Home  BADM449   Handout #10 Joseph T. Mahoney

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:

  1. You need less time to instruct workers.
  2. Workers become more skillful in their movements.
  3. You develop better operation sequences and better machine feeds and speeds.
  4. Machines and tooling are continually improved.
  5. Rejections and rework decrease.
  6. Manufacturing lots are larger, cutting down the set-up time proportion.
  7. Management controls are improved.
  8. "Crash measures" become uncommon.
  9. Engineering changes are less frequent.
  10. Cost-effective improvements in product design.
  11. Enriched know-how in managing and operating the business.
  12. 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


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.


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

An estimate of the learning rate is necessary in order to use learning curves, and it may be difficult to get.

Using industry averages can be risky because the type of work and competitive niches can differ from firm to firm.

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.

A complex product offers more opportunity to improve work methods, materials, and processes over the product's life.

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.

Another important estimate is that of the time required to produce the first unit because the entire learning curve is based on it.

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.

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.

The institution of incentive systems, bonus plans, zero defect programs, and so on may increase learning.

Aging of equipment can have a negative impact on learning curve advantages.

Transfer of employees can lead to an interruption or the regressing back to an earlier stage of the learning curve.

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.

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.

Last Update: January 05, 2006