Aggregate Capacity Planning and Inventory Cost Analysis for Disk Drive Production

Name: Aggregate Capacity Planning and Inventory Cost Analysis for Disk Drive Production
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Author: David Miller

An assignment on capacity planning and inventory management.

David Miller

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Aggregate Capacity Planning and Inventory Cost Analysis for Disk Drive
Production
SHOW ALL WORK!!!!
Answer Page for Selected Problems
Provide only your final answers (for example, the final numbers, selection, etc.) to the following
problems. Remember to show your work and answers for these problems on the problem
pages.
Example only: the break-even point is 100,000 units as this is the point where the cost of the
two options is equal. Below that level we prefer option A and above that we would use option C
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#2
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3
1. (17 points)
A grocery store orders paper grocery bags from a distributor. The store uses 2,300 cases of bags
per year, and its ordering cost is $65 per order. The store’s carrying cost rate is 35% of the price
per case of bags. The distributor has the following pricing structure for cases of bags:
Order Quantity (Number of cases) Price per case
1-49 $129.45
50-249 $127.95
250-999 $126.45
1000 and over $125.95
a) How many cases of bags should the store order each time if we want to select the lowest
total annual cost strategy (ordering cost plus holding cost plus material acquisition cost)?
Ans:
EOQ at different price points are:
Price – 129.45, EOQ = sqrt(2*2300*65/(35%*129.45)) = 81.23
Price – 127.95, EOQ = sqrt(2*2300*65/(35%*127.95)) = 81.7
Price – 126.45, EOQ = sqrt(2*2300*65/(35%*126.45)) = 82.19
Price – 125.95, EOQ = sqrt(2*2300*65/(35%*125.95)) = 82.35
Only the EOQ at 127.95 falls in the order quantity range allowed for that price point.
Total cost at this EOQ = 2300*127.95 + 65*2300/81.7 + 35%*127.95*81.7/2 = $297,944.23
The total annual cost at the boundary conditions for each price point is calculated below:
Price - $129.45, Order quantity = 1
Total cost = 2300*129.45 + 65*2300 + 35%*129.45/2 = $447,257.7
Price - $127.95, Order quantity = 50
Total cost = 2300*127.95 + 65*2300/50 + 35%*127.95*50/2 = $ 298,394.56
Price - $126.45, Order quantity = 250
Total cost = 2300*126.45 + 65*2300/250 + 35%*126.45*250/2 = $ 296,965.19
Price - $125.95, Order quantity = 1000
Total cost = 2300*125.95 + 65*2300/1000 + 35%*125.95*1000/2 = $311,875.75
Hence optimal cases of bags to be ordered is 250 cases

4
b) What is the resulting total cost per year (ordering cost plus holding cost plus material
acquisition cost) for this strategy and the next lowest cost strategy?
Ans:
a) Total cost per year = $296,965.19
Next lowest cost occurs at the EOQ with the price point of $127.95 i.e. $297,944.23
c) If the store has only enough storage space for 100 cases of bags, how many should it
order each time? Why?
Ans:
Storage space = 100 cases
Hence order quantity <= 100 as the peak inventory in a system = Order quantity while minimum
inventory is 0.
As the EOQ of 81.7 at price point of $127.45 results in second lowest cost and also satisfies
storage constraint, no of bags to be ordered is 81.7
If a calculated order quantity is a fraction of a case, leave it as a fractional amount.

5
2. (25 points)
The Austin, Texas plant of Computer Products produces disk drives 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 drives are as follows:
1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
2,340 2,700 2,610 2,520
Ample machine capacity exists to produce the forecast. Each disk drive takes an average of 20 labor-
hours. In addition, you have collected the following information:
a. Inventory holding or carrying cost is $100 per disk drive per quarter. The holding cost is based on the
inventory at the end of each 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 zero disk drives.
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 floppy 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 any quarter, if there is a backlog, this backlog will be filled before the demand for
that period is filled.
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 you provide the
material
i. Demand is projected to increase this year. Demand during the fourth quarter of the prior year was
2,340 units. The demand for the first quarter of the next year (year following the year you are
analyzing) is projected to be at the 2,700 unit level.
a) You want to maintain a work force capable of producing 2,520 in a quarter and either using
overtime or outsourcing as explained next for any disk units over this quantity that are required in
a quarter. If additional capacity is needed during quarters one and two, the company will use
overtime to meet the additional demand during each of these periods. During quarters three and
four, the company will use outsourcing if needed to meet the demand during each of these
periods. The company will only produce what is required during a quarter and underutilization
will occur if all of the production capacity is not required. What is the total cost of this option,
excluding the material cost? Be sure to include any hiring and layoff costs.

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1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
Demand 2,340 2,700 2,610 2,520
Beginning Inventory 0 0 0 0
Normal Production 2340 2520 2520 2520
Overtime 180 0 0
Outsourced production 90 0
Ending Inventory 0 0 0 0
No of labor-hours required 50400 50400 50400 50400
Labor rate per hour 20.00 20.67 21.33 22.00
Labor cost 1008000 1041600 1075200 1108800
Overtime rate 30 31 32 33
Overtime hours 0 3600 0 0
Overtime cost 0 111600 0 0
Outsourcing cost 0 0 42750 0
No of workers required 140 140 140 140
No of workers hired 140 0 0 0
No of workers fired 0 0 0 0
Hiring Cost 112000 0 0 0
Firing Cost 0 0 0 0
Total Cost 1120000 1153200 1117950 1108800
Cumulative cost 4499950
b) The company will maintain a work force capable of producing 2,340 units in a quarter. It will allow
backlogs to occur until the fourth quarter when it will outsource all demand that cannot be met with
its own workforce. All workers will be fully utilized each quarter. In other words, there is no
underutilization. No overtime is worked during any quarter. What is the total cost of this option,
excluding the material cost? Be sure to include any hiring and layoff costs.

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7
1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
Demand 2,340 2,700 2,610 2,520
Beginning Inventory 0 0 0 0
Normal Production 2340 2340 2340 2340
Outsourced production 0 810
Ending Inventory 0 0 0 0
Backlog 0 360 630 0
No of labor-hours required 46800 46800 46800 46800
Labor rate per hour 20.00 20.67 21.33 22.00
Labor cost 936000 967200 998400 1029600
Outsourcing cost 0 0 0 384750
Backlog cost 0 108000 189000 0
No of workers required 130 130 130 130
No of workers hired 130 0 0 0
No of workers fired 0 0 0 0
Hiring Cost 104000 0 0 0
Firing Cost 0 0 0 0
Total Cost 1040000 1075200 1187400 1414350
Cumulative cost 4716950

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Operations Management

Aggregate Capacity Planning and Inventory Cost Analysis for Disk Drive Production

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