Operations Management: Processes and Supply Chains, 12e (Krajewski)
Supplement I Learning Curve Analysis
1) The learning effect can be represented by a line called a learning curve.
2) The first learning curve was developed by the aircraft industry.
3) An 80% learning rate means that the time falls by 20% at each doubling of output.
4) Which of the following statements about learning curves is generally true?
A) Management can decide to achieve a certain rate of learning.
B) Learning curves were first quantified by the U.S. Postal Service.
C) Using the “doubling” model, a learning curve with a rate of learning of 70 percent means the tenth unit
takes 70 percent of the time that the twentieth unit will take.
D) Learning curves are recognition of the concept that the time a task takes usually decreases with
experience.
5) Which one of the following statements is true about the relationship between learning curves and
competitive strategy?
A) Knowing where your process is on the learning curve will enable you to make frequent product
modifications.
B) Firms that emphasize low cost in their competitive strategy strive to move down the learning curve by
increasing volume.
C) Learning curves enable managers to project fixed manufacturing costs for future production
quantities.
D) Projecting the impact of learning curves into the future is one effective way of reducing the impact of
environmental uncertainty.
6) Which one of the following is an assumption of learning curves?
A) The cumulative time of production decreases as production increases.
B) Time reduction per unit increases as cumulative production increases.
C) The same learning curve should be used when a company increases its level of automation.
D) The reduction in time per unit follows an exponential curve.
7) Once the learning curve has flattened, i.e., reached a mostly horizontal shape, the per-unit time could
be described as ________.
8) A business that relies on learning effects to achieve their strategic objectives is most likely in a ________
volume ________ variety production sector.
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I.2 Developing Learning Curves
1) One assumption about learning curves is that the reduction in time obeys a normal distribution.
2) One assumption about learning curves is that the reduction in time will increase as output increases.
3) A task that obeys learning effects will, in general, have a positive result to the equation tn+1tn, where
tn is the completion time of the nth unit.
4) Which one of the following statements is not a typical assumption related to developing learning
curves?
A) The total direct labor hours needed to produce the first 100 units will be double the amount of hours
needed to build the first 50 units.
B) The direct labor needed per unit will decrease at a declining rate as cumulative production increases.
C) The direct labor hours per unit will decrease according to an exponential curve as cumulative
production increases.
D) The direct labor needed to produce the 50th unit will always be more than the direct labor needed to
produce the 51st unit.
5) The annual report for Luddite Corporation boasted of their ERP implementation and noted that, “while
there were initially some growing pains, our learning rate for this system has been calculated at 100%.”
What are the implications of this statement?
A) Luddite Corporation is twice as fast processing transactions now.
B) Luddite Corporation is twice as slow processing transactions now.
C) Luddite Corporation processes transactions at the same rate now.
D) Luddite Corporation processes transactions instantaneously (takes zero time) now.
6) Under learning curve theory, with a learning rate of 70 percent, the:
A) time to produce the second unit will be 70 percent less than the time to produce the first unit.
B) time to produce the second unit will be 30 percent less than the time to produce the first unit.
C) cumulative average time per unit after producing the first 100 units will be 70 percent less than the
average time per unit of the first 50 units.
D) average time per unit will be cut in half for every 70 units.
7) Which one of the following statements about learning curves is false?
A) The direct labor for the n+1st unit will always be less than the direct labor required for the nth unit.
B) The reduction in time will follow an exponential curve.
C) A benefit of learning curves is that they are unaffected by factors such as product complexity and the
rate of capital additions.
D) Using industry averages for learning curves can be risky because the type of work and competitive
niches can differ from firm to firm.
8) The first unit took fifteen days to finish and the second unit was finished a mere 13.5 days later. How
many more days will pass before the tenth unit is finished?
A) 91.5
B) 119.9
C) 109.3
D) 129.5
9) The first unit took fifteen days to finish and the second unit was finished a mere 13.5 days later. How
long will it take to finish the eighth unit?
A) 10.7 days
B) 10.9 days
C) 10.5 days
D) 11.1 days
10) The first two units took 28.5 days to finish and the subsequent two units took 24.8431 days to
complete. What is the learning rate?
