Question

Management at the Kerby Corporation has determined the following aggregated demand schedule (in units): Month 1 2 3 4 Demand 500 800 1,000 1,400 Month 5 6 7 8 Demand 2,000 3,000 2,700 1,500 Month 9 10 11 12 Demand 1,400 1,500 2,000 1,200 An employee can produce an average of 10 units per month. Each worker on the payroll costs $2,000 in regular-time wages per month. Undertime is paid at the same rate as regular time. In accordance with the labor contract in force, Kerby Corporation does not work over- time or use subcontracting. Kerby can hire and train a

Answer 1

For Level plan,

Add up the total demand = 500 + 800 + 1,000 + 1,400 + 2,000 + 3,000 + 2,700 + 1,500 + 1,400 + 1,500 + 2,000 + 1,200
Total Demand for 12 months = 19,000 units
Average Demand for month = 19,000 / 12 = 1,583.33 units

It is given that a single worker can produce 10 units per month, that implies for producing 1,583 units we need
1,583.33/10 = 158 employees (or) if you want to round off up front we may need 159 employees

For Chase Plan,

The total demand for the month is as it is taken up for production and we calculate individual number of workers required for the respective months. So for,

Month 1 = Demand = 500 ; Number of workers = 500/10 = 50
Month 2 = Demand = 800 ; Number of workers = 800/10 = 80
Month 3 = Demand = 1,000 ; Number of workers = 1,000/10 = 100
Month 4 = Demand = 1,400 ; Number of workers = ,400/10 = 140
Month 5 = Demand = 2,000 ; Number of workers = 2,000/10 = 200
Month 6 = Demand = 3,000 ; Number of workers = 3,000/10 = 300
Month 7 = Demand = 2,700 ; Number of workers = 2,700/10 = 270
Month 8 = Demand = 1,500 ; Number of workers = 1,500/10 = 150
Month 9 = Demand = 1,400 ; Number of workers = 1,400/10 = 140
Month 10 = Demand = 1,500 ; Number of workers = 1,500/10 = 150
Month 11 = Demand = 2,000 ; Number of workers = 2,000/10 = 200
Month 12 = Demand = 1,200 ; Number of workers = 1,200/10 = 120

Mixed strategy Production Plan

Mixed Strategy
Month	1	2	3	4	5	6	7	8	9	10	11	12
Demand	500	800	1000	1400	2000	3000	2700	1500	1400	1500	2000	1200
Beginning inventory	0	1130	1960	2590	2820	2450	1080	10	0	0	0	0
Production required	500	-330	-960	-1190	-820	550	1620	1490	1400	1500	2000	1200
Regular workforce	163	163	163	163	163	163	163	149	140	150	200	120
Regular production	1630	1630	1630	1630	1630	1630	1630	1490	1400	1500	2000	1200
Ending inventory	1130	1960	2590	2820	2450	1080	10	0	0	0	0	0
Workers hired	0	0	0	0	0	0	0	0	0	10	50	0
Workers fired	0	0	0	0	0	0	0	14	9	0	0	80
Cost:
Month	1	2	3	4	5	6	7	8	9	10	11	12
Production cost per worker ($2000/month)	$326,000	$326,000	$326,000	$326,000	$326,000	$326,000	$326,000	$298,000	$280,000	$300,000	$400,000	$240,000
Inventory holding cost ($32/unit/month)	$36,160	$62,720	$82,880	$90,240	$78,400	$34,560	$320	$0	$0	$0	$0	$0
Hiring cost ($2000 per worker)	$0	$0	$0	$0	$0	$0	$0	$0	$0	$20,000	$100,000	$0
Firing cost ($500 per worker)	$0	$0	$0	$0	$0	$0	$0	$7,000	$4,500	$0	$0	$40,000
Total monthly cost	$362,160	$388,720	$408,880	$416,240	$404,400	$360,560	$326,320	$305,000	$284,500	$320,000	$500,000	$280,000
Total cost												$4,356,780