UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
College of Business
Department of Business Administration
BADM449 Strategic Management/Business Policy
Learning Curves
An important source of technological advance in many industries (e.g., farm tractors, power
tools, locomotives, oceangoing tankers, aircraft, and digital computers) is the learning curve. The
learning curve was first developed in the aircraft industry prior to World War II, when analysts
discovered that the direct labor input per airplane declined with considerable regularity as the
cumulative number of planes produced increased. For the industry, once production started, the
direct labor for the 8th unit was only 80 percent of that for the 4th unit, the direct labor for the 12th
unit was only 80 percent of that for the 6th unit, and so on. In each case, each doubling of the
quantity reduced production time by 20 percent. [Of course, for any given product and company,
the rate of learning may be different.]
Sources of Gain:
- You need less time to instruct workers.
- Workers become more skillful in their movements.
- You develop better operation sequences and better machine feeds and speeds.
- Machines and tooling are continually improved.
- Rejections and rework decrease.
- Manufacturing lots are larger, cutting down the set-up time proportion.
- Management controls are improved.
- "Crash measures" become uncommon.
- Engineering changes are less frequent.
- Cost-effective improvements in product design.
- Enriched know-how in managing and operating the business.
- Better use of materials, more efficient inventory handling, more efficient distribution
methods, and computerization and automation of assorted production, sales, and clerical
tasks.
Developing Learning Curves
In the following discussion and applications we focus on direct labor hours per unit, although
we could as easily have used costs. When we develop a learning curve, we make the following
assumptions.
- The direct labor required to produce the n + 1st unit will always be less than the direct labor required for the nth unit.
- Direct labor requirements will decrease at a declining rate as cumulative production increases.
- The reduction in time will follow an exponential curve.
In other words, the production time per unit is reduced by a fixed percentage each time
production is doubled. We can use a logarithmic model to draw a learning curve. The direct labor
required for the nth unit, kn, is
kn = k1 nb
where
- k1 = direct labor hours for the first unit
- n = cumulative number of units produced
- b = log r/log 2
- r = learning rate
We can also calculate the cumulative average number of hours per unit for the first n units with the
help of Table 1 below. Table 1 contains conversion factors that, when multiplied by the direct labor
hours for the first unit, yield the average time per unit for selected cumulative production quantities.
- Table 1
- Conversion Factors for the Cumulative Average Number of
Direct Labor Hours Per Unit
80% learning rate
(n = cumulative production)
n n n
1 1.00000 19 0.53178 37 0.43976
2 0.90000 20 0.52425 38 0.43634
3 0.83403 21 0.51715 39 0.43304
4 0.78553 22 0.51045 40 0.42984
5 0.74755 23 0.42984 64 0.37382
6 0.71657 24 0.49808 128 0.30269
7 0.69056 25 0.49234 256 0.24405
8 0.66824 26 0.48688 512 0.19622
9 0.64876 27 0.48167 600 0.18661
10 0.63154 28 0.47191 700 0.17771
11 0.61613 29 0.46733 800 0.17034
12 0.60224 30 0.46293 900 0.16408
13 0.58960 31 0.46293 1000 0.15867
14 0.57802 32 0.45871 1200 0.14972
15 0.56737 33 0.45464 1400 0.14254
16 0.55751 34 0.45072 1600 0.13660
17 0.54834 35 0.44694 1800 0.13155
18 0.53979 36 0.44329 2000 0.12720
90% learning rate
(n = cumulative production)
n n n
1 1.00000 19 0.73545 37 0.67091
2 0.95000 20 0.73039 38 0.66839
3 0.91540 21 0.72559 39 0.66595
4 0.88905 22 0.72102 40 0.66357
5 0.86784 23 0.71666 64 0.62043
6 0.85013 24 0.71251 128 0.56069
7 0.83496 25 0.70853 256 0.50586
8 0.82172 26 0.70472 512 0.45594
9 0.80998 27 0.70106 600 0.44519
10 0.79945 28 0.69754 700 0.43496
11 0.78991 29 0.69416 800 0.42629
12 0.78120 30 0.69090 900 0.41878
13 0.77320 31 0.68775 1000 0.41217
14 0.76580 32 0.68471 1200 0.40097
15 0.75891 33 0.68177 1400 0.39173
16 0.75249 34 0.67893 1600 0.38390
17 0.74646 35 0.67617 1800 0.37711
18 0.74080 36 0.67350 2000 0.37114
Example 1 Using Learning Curves to Estimate Direct Labor Requirements
A manufacturer of diesel locomotives needs 50,000 hours to produce the first unit. Based on past
experience with products of this sort, you know that the rate of learning is 80 percent.
Use the logarithmic model to estimate the direct labor required for the 40th diesel locomotive and
the cumulative average number of labor hours per unit for the first 40 units.
Solution:
- The estimated number of direct labor hours required to produce the 40th unit is:
kn = k1 nb
k40 = 50,000 (40)(log 0.8/log 2)
= 50,000 (40)(-0.322)
= 50,000 (0.30488)
= 15,244 hours
We calculate the cumulative average number of direct labor hours per unit for the first 40 units with
the help of Table 1. For a cumulative production of 40 units and an 80 percent learning rate, the
factor is 0.42984. The cumulative average direct hours per unit is
50,000 (0.42984) = 21,492 hours.
Example #2
Bellweather has a contract for 60 portable electric generators. The labor-hour requirement for
manufacturing the first unit is 100. With that as given, Bellweather planners develop an aggregate
capacity plan using learning-curve calculations. They use a 90 percent learning curve, based on
previous experience with generator contracts.
