Carson College of Business
MgtOp 340—Operations Management
Professor Munson
Topic 11
Learning Curves
“Another relatively easy cost-reduction scheme would be to rethink aircraft design so that all parts are ‘no-handed.’ That is, there would be no left and right hinges or wing flaps or other control surfaces.
The cockpit controls would likewise be no-handed. Production learning curves in manufacturing
these items would be twice improved by not having to devote half to the left and half to the right and
would reduce significantly spares and storage parts requirements.”
Ben Rich, Skunk Works, 1994, p. 326
“The best tribute to our homegrown training program was the astounding learning curve we achieved
in the first couple of years [on the F117A fighter jet]. Building only two airplanes every three months, we enjoyed a better learning curve–78 percent–than other manufacturers had reported while
building twenty-five airplanes a month.”
Ben Rich, Skunk Works, 1994, p. 89
DaimlerChrysler in Toluca, Mexico–Manufacturing the PT Crusier:
At first–one car per day
Then improvement efforts were initiated.
After 2 weeks–one car per 10 minutes
After 4 weeks–one car per 4 minutes
Eventually–one car per 80 seconds
, 08/08/01
“There is no substitute for experience.”
Anonymous
Learning Curves (a.k.a. Experience Curves)
A learning curve displays the relationship
between the per unit cost (or time) and the
cumulative quantity produced of a product.
|Process|
|time |
|per |
|unit |
|(hr) |
0.30
0.25
0.20
0.15 Learning
curve
0.10
Learning
0.05 period Standard time
50 100 150 200 250 300
Cumulative units produced
White Water Rafting
Lower Youghiogheny River in the Ohiopyle State Park
Rapids Traversed
Rapids Traversed
Why do costs decrease with production?
( workers complete tasks more efficiently
( automation
( changes in methods or personnel
( changes in tools
( more specialization of labor
( changes in product design
( changes in supervision
( improved production scheduling and inventory control
WARNING: Learning is based on
cumulative units produced, not the simple
passage of time.
Basic Learning Curve Premise
The production cost (or time) per unit is
reduced by a fixed percentage (1-L) each
time that production is doubled.
Definitions
T1 = the cost (or time) of the 1st unit
TN = the cost (or time) of the Nth unit
L = the learning rate
= % of previous cost (or time) whenever
production is doubled
b = the learning curve constant (< 0)
N = total number of units produced
Example
L = 90% and T4 = $100
Basic Learning Curve Formula
TN = T1(Nb)
Growth Rate Learning Curve Formula
[Use when computing learning from a unit (M) produced after the 1st unit (M < N)]
TN = TM[(N/M)b]
Three Methods to Compute b
Case 1: learning rate L is known
b = log (L) / log (2)
(or use the table)
Case 2: T1 and TN are known
b = log (TN / T1) / log (N)
Case 3: TP and TQ are known (Q > P > 1)
b = log (TQ / TP) / log (Q / P)
[pic]
Computing L
Step 1: Compute b using Case 2 or Case 3
Step 2: L = 2b
[pic]
Examples
1. Production Airlines manufactures small jets. The
initial jet required 400 labor days to complete.
Assuming an 80% learning rate, how many labor
days will be required for the 20th jet?
2. Suppose it costs a firm $60.00 to produce the 1st unit
and $48.00 to produce the 160th unit. What is the
learning rate for this company?
3. Suppose it costs a firm $1200 to produce the 2,000th
unit, and its learning rate is 75%. How much should it cost to produce the 8,000th unit?
Computing Cumulative Time or Cost
• The learning curve formula can be useful for estimating the time or cost of a single future unit, but it’s not efficient to compute the time or cost of a range of future units.
• Use the cumulative table to calculate a range.
• Cumulative time required for N units =
T1 × CN
where:
T1 = the cost (or time) of the 1st unit
CN = the cumulative learning curve coefficient from the table for N units
N = total number of units produced
Calculating Cumulative Time for a Segment
[pic]
Cumulative time required for units 26 through 50
= T1 × C50 − T1 × C25
= T1 × (C50 – C25)
[pic]
[pic]
Main Points of Hax and Majluf (1982)
1. A lower learning rate L implies a greater learning
effect (i.e. a faster reduction in cost or time).
2. The effects of the learning curve can be observed in
every stage of the value-added chain (e.g. R&D,
manufacturing of parts, assembly, marketing,
distribution, and retailing).
3. The potential of cost reduction is greatest in
industries with strong learning effects and fast
growing markets.
4. Boston Consulting Group:
high market share ( high cumulative production
( low unit cost (learning)
( high profits
5. High market share can be attained by:
advertising
distribution
differentiated product
low prices
6. Pricing strategies for new products:
“skimming”
Charge a high price to maximize margins on
price-insensitive customers.
“penetration pricing”
Charge a low price to maximize market share
and discourage entry of competitors.
7. Not all firms in the same industry have the same
learning rate.
8. Occasionally, shifts in the learning curve take place.
9. Bottom line: Learning curves represent a real and
important issue. They can be exploited by (1) using
various means to increase total units produced N, or
(2) using various means (investments) to improve the
learning rate L.
Learning Rate Rule of Thumb
80% learning curves are generally accepted as
standard.
Applications of Learning Curve
Theory
( manpower planning and scheduling
( negotiated purchasing/contract bids
( pricing new products
( budgeting/financial planning
( inventory theory
Realistic Example
Two firms are competing in the same market with products that are considered to be substitutes
for each other. Snooty is an old established firm with a great deal of experience; cumulative
production to date has been 100,000 units. Some years ago, it produced its first unit at a cost of
$100, and it has been enjoying a 95% experience curve ever since. Snooty is the price leader,
with current prices set at $85 per unit, which other producers followed until Luscious entered the market with a $40 price. The president of Snooty is astounded that Luscious is so foolish as to tryto compete because Snooty’s experience in the field is so great.
Luscious has just entered the market after spending a great deal on the research and development of new process technology. After setting up the initial highly automated plant, the cost of the
first unit was $150. The news got around the industry, and upon hearing it, the president of
Snooty laughed and said, “Aye Carumba, another bust for automation.” Since establishing the
plant, Luscious has allocated funds generously to the research and development of process
technology and has made significant improvements in the original plant.
Luscious initially priced its product at the industry rate of $85 per unit, but it soon dropped its
price to its present $40. This pricing policy has turned the industry upside down and business
has been brisk indeed—Luscious has already produced 5,000 units. Having kept careful records
on costs, the president of Luscious notes gleefully that it is on an 85% experience curve. She
is particularly delighted because, having originally been a plant manager for Snooty, she is aware of its costs and experience curve data.
The president of Snooty is puzzled, “How can Luscious undercut us? It must be losing money
on every unit; it is actually pricing below our cost!
How do you analyze this situation? Can Snooty possibly make out with its present pricing
policy?
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