Home BADM449 Handout #10 | Joseph T. Mahoney |
College of Business Department of Business Administration BADM449 Strategic Management/Business Policy
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.
where
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.
(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 0.1272090% 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
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:
kn = k1 nb
= 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.
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.
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 (.81) = 81 hours
This result may be obtained more simply by 100 (.9) (.9) = 100 (.81) = 81 hours
For the 8th unit,
= 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
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 |