Question

Suppose you have been given responsibility for developing the six-month aggregate production plan at Soda Galore, a manufacturer of soft drinks. Your company makes three types of soft drinks: regular, diet, and super-caffeinated. Fortunately, all three types are made using the same production process, and the costs related to switching between the three types are so minimal that they can be ignored. Thus, you can treat your problem as an aggregate planning exercise where the planning unit is cases of soft drinks, regardless of what types of drinks they are.

January	16,000
February	24,000
March	32,000
April	32,000
May	60,000
June	88,000
Total Demand	252,000
Average Monthly Demand	42,000

Current Workforce	10 workers
Average Monthly Output per Worker	2000 cases per month
Inventory Holding cost	$0.30 per case per month
Regular wage rate	$36 per hour
Regular production hours/ month/ worker	$100
Overtime wage rate	$54 per worker
Hiring cost	$1000 per worker
Firing cost	$1500 per worker
Subcontracting cost	$2.90 per case
Beginning inventory	7,000 (all safety stock)

A)Total cost is workforce size adjusted

Total cost if overtime production used

Total cost if subtracting used

B)After much internal discussion, the company decides to maintain a permanent workforce of 10 production workers. Given the same planning information and this new requirement, develop a six-month production plan based on hybrid production. Determine the cost of the hybrid production plan. Use the overtime cost.

Answer 1

A)Total cost is workforce size adjusted
Month	Demand	Beg. Inv.	Reg. Prod	OT	Subcontract	End. Inv.	# workers	# hired	# fired
January	16,000	7000	16,000	0	0	7,000	8	0	2
February	24,000	7,000	24,000	0	0	7,000	12	4	0
March	32,000	7,000	32,000	0	0	7,000	16	4	0
April	32,000	7,000	32,000	0	0	7,000	16	0	0
May	60,000	7,000	60,000	0	0	7,000	30	14	0
June	88,000	7,000	88,000	0	0	7,000	44	14	0
Total	252,000	42,000	252,000	0	0	42,000	126	36	2
Average Monthly Demand	42,000
					Costs
Current Workforce	10	workers		Regular Production	$453,600
Average Monthly Output per Worker	2000	cases per month		Inventory Holding cost	$12,600
Inventory Holding cost	$0.30	per case per month		Hiring cost	$36,000
Regular wage rate	$36	per hour		Firing cost	$3,000
Regular production hours/ month/ worker	100	hours		Total Cost	$505,200
Overtime wage rate	$54	per worker
Hiring cost	$1,000	per worker
Firing cost	$1,500	per worker
Subcontracting cost	$2.90	per case
Beginning inventory	7,000	(all safety stock)
(assuming we need to maintain a safety stock of 7000 units)

b)

Total cost if overtime production used
Month	Demand	Beg. Inv.	Reg. Prod	OT	Subcontract	End. Inv.	# workers	# hired	# fired
January	16,000	7000	20,000	0	0	11,000	10	0	0
February	24,000	11,000	20,000	0	0	7,000	10	0	0
March	32,000	7,000	20,000	12000	0	7,000	10	0	0
April	32,000	7,000	20,000	12000	0	7,000	10	0	0
May	60,000	7,000	20,000	40000	0	7,000	10	0	0
June	88,000	7,000	20,000	68000	0	7,000	10	0	0
Total	252,000	46,000	120,000	132,000	0	46,000	60	0	0
Average Monthly Demand	42,000
					Costs
Current Workforce	10	workers		Regular Production	$216,000
Average Monthly Output per Worker	2000	cases per month		Overtime cost	$3,564
Inventory Holding cost	$0.30	per case per month		Subcontracting cost	$0.00
Regular wage rate	$36	per hour		Inventory Holding cost	$13,800
Regular production hours/ month/ worker	100	hours		Hiring cost	$0
Overtime wage rate	$54	per worker		Firing cost	$0
Hiring cost	$1,000	per worker		Total Cost	$233,364
Firing cost	$1,500	per worker
Subcontracting cost	$2.90	per case
Beginning inventory	7,000	(all safety stock)
(assuming we need to maintain a safety stock of 7000 units)

c)

Total cost if subtracting used
Month	Demand	Beg. Inv.	Reg. Prod	OT	Subcontract	End. Inv.	# workers	# hired	# fired
January	16,000	7000	20,000	0	0	11,000	10	0	0
February	24,000	11,000	20,000	0	0	7,000	10	0	0
March	32,000	7,000	20,000	0	12000	7,000	10	0	0
April	32,000	7,000	20,000	0	12000	7,000	10	0	0
May	60,000	7,000	20,000	0	40000	7,000	10	0	0
June	88,000	7,000	20,000	0	68000	7,000	10	0	0
Total	252,000	46,000	120,000	0	132,000	46,000	60	0	0
Average Monthly Demand	42,000
					Costs
Current Workforce	10	workers		Regular Production	$216,000
Average Monthly Output per Worker	2000	cases per month		Overtime cost	$0
Inventory Holding cost	$0.30	per case per month		Subcontracting cost	$382,800
Regular wage rate	$36	per hour		Inventory Holding cost	$13,800
Regular production hours/ month/ worker	100	hours		Hiring cost	$0
Overtime wage rate	$54	per worker		Firing cost	$0
Hiring cost	$1,000	per worker		Total Cost	$612,600
Firing cost	$1,500	per worker
Subcontracting cost	$2.90	per case
Beginning inventory	7,000	(all safety stock)
(assuming we need to maintain a safety stock of 7000 units)

d)

B) hybrid production plan
Month	Demand	Beg. Inv.	Reg. Prod	OT	Subcontract	End. Inv.	# workers	# hired	# fired
January	16,000	7000	20,000	0	0	11,000	10	0	0
February	24,000	11,000	20,000	0	0	7,000	10	0	0
March	32,000	7,000	20,000	12000	0	7,000	10	0	0
April	32,000	7,000	20,000	12000	0	7,000	10	0	0
May	60,000	7,000	20,000	40000	0	7,000	10	0	0
June	88,000	7,000	20,000	68000	0	7,000	10	0	0
Total	252,000	46,000	120,000	132,000	0	46,000	60	0	0
Average Monthly Demand	42,000
					Costs
Current Workforce	10	workers		Regular Production	$216,000
Average Monthly Output per Worker	2000	cases per month		Overtime cost	$3,564
Inventory Holding cost	$0.30	per case per month		Subcontracting cost	$0
Regular wage rate	$36	per hour		Inventory Holding cost	$13,800
Regular production hours/ month/ worker	100	hours		Hiring cost	$0
Overtime wage rate	$54	per worker		Firing cost	$0
Hiring cost	$1,000	per worker		Total Cost	$233,364
Firing cost	$1,500	per worker
Subcontracting cost	$2.90	per case
Beginning inventory	7,000	(all safety stock)
(assuming we need to maintain a safety stock of 7000 units)