Dwayne Cole, owner of a Florida firm that manufactures display cabinets, develops an 8-month aggregate plan. Demand and capacity (in units) are forecast as follows:
|
Capacity Source (Units)
|
Jan.
|
Feb.
|
Mar.
|
Apr.
|
May
|
June
|
July
|
Aug.
|
|
Regular time
|
235
|
255
|
290
|
300
|
300
|
290
|
300
|
290
|
|
Overtime
|
20
|
24
|
26
|
24
|
30
|
28
|
30
|
30
|
|
Subcontract
|
12
|
16
|
15
|
17
|
17
|
19
|
19
|
20
|
|
Demand
|
255
|
294
|
321
|
301
|
330
|
320
|
345
|
340
|
The cost of producing each unit is $1,000 on regular time, $1,300 on overtime, and $1,800 on a subcontract. Inventory carrying cost is $200 per unit per month. There is no beginning or ending inventory in stock, and no backorders are permitted from period to period. Let the production (workforce) vary by using regular time first, then overtime, and then subcontracting.
a) Set up a production plan that minimizes cost by producing exactly what the demand is each month. This plan allows no backorders or inventory. What is this plan's cost?
b) Through better planning, regular-time production can be set at exactly the same amount, 275 units, per month. If demand cannot be met there is no cost assigned to shortages and they will not be filled. Does this alter the solution?
c) If overtime costs per unit rise from $1,300 to $1,400, will your answer to (a) change? What if overtime costs then fall to $1,200?