earliest MODULE
E:
LEARNIN
G
CURVES
4.
The application of learning curves appears in the work of
architect Frank Lloyd Wright.
False (Introduction, easy)
5.
1.
Experi
ence
curves
may
be
valid
for
industr
ial
applic
ations,
but
have
no role
in
service
s such
as
health
care
proced
ures.
False
(Introducti
on, easy)
2.
Experience
curves are the
opposite of
learning curves
as one rises, the
other falls.
False
(Introducti
on, easy)
3.
premise that people and organizations become better at their tasks
as the tasks are repeated.
True (Introduction, moderate)
Learning
curves are
based on
the
Learning curves can only be applied to labor.
False (Introduction, moderate)
6.
If the learning rate for a process is 100 percent, then each unit
in a series of units will have the same labor requirements.
True (Introduction, moderate)
7.
If the first unit in a series of units takes 200 days to complete, and
the learning rate is 80%, then the second unit will take 160 days.
True (Introduction, easy) {AACSB: Analytic Skills}
8.
An 80% learning curve means that with each unit increase in
production, labor requirements fall by
20%.
False (Introduction, moderate)
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.
True (Introduction, easy)
10.
The learning rate in the steel industry and the learning rate
in heart surgery have both been estimated at 79 percent.
True (Introduction, and Learning curves in services and
manufacturing, moderate)
11.
A project manager bases his time and labor estimates on a learning
rate of 86%. The actual learning rate turns out to be 89%. The
manager, because of the decreased learning, will complete his
project in more time and with more labor use.
True (Learning curves in manufacturing and services,
moderate)
12.
The learning curve may not be permanent; it can be disrupted by
changes in process, personnel, or product.
True (Learning curves in services and manufacturing,
moderate)
5
6
5
1 3.
Learning curves can be used to establish budgets.
True (Learning curves in services and manufacturing,
moderate)
14.
The arithmetic approach (or successive doubling approach) to learning curve calculations
allows us to determine the hours required for any unit.
False (Applying the learning curve,
moderate)
15.
The logarithmic approach to learning curve calculations allows us to determine the hours
required for any unit.
True (Applying the learning curve,
moderate)
16.
The learning curve coefficient approach may be simpler to use than the logarithmic
approach, but it requires the presence of a table of learning coefficients.
True (Applying the learning curve,
moderate)
17.
In the formula TN=T1Nb for the learning curve, the exponent b is the learning rate,
expressed as a decimal.
False (Applying the learning curve,
moderate)
18.
A firm that successfully pursues a steeper-than-industry-average learning curve and
manages costs down may still fail if, by underestimating a strong competitor, it fails to
gain the added volume necessary for the learning curve to exist.
True (Strategic implications of learning curves,
moderate)
19. On an ordinary graph, unit times decrease at a decreasing rate, but on a log-log graph, the
learning
"curve" appears as a straight
line.
True (Strategic implications of learning curves,
moderate)
20.
Reevaluation of learning curves is inappropriate.
False (Limitations of learning curves,
moderate)
MULTIPLE CHOICE
21.
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
b
(Introduction,
moderate)
22.
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.
c
(Introduction,
moderate)
566
2 3.
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
d (Introduction, easy)
24. Learning curves have a variety of purposes, which can be placed into these broad
categories:
a. services, industry, and
military b. internal, external,
and strategic
c. wholesale, distribution, and retail
d. arithmetic, logarithmic, and learning coefficients
e. positive learning, neutral learning, and negative learning
b (Introduction, easy)
25.
Learning curves (or experience curves) were first applied to industry by
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
c (Introduction, easy)
who
26.
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
b.
16.2 c.
18
d. 20
e. 54.2
b (Introduction, easy) {AACSB: Analytic Skills}
27.
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
these
e (Introduction, easy)
28.
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.
e (Introduction, easy)
567
2 9.
30.
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. exponential
curve
c
(Introduction,
easy)
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.
d
(Introduction,
moderate)
31. 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.
c
(Introduction,
moderate)
32.
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. always based on a constant work force
a
(Introduction,
easy)
33.