A) 80%
B) 85%
C) 90%
D) 95%
11) Centurion Processing finishes the first unit in 100 hours and learns at a 75% rate. Their competitor,
Ochenta Incorporated, completes their first unit in 80 hours but learns at an 80% rate. If they match total
output with each other how many more units must each fierce rival make before Centurion is faster than
Ochenta?
A) four more
B) six more
C) eight more
D) ten more
12) Centurion Processing finishes the first unit in 120 hours and learns at a 70% rate. Their competitor,
Ochenta Incorporated, completes their fist unit in 80 hours but learns at an 80% rate. If they match total
output with each other how many units must each fierce rival make before Centurion‘s cumulative
processing time is lower than Ochenta’s?
A) 30 units
B) 33 units
C) 36 units
D) 39 units
13) The fifth unit took 36.3406 hours to produce and the eighth unit took only 32.549 hours. If the
producer, who shall remain nameless (for obvious reasons) learns at a constant rate, how long did the
first unit take?
A) 49 hours
B) 53 hours
C) 57 hours
D) 61 hours
14) In Troix City, the learning rate is based on a tripling of output instead of the traditional doubling. The
first unit of a long production run was produced in 25 hours. The process has an estimated learning rate
of 90 percent. At what level of output will the cumulative production time exceed 200 hours?
A) 8 units
B) 9 units
C) 10 units
D) 11 units
15) In Troix City, the learning rate is based on a tripling of output instead of the traditional doubling. The
first unit of a long production run was produced in 25 hours. The process has an estimated learning rate
of 90 percent. How long will the 15th unit take to produce?
A) 18.67 hours
B) 19.28 hours
C) 20.74 hours
D) 17.23 hours
16) In Troix City, the learning rate is based on a tripling of output instead of the traditional doubling. The
first unit of a long production run was produced in 25 hours. The process has an estimated learning rate
of 80 percent. How long will the 9th unit take to produce?
A) 22 hours
B) 20 hours
C) 18 hours
D) 16 hours
17) In Troix City, the learning rate is based on a tripling of output instead of the traditional doubling. The
first unit of a long production run was produced in 20 hours. In Deux City across the river, the learning
rate is based on the usual doubling of output. The first unit of the production run in Deux City took 30
hours. At what level of output will the workers in Deux City become faster than those in Troix City if
both locations enjoy an 80% learning rate?
A) 27 units
B) 31 units
C) 35 units
D) 39 units
18) Given that the third unit took 100 minutes and the rate of learning is 80 percent, how much time will
it take to build unit 96?
A) fewer than or equal to 30 minutes
B) greater than 30 minutes but fewer than or equal to 35 minutes
C) greater than 35 minutes but fewer than or equal to 40 minutes
D) greater than 40 minutes
19) It took 100 hours to produce the first unit and 95 hours to produce the second unit. How many hours
are required to produce the eighth unit? [Note: a calculator is required to answer this question.]
A) fewer than or equal to 60 hours
B) greater than 60 hours but fewer than or equal to 75 hours
C) greater than 75 hours but fewer than or equal to 90 hours
D) greater than 90 hours
20) It took 100 hours to produce the first unit and the learning rate is 80 percent. How much time will it
take to produce units 16 through 20? Refer to the copy of Table I.1 appended to this exam.
A) fewer than or equal to 160 hours
B) greater than 160 but fewer than or equal to 170 hours
C) greater than 170 but fewer than or equal to 180 hours
D) greater than 180 hours
21) Given that the fifth unit took 10 hours to build and the learning rate is 90 percent, how much time will
it take to build units 11 through 15? Refer to the copy of Table I.1 appended to this exam.
A) fewer than or equal to 38 hours
B) greater than 38 hours but fewer than or equal to 40 hours
C) greater than 40 hours but fewer than or equal to 42 hours
D) greater than 42 hours
22) A company is introducing a new product. The first unit took 1,000 hours to complete, and the fourth
unit took 750 hours to complete. What is the rate of learning for this product?
A) less than 40 percent
B) greater than or equal to 40 percent but less than 60 percent
C) greater than or equal to 60 percent but less than 80 percent
D) greater than 80 percent
23) The mathematical model that is used to generate a learning curve is ________.
24) The learning rate depends on factors such as ________ and ________, while replacing direct labor
hours with _________ alters the learning rate, giving less opportunity to make reductions in the required
hours per unit.