- The labor requirement for the second generator is:
k2 = k1 nb
= 100 (2)log 0.9/log 2
= 100 (2)-.152
= 100 (.9) = 90 hours
This result for the second unit, 90, is expected, since for a 90 percent learning curve there is a 10
percent learning between doubled quantities. For the fourth unit,
- = 100 (4)-.152
= 100 (.81) = 81 hours
This result may be obtained more simply by 100 (.9) (.9) = 100 (.81) = 81 hours
For the 8th unit,
- = 100 (8)-.152
= 100 (0.729) = 72.0 hours
This result is also obtained by 100 (.9) (.9) (.9) = 72.9 hours
This way of avoiding logarithms works for the 16th, 32nd, 64th, and so on units, that is, for
any unit that is a power of 2; but for the 3rd, 5th, 6th, 7th, 9th, and so forth units, the logarithmic
calculation is necessary. Table 2 below displays some of the results of the learning-curve
calculations. With those figures, Bellweather may assign labor based on the decreasing per-unit
labor-hour requirements. For example, the 60th generator requires 53.7 labor-hours, which is only
about half that required for the first unit. Completion of finished generators can be master scheduled
to increase at the 90 percent learning-curve rate.
Generator Number Labor Hours Required Cumulative Labor-Hours Required
1 100 100.0
2 90 190.0
3 84.6 274.6
10 70.5 799.4
20 63.4 1,460.8
30 59.6 2,072.7
40 57.1 2,654.3
50 55.2 3,214.2
60 53.7 3,757.4
Using Learning Curves
- Bid Preparation
- Estimating labor costs is an important part of preparing bids for large jobs.
Knowing the learning rate, the number of units to be produced, and wage rates, the estimator can arrive at the cost of labor by using a learning curve. After calculating expected labor and material costs, the estimator adds the desired profit to obtain the total bid amount.
- Financial Planning
- Learning curves can be used in financial planning to help the financial planner determine the amount of cash needed to finance operations. Learning curves provide a basis for comparing prices and costs. They can be used to project periods of financial drain, when expenditures exceed receipts. They can also be used to determine a contract price by identifying the average direct labor costs per unit for the number of contracted units. In the early stages of production the direct labor costs will exceed that average, whereas in the later stages of production the reverse will be true. This information enables the financial planner to arrange financing for certain phases of operations.
- Labor Requirements
- For a given production schedule, the analyst can use learning curves to project direct labor requirements. This information can be used to estimate training requirements and develop hiring plans.
Managerial Considerations in the Use of the Learning Curves
- (1)
- An estimate of the learning rate is necessary in order to use learning curves, and it may
be difficult to get.
- (2)
- Using industry averages can be risky because the type of work and competitive niches
can differ from firm to firm.
- (3)
- The learning rate depends on factors such as product complexity and the rate of capital
additions. The simpler the product, the less pronounced is the learning rate.
- (4)
- A complex product offers more opportunity to improve work methods, materials, and
processes over the product's life.
- (5)
- Replacing direct labor hours with automation alters the learning rate, giving less opportunity to make reductions in the required hours per unit. Typically, the effect of each
capital addition on the learning curve is significant.
- (6)
- Another important estimate is that of the time required to produce the first unit because
the entire learning curve is based on it.
- (7)
- Learning curves provide their greatest advantage in the early stages of new product or
service production. As the cumulative number of units produced becomes large, the
learning curve effect is less noticeable.
- (8)
- Learning curves are dynamic because they are affected by various factors. For example,
a short product or service life cycle means that firms may not enjoy the flat portion of the
learning curve for very long before the product or service is changed or a new one is
introduced. In addition, organizations utilizing team approaches will have different learning
rates than they had before they introduced teams. Total quality management and continual
improvement programs also will affect learning curves.
- (9)
- The institution of incentive systems, bonus plans, zero defect programs, and so on may
increase learning.
- (10)
- Aging of equipment can have a negative impact on learning curve advantages.
- (11)
- Transfer of employees can lead to an interruption or the regressing back to an earlier
stage of the learning curve.
- (12)
- Perhaps the greatest limitation of the learning curve is that the benefits run out simply
because of product obsolescence. But even before maturity is reached, the cost
reductions due to learning will provide diminishing returns.
- (13)
- Zealous pursuit of learning curve advantages can blind a firm to the need to (a) respond
to changes in customer needs and product uses; (2) match or better the product innova-
tions of rivals; and (3) shift to an even more innovative production technology.
Case Example:
The experience of the Ford Motor Company from 1908 to 1923 illustrates how a learning curve
advantage can lead a firm to focus obsessively on costs and thus ignore trends, fail to innovate, and
end up with an obsolete product. The Model T had a well-defined 85 percent learning curve. It is
worth noting that the steady cost reduction did not just happen. It was caused, in part, by the
building of the huge River Rouge plant, a reduction in the management staff from 5 to 2 percent of
all employees, extensive vertical integration, and the creation of the integrated, mechanized
production process by conveyors.
However, in the early 1920s, consumers began to request heavier, closed-body cars that
offered more comfort. As Alfred P. Sloan, Jr., the head of General Motors during this time, noted,
"Mr. Ford ... had frozen his policy to the Model T ... preeminently an open-car design. With its light
chassis, it was unsuited to the heavier closed body, and so in less than two years (by 1923) the closed
body made the already obsolescent design of the Model T noncompetitive."
As a result, in May of 1927 Henry Ford was forced to shut down operations for nearly a year
at a cost of $200 million to retool so that he could compete in the changed marketplace. It seems
clear that the very decisions that allowed Ford to march down the learning curve made it difficult
for the company to react to the changing times and to competition. The standardized product,
extensive vertical integration, and single-minded devotion to production improvements all tended
to create an organization that was ill-suited to respond to the changing environment --- indeed an
organization whose goals and thrust were intimately involved with preserving the status quo, the
existing product.
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