Learning Curve Solutions
1. Captain Nemo, the owner of the Suboptimum Underwater Boat Company (SUB),
is puzzled. He has a contract of 11 boats and has completed 4 of them. He has
observed that his production manager, young Mr. Overick, has been reducing the
number of people working on the contract. The first boat, for example, required
225 workers, while 45 fewer workers were required for the second boat. Overick
has told them that “This is just the beginning!” and that he will complete the last
boat in the current contract with only 100 workers. Overick is banking on the
learning curve, but has he gone too far?
SOLUTION:
Number of workers required for second boat = 225 – 45 = 180
The learning rate is: b = 180/225 = 0.80 (80% learning curve)
K = 225 (number of workers needed for the first boat)
n = ln(b)/ln(2) = ln(0.80) / ln(2) = -0.223 / 0.693 = -0.322
Y(x) = Kxn
Y(11) = 225(11)-0.322 = 103.95
Unfortunately, young Mr. Overick has overestimated the learning curve… he will
NOT be able to produce the 11th boat with only 100 workers.
2. SUB has produced the first unit of a new line of minisubs at a cost of $500,000 $200,000 for materials and $300,000 for labor. It has agreed to accept a 10%
profit, based on cost, and is willing to contract on the basis of a 70% learning
curve. What will be the contract price for three minisubs?
SOLUTION:
K = 300,000 (do not include the cost of materials in the learning curve)
n = ln(b)/ln(2) = ln(0.70) / ln(2) = -0.357 / 0.693 = -0.515
The learning curve is: Y(x) = Kxn
Labor cost for second sub: Y(2) = 300,000(2)-0.515 = 209,938
Labor cost for third sub: Y(3) = 300,000(3)-0.515 = 170,374
Total cost for 3 subs:
Sub #1
200,000 + 300,000 = 500,000 (material + labor)
Sub #2
200,000 + 209,938 = 409,938
Sub #3
200,000 + 170,374 = 370,374
-----------1,280,312
With a 10% profit margin: 1,280,312(1.10) = 1,408,343
The contract price for three subs should be $1,408,343.
3. A job applicant is being tested for an assembly line position. Management feels
that steady-state times are reached after 1,000 performances. Regular assembly
line workers are expected to perform the task within 4 minutes. If the job
applicant performed the first test operation in 10 minutes and the second in 9
minutes, should this applicant be hired?
SOLUTION:
Time needed for the first test operation: K = 10
The learning rate is: b = 9/10 = 0.90
n = ln(0.90)/ln(2) = -0.105 / 0.693 = -0.152
The learning curve is: Y(x) = Kxn
Amount of time needed for the 1000th unit: Y(1000) = 10(1000)-0.152 = 3.5
Yes, this applicant should be hired because once she reaches steady-state (after
1000 operations) she will take 3.5 minutes to perform the operation.