Which of the following statements comparing learning rates to improvement rates is true?
a. The learning rate is the same as the improvement
rate.
b. The learning 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 rates apply to labor only, while improvement rates apply to all
resources. e. "Learning rates" is American usage, while "improvement rates"
is British.
c (Learning curves in services and manufacturing,
easy)
34.
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
d (Learning curves in services and manufacturing,
moderate
568
3 5.
The learning rate depends on the characteristics of a company. Which one of the
following companies usually has the lowest learning rate and, therefore, the most
learning?
a. a product-focused company which produces high-volume products to
stock
b. a process-focused company which accepts orders from different customers with
different specifications
c. a company with a newly-installed flexible manufacturing system
(FMS)
d. a continuous process
company e.
a labor intensive
company
e (Learning curves in services and manufacturing,
difficult)
36.
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. Learning at a capital intensive operation will usually be LESS than it is for a labor
intensive operation.
c. Learning for simple products will usually be MORE than it is for complex
products. d. Learning curves can be used only for individuals, not for the
whole organization
e. None of the above is
true.
b (Learning curves in services and manufacturing,
moderate)
37.
The learning rate 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 logarithmic method. The coefficient b for that calculation is approximately
a. -.096
9
b.
-.2231 c.
-.3219
d. .80
e. 1.903
c (Learning curves in services and manufacturing, moderate) {AACSB: Analytic
Skills}
38.
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
logarithmic method. The coefficient b for that calculation is approximately
a. -.1053
b.
-.1520 c.
-.3219
d. .6931
e. 8.1
b (Learning curves in services and manufacturing, moderate) {AACSB: Analytic
Skills}
39.
The first unit of a product took 832 hours to build, and the learning rate is 75%. How
long will it take to make the 10th unit? (Use at least three decimals in the exponent if you
use the logarithmic 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
d (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
569
4 0.
The first unit of a product took 832 hours to build, and the learning rate is 75%. How
long will it take to make the 30th unit? (Use at least three decimals in the exponent if you
use the logarithmic 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
b (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
41.
The first unit of a product took 832 hours to build, and the learning rate is 90%. How
long will it take to make the 25th unit? (Use at least three decimals in the exponent if you
use the logarithmic approach.)
a. time 500
hours b.
5 00 <
time 525 c. 525
< time 530 d.
530 < time 550
e. time > 550
b (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
42.
The first unit of a product took 50 hours to build, and the learning rate is 80%. How long
will it take to make the third unit? (Use at least three decimals in the exponent if you use
the logarithmic approach.)
a. under
30
hours
b.
about 32
hours c. about 35
hours d.
about
50
hours
e.
about
75
hours
c (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
43.
The first unit of a product took 50 hours to build, and the learning rate is 85%. How long
will it take to make the 10th unit? (Use at least three decimals in the exponent if you use
the logarithmic approach.)
a. less than 24
hours
b.
from 25 to 30
hours c.from 30 to 35
hours d. from 35 to
40 hours e.
more
than 40 hours
b (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
4 4.
The first unit of a product took 1,000 hours to build and the learning curve is 85%. How
long will it take to make the first 5 units? (Use Table E.3)
a. less than 4,005
hours
b.
from 4,005 to 4,015
hours c.from 4,015 to 4,025
hours d.
from 4,025 to
4,035 hours e. from 4,035
to 4,045 hours
d (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
570
4 5.
The first unit of a product took 900 hours to build and the learning curve is 90%. How
long will it take to make the first 3 units? (Use Table E.3)
a. less than or equal to 2,470
hours
b.
from 2,470 to 2,472
hours c.from 2,472 to 2,475
hours d.
from 2,475 to
2,478 hours e. from 2,478
to 2,481 hours
b (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
46.
The first unit of a product took 80 work days. The learning rate is estimated to be 90%.
The time for the fourth unit will be about
work days and the time for the first four
units will be about
work days. (Use Table
E.3)
a. 51;
250
b.
250; 51 c.
65;
285
d. 51; cannot be
determined e. 65; cannot
be determined
c (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
47.
A defense contractor has just started producing turbines for a new government contract.
