Supplement
I Learning Curve Analysis
1. The Learning Curve Concept
• Organizational learning
o Automation
o Productivity improvements
▪ Better processes
▪ Individual learning
• Learning effect
o Learning curve displays the relationship between the total direct labor per unit and
the cumulative quantity of product or service produced.
o Sometimes called manufacturing progress function or experience curve, but
principles are the same
1. Background
a. First developed in aircraft industry. Each doubling of quantity reduced per-unit
production time by 20%.
b. Rate of learning may be different for different products and different companies.
2. Learning curves and competitive strategy
2. Developing Learning Curves
• The direct labor required for the nth unit kn, is
b
nnkk 1
=
where
k1 = direct labor hours for the 1st unit
n = cumulative number of units produced
2log
logr
b=
r = learning rate (as decimal)
• Assumptions
o The direct labor required to produce the n + 1st unit will always be less than the direct
labor required for the nth unit.
o The direct labor required to produce the n + 1st unit will always be less than the direct
labor required for the nth unit.
o The reduction in time will follow an exponential distribution.
• Estimating Direct Labor Requirements. Use Application I.1 for an exercise using the
learning model.
The first unit of a new product is expected to take 1000 hours to complete. If the rate of
learning is 80 percent, how much time should the 50th unit take?
Given
k1 = 1,000 n = 50 r = 0.80
Calculations
hoursk
k
nkk b
n
8.283
)283827.0(1000
)50(1000
)50(1000
50
32192.0
)2log/8.0(log
50
1
=
=
=
=
=
−
Students will need to use a calculator that takes logs to get these results.
• Use Example I.1 Diesel Locomotive Manufacturer
• Tutor I.1 in MyLab Operations Management provides a new example for learning curve
analysis.
3. Using Learning Curves
1. Bid preparation
a. Use learning curves to estimate labor cost.
b. Add materials costs and desired profit to obtain total bid amount.
4. Estimating Cumulative Labor Hours. Use Application I.2 for an example of using the
learning model to test budget constraints.
A company has a contract to make a product for the first time. The total budget for the 38–
unit job is 15,000 hours. The first unit took 1000 hours, and the rate of learning is expected to
be 80 percent.
a. Do you think the 38-unit job can be completed within the 15,000-hour budget?
hoursTotal
Average
581,16)38(34.436
34.436)43634.0(1000
38
38
==
==
Conclusion: Trouble
b. How many additional hours would you need for a second job of 26 additional units?
hours
TotalTotal
hoursTotal
Average
343,7
581,16924,23
924,23)64(82.373
82.373)37382.0(1000
3864
64
64
=
−=−
==
==
4. Managerial Considerations in the Use of Learning Curves
• An estimate of the learning rate is necessary in order to use learning curves, and it may be
difficult to obtain a good estimate of the learning rate for an organization.
• The simpler the service or product, the less the learning rate.
• The entire learning curve is based on the time required for the first unit, which may itself be