25) What are the three major assumptions of the learning curve?
26) A contractor is preparing a bid to install swimming pools at a new housing addition. The estimated
time to build the first pool is 35 hours. The contractor estimates a 90 percent learning rate; what is the
estimated time to install all 30 pools? Refer to the copy of Table I.1 appended to this exam.
27) The estimated time to produce the first unit is 100 hours. If a 90 percent learning rate is applicable,
what is the estimated time of producing the first ten units? Refer to the copy of Table I.1 appended to this
exam.
28) Tim usually exhibits a 90% learning rate for the mechanical tasks he undertakes. His next big project,
the fence along the street, will require 24 iterations of the fencepost task. If he has 40 hours available to
work on the project, how fast must he perform the first iteration in order to finish all 24 within his
allotted time? Refer to the copy of Table I.1 appended to this exam.
29) Tim usually exhibits an 80% learning rate for the mechanical tasks he undertakes. His next big project,
the fence along the street, will require 35 iterations of the fencepost task. If he has 80 hours available to
work on the project, how fast must he perform the first iteration in order to finish all 35 within his
allotted time? Refer to the copy of Table I.1 appended to this exam.
30) Two contract labor companies are competing for work being outsourced by Febrero SpA. One
contractor, Terza, has a learning rate governed by a tripling of output at a 90% rate and the other
contractor, Segundo, has a learning rate governed by the conventional doubling of output at a 90% rate.
Both Terza and Segundo take 20 minutes to complete the first unit they are given for bid estimation
purposes. How many more units must Terza make than Segundo before their time per unit drops below
15 minutes? [Note: a calculator is required to answer this question.]
I.3 Using Learning Curves
Case I.1
The production schedule for a new product follows.
Month
No. Units
1
15
2
20
3
40
4
35
The first unit took 100 hours to complete, and the rate of learning is 80 percent. Each employee works 40
hours per month. Refer to the copy of Table I.1 appended to this exam.
1) Using the information in Case I.1, how much time will it take to produce the units in month 1?
A) fewer than 800 hours
B) greater than or equal to 800 hours but fewer than 1,100 hours
C) greater than or equal to 1,100 hours but fewer than 1,500 hours
D) greater than 1,500 hours
2) Using the information in Case I.1, what is the minimum number of employees needed in month 3?
A) fewer than 20 employees
B) greater than or equal to 20 employees but fewer than 30 employees
C) greater than or equal to 30 employees but fewer than 40 employees
D) greater than 40 employees
3) The production for a new product follows:
Month
Units
1
4
2
5
3
6
4
7
The first unit will take 2,000 hours to produce and the learning rate is 90 percent. Currently, the company
employs 40 workers, who each work 200 hours regular time per month. In which months will overtime be
needed for the production schedule shown? Refer to the copy of Table I.1 appended to this exam.
A) month 4 only
B) months 3 and 4 only
C) months 1 and 2 only
D) month 1 only
4) How are learning curves useful in financial planning?
5) For a company that produces hand held calculators, the Operations Manager knows that in the early
stages of production for a new product, the expenditures exceed receipts, whereas in the latter stages, the
reverse is true. Give an explanation for this phenomenon.
6) When production time standards are being developed for a brand new process for several of the hand
assembly components of the production line, what are the implications of learning effects on the time
standards and the line balance? What could be done to address this situation?
1) The simpler the product, the more pronounced the learning rate.
2) Learning curves provide their greatest advantage in the early stages of new service or product
production.
3) As the cumulative number of units produced becomes large, the:
A) learning effect is more noticeable.
B) learning effect increases.
C) learning effect is less noticeable.
D) learning effect decreases.
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4) Which statement regarding the effect of automating some of the direct labor in a process is best?
A) The overall learning rate should be unaffected.
B) The overall learning rate will probably decrease.
C) The overall learning rate will probably increase.
D) The learning rate for the automated portion of the process should be higher than the learning rate for
the portion that is not automated.
5) Why is the learning rate more pronounced for complex products than for simple products?
6) What are some managerial considerations when using learning curves?
Answer: Although learning curves can be useful tools for operations planning, managers should keep
several things in mind when using them. First, an estimate of the learning rate is necessary in order to use