The first turbine took 7000 hours to produce. If the learning curve is 90%, how long will it
take to produce the 10th turbine? (Use at least three decimals in the exponent if you use
the logarithmic approach.) a. less than 4800 hours
b.
from 4800 to 4900
hours
c. from 4900 to 5000
hours d.
from 5000 to
5100 hours e. over 5100
hours
c (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
48.
A defense contractor has just started producing engines for a new government contract.
The first engine took 800 hours to produce. If the learning rate is 80%, how long will it
take to produce the first 20 engines? (Use at least three decimals in the exponent if you
use the logarithmic approach.) a.
less than or equal to 1000 hours
b. from 1000 to 8000
hours c.from 8000 to 8500
hours d. from 8500 to
10000 hours e. 10,000 or
more hours
c (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
49.
It took 60 hours to make the first unit of a product. After the second and third units were
made, the learning rate was estimated to be 80%. At $10 per hour, estimate the labor bill
for the fourth unit. (Use at least three decimals in the exponent if you use the logarithmic
approach.)
a. $400
or
less
b. from $400 to
$420 c. from $420 to
$440
d. from $1800 to
$2000 e.
over
$2000
a (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
571
5 0.
A manager is trying to estimate the appropriate learning curve for a certain job. The
manager notes that the first four units had a total time of 30 minutes. Which learning curve
would yield approximately this result if the first unit took 9 minutes?
a. 0.70
b. 0.75
c. 0.80
d. 0.85
e. 0.90
d (Applying the learning curve, difficult) {AACSB: Analytic
Skills}
51.
Which one of the following courses of actions would not be taken by a firm wanting to
pursue a learning curve steeper than the industry average?
a. following an aggressive pricing
policy b. focusing on continuing cost
reduction
c. keeping capacity equal to demand to control
costs
d. focusing on productivity
improvement e.
building on
shared experience
c (Strategic implications of learning curves,
moderate)
52.
Which of the following is false regarding learning curves?
a. Learning curves differ from company to
company.
b. Learning curves can always be used for indirect
labor. c.
Changes in personnel can change the
learning curve.
d. The learning curve may spike for a short time even if it is going to drop in the
long run.
e. All of the above are
true.
b (Limitations of learning curves,
moderate)
53.
Which of the following is a limitation of the use of learning curves?
a. Change in personnel, design, or procedure leave the learning curve
unchanged. b. Learning curves are applicable to services as well as to
manufacturing.
c. The culture of the workplace may alter the learning
curve.
d. Direct labor and indirect labor follow the same learning
curves.
e. Applications of learning curves are of tactical, not strategic,
importance.
c (Limitations of learning curves,
easy)
54.
Which of the following is not a limitation of the use of learning curves?
a. Any change in personnel, design, or procedure can alter the learning
curve. b. Time measurements on early units completed must be
accurate.
c. The culture of the workplace may alter the learning
curve.
d. Direct labor and indirect labor may not follow the same learning
curves. e.
All of these are limitations of learning curves.
e (Limitations of learning curves,
easy)
FILL-IN-THE-BLANK
55.
The earliest industrial application of learning curves came from a report by
T. P. Wright (Introduction,
easy)
572
.
5 6.
are based on the premise that people and organizations get better at their
tasks as the tasks are repeated.
Learning curves (Introduction, easy)
57.
If the learning rate for a process is 80 percent, that same process has a 20 percent
.
improvement rate (Learning curves in services and manufacturing, moderate)
58.
Failure to consider the effects of learning can lead to
of labor needs.
overestimates (Learning curves in services and manufacturing, moderate)
59.
The
is the simplest approach to learning curve problems.
arithmetic approach (Applying the learning curve, moderate)
60.
To use the table of learning curve coefficients, you must specify
and
the learning rate, the unit of interest (Applying the learning curve, moderate)
61.
When learning curves are plotted on
scales, the "curves" become straight lines.
logarithmic or log-log (Strategic implications of learning curves, ANSWERS
62.
Describe easy)
.
SHORT the earliest application of learning curve concepts to industry.
T. P. Wright, working for Curtis-Wright Corp. in the 1930s, described how labor
costs of building aircraft decreased with learning. (Introduction, easy)
63.
