CASE 1: LEARNING

CURVE ANALYSIS

Group 7

Problem #1

The ABC Company has just been given the

following production schedule for ski-lift

gondola cars. This product is considerably

different from any others the company has

produced. Historically, the company‘s learning

rate has been 80% on large projects. The first

unit took 1,000 hours to produce.

a. Estimate how many hours would be required to complete the 38th unit.

Month Units Cumulative

1 3 3

2 7 10

3 10 20

4 12 32

5 4 36

6 2 38

Solutiona) a. We use the learning curve formulas to

calculate the time required for the 38th unit:

a. Given: L=0.80 T1= 1000 hrs.

T38 = T1 (N (log L/log 2))

= 1000 (38 log 0.80/log 2)

= 310.04 hrs

• b. If the budget only provides for a maximum

of 30 direct labor employees in any month and

a total of 15,000 direct labor hours for the

entire schedule, will the budget be adequate?

Assume that each direct labor employee is

productive for 150 work hours each month.

Mont

hs Units

Cummulative

Units

Cumulative

Average

Cumulative

Average Time per

Unit

Cumulative Total

Hours for all Units

1 3 3 0.834034568 834.034568 2502.103704

2 7 10 0.631537303 631.5373025 6315.373025

3 10 20 0.524247142 524.2471422 10484.94284

4 12 32 0.45870687 458.7068697 14678.61983

5 4 36 0.443285172 443.2851721 15958.26619

6 2 38 0.436342826 436.3428259 16581.02738

Cumulative Hours

Number of hours per month.

Month

1 2502.103704 - 0 = 2502.103704 hrs

2 6315.373025-2502.103704= 3813.269321 hrs

3 10484.94284-6315.373025 = 4169.569815 hrs.

4 14678.61983-10484.94284= 4193.67699 hrs.

5 15958.26619-14678.61983= 1279.64636 hrs.

6 16581.02738-15958.26619= 622.76119 hrs.

Direct Labor Hours

Month Direct Labor Workers by Month

1 (2,502.1 hr)/(150 hr) = 16.7, or 17

2 (3,813.3 hr)/(150 hr) = 25.4, or 26

3 (4,169.6 hr)/(150 hr) = 27.8, or 28

4 (4,193.7 hr)/(150 hr) = 27.9, or 28

5 (1,279.7 hr)/(150 hr) = 8.5, or 9

6 (622.5 hr)/(150 hr) = 4.2, or 5

Conclusion:

*The schedule is sufficient in terms of the

maximum direct labor required in any month because

it never exceeds 30 employees. However, the total

cumulative hours are 16,581, which exceeds the

budgeted amount by 1,581 hours. Therefore, the

budget will not be adequate.

Problem 2

XYZ Company has $200,000 in cash, no inventory, and a 90

percent learning curve. To reduce the complexity of this problem, ignore

the hiring and training costs associated with dramatically increased

production. Employees are paid $20 per hour every Friday for that

week‘s work. XYZ has received an order to build 1,000 oak desks over

the next 15 weeks. Materials cost $400 per desk. Suppliers make

deliveries each Monday and insist on cash upon delivery. The first desk

takes 100 hours of direct labor to build. XYZ will be paid $1,500 per

desk two weeks after the desks are delivered. Should XYZ take this

order?

Additional Assumptions:

• Products are delivered at the end of each week.

Cash inflow from sales occurs at the end of the week.

Given: $ 20 per hour

100 hours per desk

$ 400 material cost per desk

$ 20 per hour x 100 hours per desk

= $ 2000 per desk

Cost:

$ 400 material cost per desk + $ 2000 per desk

= $ 2400 per desk

Week Units Total cost Inflows every after 2 weeks

1 2 4800

2 4 9600

3 8 19200 3000

4 12 28800 6000

5 14 33600 12000

6 24 57600 18000

7 64 153600 21000

8 128 307200 36000

9 128 307200 96000

10 128 307200 192000

11 88 211200 192000

12 100 240000 192000

13 100 240000 132000

14 100 240000 150000

15 100 240000 150000

150000

150000

Cash Outflows & Inflows

0

50000

100000

150000

200000

250000

300000

350000

0 2 4 6 8 10 12 14 16

Val

ues

Weeks

Cash Flow Chart

Total cost Inflows every after 2 weeks

Conclusion:

The company should not take the

order, because the total cost exceed the

cash inflow every after two weeks.