The learning
curve is a mathematical management tool normally used by manufacturing companies
to evaluate productivity gains caused by organizational learning.

Companies
can obtain many benefits from using a theoretical learning curve in their production
scheduling and general future prognosis of effectiveness.

*Firstly*, if learning curve improvements are not considered
when creating productions schedules, the result might be idle production facilities,
where both workers and machinery are not creating any value. *Secondly*,
companies may decline additional work, because the company does not take the
learning curve’s effect on production capacity into consideration. *Thirdly*, companies could also use the learning curve to negotiate
with suppliers, who should also be able to learn over time, and hence become
less expensive. *Fourthly*, companies
may be able to give a future prognosis of the development of production costs,
and thereby analyze the future effect of the organizational learning on profitability.

The
examples above are however not exhaustive and companies might very well find
several other good uses of the learning curve.

**Calculating the learning curve.**

In
this article, two ways of calculating the learning curve is presented – The
arithmetic approach and the logarithmic approach.

**Arithmetic approach**
The basic
thesis of the learning curve is that every time the produced volume is doubled,
labour per unit will decline by a constant rate, which is normally referred
to as the learning rate.

Nth
Unit Produced |
Hours
for Nth Unit |

1 |
1000 |

2 |
800
= (0.8*1000) |

4 |
640
= (0.8*800) |

8 |
512
= (0.8*640) |

16 |
410
= (0.8*512) |

The example above uses a learning rate of 80%. The hours used for producing
is therefore 20% less every time the actual produced amount has been doubled.
The problem above is however that we cannot see how much labour will be required
for units that are not equal to the doubled values. For calculating labour consumption
for units that are not equal to the doubled values, we will have to use the
logarithmic approach.

**Logarithmic approach**

The logarithmic
approach lets us determine the labour consumption for every Nth unit using this
formula.

T_{N }=
T_{1}(N^{b})

Where:

T_{N }=
Time for the Nth_{ }Unit

T_{1 }=
Hours to produce the first unit

b = (Log of
the learning rate/Log 2) = Slope of the learning curve

If the learning
rate for a given operation is 80%, and the first produced unit took 1.000 hours,
the hours needed for the thirteenth unit can be calculated as follows:

T_{N }=
T_{1}(N^{b})

T_{13} =
(1000 hours(13^{b})

= (1000)(13^{log0,8/log2})

= (1000)(13^{-0,322})
= 438 hours

The thirteenth
produced unit will therefore take 438 hours to produce. At the end of the article,
the characteristic learning curve slope is depicted in a graphical chart.