In addition to labor, to which other variables have learning curves been applied?
The text cites materials and purchased components. The text also names surgical
survival rates as a variable that improves with learning. (Introduction, easy)
64.
What is the basic premise underlying the learning curve?
The basic premise underlying the learning curve is that organizations, like people,
become better at their tasks as the tasks are repeated. (Introduction, easy)
65.
Why do different organizations have different learning curves?
The rate of learning varies depending upon the quality of management and the
potential of the process and product. (Learning curves in services and
manufacturing, moderate)
66.
When comparing a 70% learning curve versus a 90% learning curve, which one results
in a more rapid reduction in labor requirements? Why?
Learning curves are defined in terms of the complements of their improvement rates.
A 70%
learning curve implies a 30% decrease in time each time the number of replications is
doubled. A 90% learning curve implies a 10% decrease in time each time the number
of replications is doubled. Therefore, the reduction in labor requirements is more
rapid at 70% than at 90%. (Learning curves in services and manufacturing,
moderate)
67.
What problems in scheduling can arise if adjustments for learning curve effects in
operations are not made?
Labor and productive facilities being idle a portion of the time; and firms may refuse
additional work because improvements that result from learning are not
considered. (Learning curves in services and manufacturing, moderate)
573
68.
"By tradition, learning rates are defined in terms of the complements of their
improvement rates." Explain.
The improvement in labor usage might be expressed as a 10% reduction. The
complement of
10% is 90%. We refer to learning not by the 10% improvement, but by improvement
to 90%
of the old value. The latter number, not the former, expresses learning rates.
(Learning curves in services and manufacturing, moderate)
69. Two manufacturers have very different learning rates; one is under 70% while the other is
over
80%. What factors might lead to such a gap?
The two firms might not have the same labor content in their output: learning is
generally associated with high labor content output. The two firms might not have
equally standardized outputs; if the product keeps changing, there is limited basis
for learning to occur. One firm might be engaged in high-volume, standardized
production where little learning remains. (Learning curves in services and
manufacturing, moderate)
70.
Explain how learning curves might be applied in a scheduling application.
Learning curves can determine the total labor required to produce a specified
number of units. Knowing the unit and total labor requirements, managers can
better calculate how long before each unit will be finished, and can schedule
shipment of finished goods accordingly. Also, managers can determine how many
workers to schedule during the manufacturing process; that number might fall as
learning takes place. (Introduction, easy)
{AACSB: Reflective Thinking}
71.
Explain how learning curves might be applied in a bid preparation application.
Learning curves can determine the reduction in labor and/or materials required to
produce a specified number of units. Knowing these cost components, managers are
better prepared to determine what to bid and when to promise finished goods.
(Introduction, easy) {AACSB: Reflective Thinking}
72.
Identify one advantage and one disadvantage of the arithmetic approach over the
logarithmic approach to learning curve calculations.
Advantage: simplest approach to learning curve problems. Disadvantage: can't
find values for every value of n, only for exact doublings. (Applying learning
curves, moderate)
73.
What cautions are in order when using learning curves?
The cautions when using learning curves include:
1. Estimates for each organization should be developed rather than applying someone
else's.
2. When current information becomes available, reevaluation is appropriate.
3. Any change in personnel, design, or procedure can be expected to alter the learning
curve.
4. Learning curves do not always apply to indirect labor and materials.
5. The culture of the work place, as well as resource availability and changes in the
process, may alter the learning curve. (Limitations of learning curves, moderate)
7 4.
What can cause a learning curve to vary from a smooth downward slope?
Several factors can affect the smooth downward slope of a learning curve,
including new technology, phasing out of a product line, moving experienced
employees to a new line. (Limitations of learning curves, moderate)
574
PROBLEMS
75.
In the logarithmic approach to learning curve calculations, you have used the
formula = T ( b
) . For a problem with a 92 percent learning rate, what is b?
T
N1
N
log r
log .92
.03621
b=
log 2 = log 2 = .30103 = .12029 . (Applying the learning curve, moderate)
{AACSB: Analytic Skills}
76.
