Question

The Austin, Texas plant of Computer Products produces disk units for personal and small business computers. Gerald Knox, the plant’s production planning director, is looking over next year’s sales forecasts for these products and will be developing an aggregate capacity plan for the plant. The quarterly sales forecasts for the disk units are as follows:

1st Quarter	2nd Quarter	3rd Quarter	4th Quarter
2,310	1,980	1,980	2,340

Ample machine capacity exists to produce the forecast. Each disk unit takes an average of 20 labor-hours. In addition, you have collected the following information: a. Inventory carrying cost is $100 per disk unit per quarter. The cost is applied to all units in inventory at the end of a quarter. b. The plant works the same number of days in each quarter, 12 five-day weeks, 6 hours per day. c. Beginning inventory is 150 disk units. These will be used to help satisfy the 1st Quarter demand. d. In a backlog situation, the customer will wait for his order to be filled but will expect a price reduction each quarter he waits. The backlog costs are $300 per disk for the first quarter the customer waits, $700 for the second quarter the customer waits, and $900 for the third quarter the customer waits. In filling orders, backlogged items will always be filled before current quarter items, e. The cost of hiring a worker is $800 while the cost of laying off a worker is $950. f. The straight time labor rate is $20 per hour for the first quarter and increases to $22 per hour in the fourth quarter. g. Overtime work is paid at time and a half (150%) of the straight time work. h. Outsourcing (contract work) is paid at the rate of $475 per disk unit for the labor and Computer Products provides the material. i. Demand during the fourth quarter of the prior year was 1,800 units and was fulfilled using a workforce working at full utilization. The demand for the first quarter of the next year (year following the year you are analyzing) is projected to be at the 2,340 unit level. Compare the following two sales and operations plans. i) The company will use a matching (chasing) demand strategy for the first two quarters. For quarters three and four, it will use a level production strategy with no overtime, no shortages during these quarters and no inventory leftover at the end of the fourth quarter. What is the total cost of this option, excluding the material cost? ii) The company will establish in quarter one and then maintain a workforce capable of producing 2,160 units in a quarter. If there are more workers in a quarter than required to produce the demand for that quarter, only the units required will be produced in that quarter and there will be underutilization. If demand is greater in a quarter than can be produced by the available workforce using straight time labor, the excess units will be outsourced. What is the total cost of this option, excluding the material cost?

Answer 1

Available production hours per quarter = 12*5*6 = 360 hours

Production per quarter per worker = 360/20 = 18

Demand during fourth quarter was = 1800

Workers during fourth quarter = 1800/18 = 100

Forecast for Q1 of next year = 2340

Workers required in Q1 of next year = 2340/18 = 130

i) Chase demand for Q1-2, Level demand for Q3-4

EXCEL FROMULAS:

i) Chase demand for Q1-2, Level demand for Q3-4
Month		1	2	3	4
Demand		2310	1980	1980	2340
Production
Regular time		=C12*$I$14*$I$15*$I$16/$I$17	=D12*$I$14*$I$15*$I$16/$I$17	=E12*$I$14*$I$15*$I$16/$I$17	=F12*$I$14*$I$15*$I$16/$I$17
Overtime
Subcontract
Ending inventory	150			180
Backlog
Balance		=B8-B9-C3-C8+C9+C5+C6+C7	=C8-C9-D3-D8+D9+D5+D6+D7	=D8-D9-E3-E8+E9+E5+E6+E7	=E8-E9-F3-F8+F9+F5+F6+F7
Workers	100	=B12+C13-C14	=C12+D13-D14	=D12+E13-E14	=E12+F13-F14
Hires		20		10
Lay off			10
Costs
Holding		=C8*$I$2	=D8*$I$2	=E8*$I$2	=F8*$I$2
Backorder		=C9*$I$3	=D9*$I$3	=E9*$I$3	=F9*$I$3
Hiring		=C13*$I6	=D13*$I6	=E13*$I6	=F13*$I6
Layoff		=C14*$I7	=D14*$I7	=E14*$I7	=F14*$I7
Straight-time		=C5*$I$17*$I$8	=D5*$I$17*$I$8	=E5*$I$17*$I$8	=F5*$I$17*$I$9
Overtime		=C6*$I$17*$I$10	=D6*$I$17*$I$10	=E6*$I$17*$I$10	=F6*$I$17*$I$11
Subcontract		=C7/2*$I12	=D7/2*$I12	=E7/2*$I12	=F7/2*$I12
Total		=SUM(C17:C23)	=SUM(D17:D23)	=SUM(E17:E23)	=SUM(F17:F23)
				Total Cost =	=SUM(C24:F24)

ii) Workforce established in first quarter = 2160/18 = 120

EXCEL FORMULAS:

ii) Maximum regular capacity of 2160							Costs
Month		1	2	3	4		Holding	100	/unit/qtr
Demand		2,310	1,980	1,980	2,340		Backorder1	300	/unit/q1
Production							Backorder2	700	/unit/q2
Regular time		2,160	1,980	1,980	2,160		Backorder3	900	/unit/q3
Overtime							Hiring	800	/worker
Subcontract					180		Layoff	950	/worker
Ending inventory	150						Straight-time-Q1-3	20	/hour
Backlog							Straight-time-Q4	22	/hour
Balance		0	0	0	0		Overtime-Q1-3	30	/hour
							Overtime-Q4	33	/hour
Regular Capacity		2160	2160	2160	2160		Subcontract	475	/hour
Workers	100	120	120	120	120
Hires		20					Weeks per quarter	12
Lay off							Days per week	5
							Hours per day	6
Costs							Labor standard	20	hours/disk
Holding		0	0	0	0
Backorder		0	0	0	0
Hiring		16,000	0	0	0
Layoff		0	0	0	0
Straight-time		864,000	792,000	792,000	950,400
Overtime		0,0	0,0	0,0	0,0
Subcontract		0	0	0	42,750
Total		880,000	792,000	792,000	993,150
				Total Cost =	3,457,150