perations Management, 11e (Heizer/Render)
Module E Learning Curves
Section 1 What Is a Learning Curve?
1) Experience curves may be valid for industrial applications, but have no role in services such as health
care procedures.
2) Experience curves are the opposite of learning curves—as one rises, the other falls.
3) Learning curves are based on the premise that people and organizations become better at their tasks as
the tasks are repeated.
4) The earliest application of learning curves appears in the work of architect Frank Lloyd Wright.
5) Learning curves can only be applied to labor.
6) If the learning curve for a process is 100 percent, then each unit in a series of units will have the same
labor requirements.
7) If the first unit in a series of units takes 200 days to complete, and the learning curve is 80%, then the
second unit will take 160 days.
8) An 80% learning curve means that with each unit increase in production, labor requirements fall by
20%.
9) A 90% learning curve implies that each time the production volume is doubled, the direct time per unit
is reduced to 90% of its previous value.
10) The fundamental premise underlying learning curve analysis is that:
A) tasks can be easily learned in organizations.
B) organizations and people become better at their tasks as the tasks are repeated.
C) learning takes place when people in organizations change.
D) total labor costs decrease as the number of production units increases.
E) doubling output cuts labor requirements per unit in half.
11) Which of the following best conveys the essence of learning curves?
A) As the number of repetitions increases, time per unit increases.
B) As the number of repetitions decreases, time per unit increases.
C) As the number of repetitions increases, time per unit decreases.
D) As the number of repetitions increases, time per unit remains constant.
E) As the number of repetitions increases, time per unit doubles.
12) A learning curve:
A) plots man-hours per dollar versus time.
B) is mathematically described by a parabola.
C) should be plotted on polar coordinate graph paper.
D) is based on the premise that organizations learn from experience.
E) follows a normal distribution.
13) Learning curves (or experience curves) were first applied to industry by ________ who was studying
________.
A) Frank Lloyd Wright; architecture
B) Frank Gilbreth; worker efficiency
C) T. P. Wright; air frame manufacture
D) Lilian Gilbreth; factory efficiency
E) Frederick W. Taylor; scientific management
14) A job with a 90% learning curve required 20 hours for the initial unit. The fourth unit should require
approximately how many hours?
A) 16.0
B) 16.2
C) 18.0
D) 20.0
E) 54.2
15) The fact that human activities typically improve when they are done on a repetitive basis is described
by a:
A) normal distribution curve.
B) binomial distribution curve.
C) learning curve.
D) Poisson distribution curve.
E) repetition curve.
16) A 100% learning curve implies that:
A) learning is taking place for all products and workers.
B) learning is taking place at the best possible level.
C) a 100% reduction in the direct labor time takes place each time the production is doubled.
D) no learning is taking place.
E) None of the above is true.
17) Which of the following statements is most appropriate with respect to a 70% learning curve?
A) There will be a 70% decrease in direct labor per unit each time the production volume doubles.
B) Each successive unit of production will take 70% of the direct labor of the previous unit.
C) There will be a 30% decrease in direct labor per unit each time production volume doubles.
D) Thirty percent of the production will be defective until full learning takes place.
E) None of the above is true.
18) The learning curve rate is:
A) the percentage of time it will take to make each unit when the production rate doubles.
B) the log-log of the annual rate change divided by the average unit cost.
C) always based on constant value dollars.
D) only considered valid after one year of data is accumulated.
E) equal to at least 75%.
19) Which one of the following statements about learning curves is TRUE?
A) A learning curve assumes that the direct labor requirements per unit will DECREASE at an
INCREASING rate as cumulative production increases.
B) A larger learning curve rate implies faster (greater) learning.
C) A learning curve graph usually follows a negative exponential curve.
D) Learning curves can be used only for individuals, not for the whole organization.
E) The formula describing the learning curve principle of doubling is computed differently when
computing unit cost as opposed to unit time.
20) The earliest industrial application of learning curves came from a report by ________.
21) ________ are based on the premise that people and organizations get better at their tasks as the tasks
are repeated.
22) Describe the earliest application of learning curve concepts to industry.
23) In addition to labor, to which other variables have learning curves been applied?
24) What is the basic premise underlying the learning curve?
Section 2 Learning Curves in Services and Manufacturing
1) The learning curve in the steel industry and the learning curve in heart transplants have both been
estimated at 79 percent.
2) A project manager bases his time and labor estimates on a learning curve of 86%. The actual learning
curve turns out to be 89%. The manager, because of the decreased learning, will complete his project in
more time and with more labor use than his estimate suggested.
3) The learning curve may not be permanent; it can be disrupted by changes in process, personnel, or
product.
4) Learning curves can be used to establish budgets.
5) Learning curves have a variety of purposes. Your text places them into which three broad categories?
A) services, industry, and military
B) internal, external, and strategic
C) wholesale, distribution, and retail
D) doubling, formula, and learning curve table
E) positive learning, neutral learning, and negative learning
6) Learning curves can be applied to a variety of purposes internal to a firm, including:
A) labor forecasting.
B) scheduling.
C) establishing costs.
D) establishing budgets.
E) all of the above
7) Which of the following statements regarding the usefulness of learning curves is FALSE?
A) An external use of learning curves is in supply chain negotiations.
B) A strategic use of learning curves is in evaluating company and industry performance.
C) An internal use of learning curves is in establishing costs.
D) An internal use of learning curves is in labor forecasting.
E) A strategic use of learning curves is in establishing budgets.
8) Which of the following statements comparing learning curve rates (L) to improvement rates is TRUE?
A) The learning curve rate is the same as the improvement rate.
B) The learning curve rate is a decimal value while the improvement rate is a percentage.
C) A 90 percent learning curve corresponds to a 10 percent rate of improvement.