In the logarithmic approach to learning curve calculations, you have used the
formula = T ( b
) . Your manager shows you a problem for which b is specified as
T
N1
-.18442.
N
What learning rate does that value represent?
The easiest way to answer is to assume T1 =1, and multiply that by 2 raised to the
power b. That will give the result 0.88, which is the learning rate. To verify, b for 88
percent learning
log r log .2 .05552
is: b =
log 2 = log 2 = .30103 = .18442 . (Applying the learning curve, moderate)
{AACSB: Analytic Skills}
77.
In the Learning-Curve Coefficients table for 70 percent learning, the sixth unit has a unit
time value of 0.398. Verify that table entry by use of the logarithmic formula. Use five
decimals in your work. The factor b for 70 percent learning is log .7 / log 2 = -.15490 / .
30103 = -.51457. For the sixth unit, the logarithmic approach results in 6-.51457 = .39773.
This differs from the table entry
only by rounding. (Applying the learning curve, moderate) {AACSB: Analytic Skills}
78.
The Learning-Curve Coefficients table reports that for 70 percent learning, the eighth
unit has a unit time value of 0.343. Verify that table entry by use of the arithmetic
method.
Successive doubling at 70 percent learning results in a factor of .700 for unit two, .490
for
unit four, and 0.343 for unit eight. (Applying the learning curve, easy) {AACSB:
Analytic
Skills}
79.
Your firm has a contract to make 20 specialty lenses for night vision equipment. The first
one took
40 hours. Learning is expected at the 85% rate. How long will it take to finish all 20 units?
The best solution method uses Table E.3. For 85 percent learning, total time for 20
units, the table factor is 12.402. Total time for all 20 units is 12.402 * 40 = 496.1
hours. (Applying the learning curve, moderate) {AACSB: Analytic Skills}
80.
Your firm has expertise with a special type of hand-finished furniture. The learning rate is
known to be 82%. If the first piece of furniture took 6 hours, use the logarithmic
approach tlo arning,ine hfactor b i= will take to d2)the-0.2863. T = T N = 6(3)
For 82% e determ the ow long t log(.82)/log( o = third unit.
=6*
0.7301 =
b
3
-0.2863
1
4.38 hours. (Applying the learning curve, moderate) {AACSB: Analytic Skills}
575
81. Your firm has expertise with a special type of hand-finished furniture. The learning rate is
known
to be 82%. If the first piece of furniture took 6 hours, estimate how long it will take to
complete the third unit.
Using the arithmetic approach, the second unit will take 0.82 * 6 = 4.92 hours and the
fourth unit will take 0.82 * 0.82 * 6 = 4.03 hours. The third unit must take an amount
of labor between these two values, but not exactly halfway. There is more absolute
improvement from unit 2 to unit 3 than from unit 3 to unit 4. A reasonable estimate
would be about 4.4 or 4.5 hours (the answer from Excel OM is 4.38 hours). (Applying
the learning curve, moderate)
{AACSB: Analytic Skills}
82. The first unit took 79 hours; the tenth took 46 hours. What learning rate is implied by the
data?
The improvement is 46/79 = 0.582 at 10 units; this closely matches the learning rate
of 85%. (Applying the learning curve, moderate) {AACSB: Analytic Skills}
83.
Your firm has expertise with a special type of hand-finished furniture. The learning rate is
known to be 82%. If the first piece of furniture took 6 hours, how long will it take to do
the second? How long will it take to do the fourth?
Use the successive doubling (arithmetic) approach. The second will take 0.82 * 6 = 4.92
hours;
the fourth will take 0.82 * 0.82 * 6 = 4.03 hours. (Applying the learning curve,
moderate)
{AACSB: Analytic Skills}
84.
You are about to undertake manufacture of a labor-intensive electronics component. The
first unit took 300 hours. You are not sure whether the learning rate is 70% or 80%. The
initial phase of the contract calls for 6 of these components.
a. How much time will it take to complete all six at 70% learning?
b. How much time will it take to complete all six at 80% learning?
