Operations and Supply Chain Management The Core

STRATEGIC CAPACITY MANAGEMENT chapter 4 117
Learning Curve Plots
A—Arithmetic Plot of 70, 80, and 90 Percent
Learning Curves
Production cost ($)
$100
90
80
70
60
50
40
30
20
10
0
90% Learning
curve
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Unit number
80%
70%
B—Logarithmic Plot of an 80 Percent
Learning Curve
20
10
9
8
7
6
4 5
3
2
Cost for a
particular unit
Average cost/unit
(cumulative)
1
1 2 3 4 5678910 20 30 40 50 60 80100 200 300 400600 1,000
Unit number
exhibit 4A.4
Logarithmic Analysis The normal form of the learning curve equation is
where
​Y​ x ​ = K ​x​ n ​
x = Unit number
Y x = Number of direct labor hours required to produce the xth unit
K = Number of direct labor hours required to produce the first unit
n = log b/log 2 where b = Learning percentage
[4A.1]
Excel:
Learning
Curves
We can solve this mathematically or by using a table, as shown in the next section.
Mathematically, to find the labor-hour requirement for the eighth unit in our example
(Exhibit 4A.3), we would substitute as follows:
Using logarithms:
​Y​ 8 ​ = (100,000)​(8)​ n ​
​Y​ 8 ​ = 100,000​(8)​ log 0.8/log 2 ​
= 100,000​(8)​ −0.322 100,000
​ = ​ _______
​(8)​ 0.322 ​ ​
100,000
= ​ _______
1.9534 ​ = 51,193
Therefore, it would take 51,193 hours to make the eighth unit. Your answers may vary
slightly due to rounding.
Learning Curve Tables When the learning percentage is known, the tables in Exhibit
4A.5 can be easily used to calculate estimated labor hours for a specific unit or for cumulative
groups of units. We need only multiply the initial unit labor hour figure by the appropriate
tabled value. An alternative way to obtain the unit and cumulative factors is from the
OSCM Tools application available at http://oscm-pro.com/tools/.
Excel:
Learning Curves