00/ton from one month to the next for the product. Raw material cannot
be stored. It has to be used up in the month in which it is obtained.
Operations begin in month 1 with a stock of 50 tons of the product. At the
end of month 12 the company should have a stock of at least 50 tons of the
product. Determine an optimum production schedule.
| Month
| Cost of Labor
($/Ton of Production)
During
| Limit on Raw
Material Availability
(enough to make
tons of product)
| Demand
(tons)
| Selling price
($/ton)
|
| Regular Time
| Overtime
|
| 1
| $4
during these
months
| $6
| 600
| 400
| 18
|
| 2
| 450
| 700
| 18
|
| 3
| 425
| 600
| 18
|
| 4
| $6
during these
months
| $9
| 1200
| 900
| 25
|
| 5
| 1300
| 900
| 25
|
| 6
| 1600
| 900
| 25
|
| 7
| 1600
| 800
| 25
|
| 8
| 1500
| 600
| 25
|
| 9
| 1300
| 800
| 25
|
| 10
| $4
| $6
| 500
| 1200
| 30
|
| 11
| 500
| 1100
| 30
|
| 12
| 500
| 1400
| 30
|