From Table E.3, 70 percent learning, the factor for total time for six units is 3.593;
for 80 percent learning, the factor is 4.299. (a) 3.593 * 300 = 1077.8 hours; (b) 4.299
* 300 = 1289.8 hours. (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
85.
A certain product under development took 200 hours for the production of its 2nd unit
and 180 hours for its 4th unit.
a. What is the learning rate?
b. How much time did the first unit take?
c. How much time would the production of the 10th unit take? (Use both the logarithmic
and the
Table E.3 b) 222.2 ours; two = T N gree? .
(a) 90%; (approach.hDo the(c) T versions a= 222) 2(10)
= 156.6 hours; from Table E.3,
222.2 *
b
10
--.152
1
0.705 = 156.7 hours. They generate the same result. (Applying the learning curve,
moderate)
{AACSB: Analytic Skills}
576
8 6.
A contractor builds large ships for the Department of Defense. A recent contract called for
12 amphibious landing platforms. It was originally estimated that the first of these would
cost $1 billion and that 80 percent learning would be appropriate. In fact, the first ship cost
$1.6 billion and the second $1.12 billion. What is the revised learning rate? What will be
the total cost of the twelve ships? Is it higher or lower than the original estimates? If the
defense department cuts the contract from 12 ships to 9, what happens to the average cost
per ship?
The original estimates called for $1 billion * 7.227 = $7.227 billion for 12 ships. The
revised learning rate is 70 percent. At the revised costs and learning rates, 12 ships
will cost $1.6 billion * 5.501 = $8.802 billion. If the contract is reduced to 9 ships, the
cost would be $1.6 billion * 4.626 = $7.402 billion. The average cost of 12 ships is
$773.5 million each; the average cost of nine is $822.4 million each. (Applying the
learning curve, moderate) {AACSB:
Analytic Skills}
87.
A small manufacturer that offers "hand crafted" furniture has developed a new style of
desk that they believe will be very successful in the marketplace. It is expected that the
first desk will take about 60 hours of craftsmen's time to complete. They expect a 90%
learning curve for this desk. How long will it take to make the 20th desk? The firm is
considering accepting an order for 25 desks. How many hours of labor will this require
for all 25?
The 20th desk will require 38.1 hours. All 25 will require 1063
hours. (Applying the learning curve, moderate) {AACSB:
Analytic Skills}
577
8 8.
Your company is making experimental turbochargers for a new design of highpowered farm tractors. The production schedule for these new components is
contained in the table below.
Month
1
2
3
4
5
Turbochargers
4
6
7
8
5
The first turbocharger, a trial unit, took 900 hours to produce. Based on your experience
with similar products, the learning factor is 85%. You have 20 employees, and each
employee works
160 hours per month. How many hours will be required in each month? In which
month(s) will overtime be required to meet the production schedule?
Use the Total time column of the 85% section of Table E.3. The first four
turbochargers
require 900 * 3.345 = 3,010 hours. The first 10 turbochargers require 900 * 7.116 =
6,404 hours. From this answer, deduce that units 5 through 10 take 6,404 3,010 =
3,394 hours. The 20 employees contribute 3200 hours per month. Therefore,
overtime is not needed in the
first month but is needed in the second. Overtime is also needed in months 3 and 4,
but not in month 5. The table below contains calculation details. (Applying the
learning curve, difficult)
{AACSB: Analytic Skills}
Month
Number of
Cumulative
1
4
4
2
6
10
3
7
17
4
8
25
5
5
30
89.
Total Time
3.345
7.116
10.898
14.801
17.091
Cumulativ
3,010
6,404
9,808
13,321
16,111
Hours
3,010
3,394
3,404
3,513
2,790
Sally suspects strongly that there is a learning curve associated with solving problems
assigned for operations management. She notes that it took her approximately 33 minutes
to solve the first problem and 20 minutes to solve the fifth problem.
a. Estimate Sally's learning percentage.
b. Using your answer from part a, estimate how much longer it will take Sally to finish
the three problems that remain.
