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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