D) Learning curve rates apply to labor only, while improvement rates apply to all resources.
E) “Learning curve rates” is American usage, while “improvement rates” is British.
9) Learning curves are:
A) the same for all products but different for different organizations.
B) the same for all organizations but different for different products.
C) the same for all organizations and all products.
D) different for different organizations and different products.
E) appropriate in services but not in manufacturing.
10) If the learning curve for a process is 80 percent, that same process has a 20 percent ________.
11) Failure to consider the effects of learning can lead to ________ of labor needs.
12) Why do different organizations have different learning curves?
13) When comparing a 70% learning curve versus a 90% learning curve, which one results in a more rapid
reduction in labor requirements? Why?
14) What problems in scheduling can arise if adjustments for learning curve effects in operations are not
made?
15) “By tradition, learning curves are defined in terms of the complements of their improvement rates.”
Explain.
16) Explain how learning curves might be applied in a scheduling application.
17) Explain how learning curves might be applied in a bid preparation application.
Section 3 Applying the Learning Curve
1) The doubling approach to learning curve calculations allows us to determine the hours required for
any unit.
2) The formula approach to learning curve calculations allows us to determine the hours required for any
unit.
3) The learning-curve table approach may be simpler to use than the formula approach, but it requires the
presence of a table of learning-curve coefficients.
4) In the formula to compute the time for the Nth unit, TN = T1(Nb), the exponent b is the learning curve
rate L, expressed as a decimal.
5) If it took 1000 hours to produce the first unit of a product, and the learning curve is 70%, how long will
it take to produce units 26 through 50?
A) 12,307 hours
B) 8,404 hours
C) 134 hours
D) 3,903 hours
E) none of the above
6) The learning curve for a product is 80 percent. The first unit took 100 hours to complete. The
manufacturer wants to determine how many hours the fifth unit will take by using the formula approach.
What is the coefficient b for that calculation?
A) -.0969
B) -.2231
C) -.3219
D) .80
E) 1.903
7) The learning rate for a product is 90 percent. The first unit took 10 hours to complete. The
manufacturer wants to determine how many hours the fourth unit will take by using the formula
approach. What is the coefficient b for that calculation?
A) -.1053
B) -.1520
C) -.3219
D) .6931
E) 8.1
8) The first unit of a product took 832 hours to build, and the learning curve is 75%. How long will it take
to make the 10th unit? (Use at least three decimals in the exponent if you use the formula approach.)
A) less than 250 hours
B) from 251 to 275 hours
C) from 276 to 300 hours
D) from 301 to 325 hours
E) 325 or more hours
9) The first unit of a product took 832 hours to build, and the learning curve is 75%. How long will it take
to make the 30th unit? (Use at least three decimals in the exponent if you use the formula approach.)
A) less than 200 hours
B) from 200 to 225 hours
C) from 225 to 250 hours
D) from 2501 to 275 hours
E) 275 or more hours
10) The first product took 10 hours to build and the learning curve is estimated to be 90%. How long will
it take to make the fourth unit?
A) 10 hours
B) 9 hours
C) 8.1 hours
D) 7.5 hours
E) none of the above
11) The second unit of production took 9 hours. If the learning curve is 90% how long did the first unit
take?
A) 9 hours
B) 10 hours
C) 8.1 hours
D) 8.5 hours
E) none of the above
12) The first unit took 10 hours and the fourth unit took 8.1 hours to complete. What is the learning
curve?
A) 100%
B) 99%
C) 95%
D) 90%
E) 80%
13) The first unit took 10 hours and the eighth unit took 1.25 hours. What is the learning curve?
A) 50%
B) 90%
C) 80%
D) 12.5%
E) none of the above
14) The first unit took 10 hours and the fourth unit 8.1 hours. What is the improvement rate?
A) 99%
B) 95%
C) 90%
D) 15%
E) 10%
15) The first unit took 10 hours and the third unit took 5.68 hours. What is the improvement rate?
A) 70%
B) 30%
C) 50%
D) 90%
E) 10%
16) The first unit of production took 10 hours with an 80% learning curve. How long will it take to
complete both the first and second units?
A) 10 hours
B) 8 hours
C) 18 hours
D) 15.7 hours
E) There is not enough information to solve the problem.
17) It took 18 hours to complete the first two products with an 80% learning curve. How long did the
second product take?
A) 8.0 hours
B) 10.0 hours
C) 18.0 hours
D) 8.1 hours
E) none of the above
18) A company negotiates a price for two aircraft that includes a reduction in labor on the second aircraft
consistent with a 70% learning curve. Suppose the first aircraft took 100 hours. If the improvement rate
changes to 20%, how will the total time to complete both aircraft change?
A) no change
B) -10 hours
C) + 10 hours
D) -50 hours
E) + 50 hours
19) Suppose that there are two products with the same first product time. However, product A has an
improvement rate of 10% while product B has an improvement rate of 20%. How much longer will it take
to make the 10th unit of product A compared to product B?
A) Both will have the identical time for the 10th unit.
B) A will take 48% more time.
C) A will take 48% less time.
D) A will take 23% less time.
E) none of the above
20) The first unit of a product took 832 hours to build, and the learning curve is 90%. How long will it
take to make the 25th unit? (Use at least three decimals in the exponent if you use the formula approach.)
A) time ≤ 500 hours
B) 500 < time ≤ 525
C) 525 < time ≤ 530
D) 530 < time ≤ 550
E) time > 550
21) The first unit of a product took 50 hours to build, and the learning curve is 80%. How long will it take
to make the third unit? (Use at least three decimals in the exponent if you use the formula approach.)
A) under 30 hours
B) about 32 hours
C) about 35 hours
D) about 50 hours
E) about 75 hours