(a) Her improvement from the first to fifth unit is 20/33 = 0.606. This value is close
to the entry 0.596 for the fifth unit under the 80% learning rate column of Table
E.3. Thus her learning rate is 80%. (b) The total for eight problems is 33 * 5.346 =
176.4 minutes. She has already spent 33 * 3.738 = 123 minutes on the first five
problems. She has 53 minutes remaining. (Applying the learning curve, moderate)
{AACSB: Analytic Skills}
578
9 0.
Joe's Manufacturing is considering bidding on a small order for 5 units. Based on similar
products that they have made in the past, they believe that the first unit will take 500 labor
hours. They also believe that there will be an 80% learning rate. How many hours of
labor should Joe include for his bid?
From Table E.3, the total time factor for 5 units and 80 percent learning is 3.738.
The total number of labor hours for all five units would be 500 * 3.738 = 1,869
hours.
(Applying the learning curve, moderate) {AACSB: Analytic Skills}
91.
A company is preparing a bid on a government contract for 40 units of a certain
product. The operations manager estimates the assembly time required for the first two
units to be 10.4 hours and 8.3 hours, respectively.
a. What is the appropriate learning curve?
b. What is the average time per unit for the 40 units?
c. Which unit, if any, will require approximately one-half the time of the first unit?
(a) The learning rate is 8.3/10.4 = 0.798 or approximately 80%. (b) The group of 40
units will take 10.4 * 17.193 = 178.8 hours total, for an average of 4.47 hours each. (c)
The 9th unit has a unit time factor of 0.493, meaning that it requires approximately
50% of the labor of the first unit. (Applying the learning curve, moderate) {AACSB:
Analytic Skills}
92.
A small manufacturer builds wooden pleasure boats in a craftsman manner by traditional
labor- intensive methods. The first boat is estimated to take 650 hours of skilled labor,
which cost $40 per hour. They currently have three workers that can work 2,000 hours a
year. They assume that there is a 90% learning rate. How many boats can they make in
their first year?
The number of hours available for the first year is 6,000 hours. Use the total time
factor from
the 90 percent column of Table E.3. The total number of hours needed to make eleven
units is
650 * 8.689 = 5,648 hours; twelve would require 650 * 9.374 = 6,093
hours. (Applying the learning curve, moderate) {AACSB: Analytic
Skills}
93.
You are a cost accountant for a firm that specializes in "small" (under 10 billion dollars)
defense contracts for specialty electronics products, such as fully portable, miniaturized
CD-ROM imaging stations and global positioning transmitters/transponders. Your
company is well respected in this field. One project up for competitive bids is a Field
Service, Hands-Free, Individual Multi-Protocol Secure Communicator (a battlefield version
of a cellular telephone, but built into each soldier's helmet, and containing necessary
encryption technology). The Department of Defense wants 8 of these experimental devices
to test their practicality. You have reviewed the contract specifications, and estimated that
the first FSHFIMPSC should require 2350 hours, and that the product is subject to a 75%
learning rate. All costs of the project (machine purchase, machine time, direct and indirect
labor, and materials) have been bundled (allocated) into an hourly labor rate of $172 per
hour. Determine the total project cost using the provided data.
From Table E.3, 2350 * 4.802 = 11,284.7 hours will be needed. At $172 per hour, the
total cost is $1,940,968.40. (Applying the learning curve, moderate) {AACSB:
Analytic Skills}
579
9 4.
A metal works fabricator is about to release a new model of his firm's copper sculpture and
fountain. The operations manager estimates that this product is subject to a 90 percent
learning rate on labor onlythe material bill is not affected by experience. The firm prices
its work based on costthe sum of materials plus 30 percent and labor plus 50 percent.
(This allows the firm to practice a little "demand management" for its very popular works.)
The first item has already been finished; the material bill was $800 and labor totaled 40
hours. The firm pays its metalworking artisans an average of $18 per hour. What should
be the asking price of the first unit? The second? Based on the pricing formula, the first
unit should be priced at $800*1.30 + 40*$18*1.50 =
$1,040 + $1,080 = $2,120. The second unit will be cheaper because of the learning
effect:
$800*1.30 + 36*$18*1.50 = $1,040 + 972 = $2,012. (Applying the learning curve,
moderate)
{AACSB: Analytic Skills}
580