Question

USE LEVEL AGGREGATE PLAN:

Cost data

Regular time labor cost per hour $10

Overtime time labor cost per hour $15

Subcontracting cost per unit $80

Back order cost per unit per period                           $20

Inventory holding cost per unit per period           $10

Hiring cost per employee $400

Firing cost per employee $500

Capacity data

Beginning workforce                                                             40 employees

Beginning inventory 0 units

Beginning backorders 0 units

Production standard per unit (hours)                       2 hours of labor per unit

Regular time available per period (hours)            160 hours per period per employee

Overtime time available per period (hours)        30 hours per period per employee

Number of days per period                                              20 days

Number of working hours per day                               8 hours

Demand data

Period 1 4,000 units                         

Period 2 3,800 units

Period 3 3,200 units

Period 4                 3,280 units   

Period 5 2,680 units                    

Period 6                 4,340 units

Period 7                 4,820 units

Period 8                 4,600 units

a: what is the production rate?

b: what is the size of workforce?

c: how many more workers should be hired at the beginning of planning?

d: how many hnjts totally will be helf as inventory?

e: what will be the backorder units?

f: the costs fir regular time are _____?

g: what are the total sales?

Answer 1

Production standard per unit (hours) = 2 hours of labor per unit

Regular time available per period (hours) = 160 hours per period per employee

Total regular production / worker / period = 160/2 = 80

Total demand = 30720

a) Level production required = Total demand / Number of periods = 30720/8 = 3840

b) Size of workforce needed = Level production required / Total regular production / worker / period = 3840/80 = 48

c) Workers hired = 48-40 = 8

d) Total held in inventory across periods = 6340 , Ending inventory is zero.

e) Backorder units are in Period 1 & 2. Total = 160 + 120 = 280

f) Total cost of regular time = $614,400

g) Total sales = Demand = 30720 , Total cost of plan = $686,600

Period	1	2	3	4	5	6	7	8
Demand	4000	3800	3200	3280	2680	4340	4820	4600	30720
Beg Inventory = Ending inventory of previous month	0	0	0	520	1080	2240	1740	760
Demand - Opening inventory	3840	3840	3840	3840	3840	3840	3840	3840
# of Workers	48	48	48	48	48	48	48	48
Normal production = # of Workers * 160 hours/2	3840	3840	3840	3840	3840	3840	3840	3840	30720
Total Production	3840	3840	3840	3840	3840	3840	3840	3840	30720
Ending inventory	0	0	520	1080	2240	1740	760	0	6340
Average inventory = (Beginning inventory + Ending inventory)/2	0	0	260	800	1660	1990	1250	380
Backorders	160	120	0	0	0	0	0	0
Number of workers Hired	8	0	0	0	0	0	0	0
Costs									Total
Regular time labor cost= # of workers *160 hours*10	$   76,800.00	$   76,800.00	$   76,800.00	$   76,800.00	$   76,800.00	$   76,800.00	$   76,800.00	$     76,800.00	$   614,400.00
Inventory holding cost = Average inventory * 10	0	0	$     2,600.00	$     8,000.00	$   16,600.00	$   19,900.00	$   12,500.00	$       3,800.00	$      63,400.00
Backorders cost = # of Backorders * 20	$     3,200.00	$     2,400.00	0	0	0	0	0	0	$        5,600.00
Hiring cost = Workers hired * 400	$     3,200.00	0	0	0	0	0	0	0	$        3,200.00
Total Cost									$   686,600.00