1

The average time per task declines by a constant percentage each time the quantity of tasks done doubles.

There is often a systematic relationship between experiencein performing a task and the time

required to do it.

Learning Curves

2

Types of Learning Curves

•Cumulative Average-Time Learning Model – cumulative average time per unit declines by a constant percentage each time the cumulative

quantity of units produced doubles•Incremental Unit-Time Learning Model –

incremental time needed to produce the last unit declines by a constant percentage each time the

cumulative quantity of units produced doubles

3

Berry Co. makes products requiring labor that follows an 80 percent learning rate. If the

first unit of such a product requires 10 hours, what is the average time for 16 units of this

product?

An 80 percent learning rate:the average time required to make 2 units is 80 percent of the time for 1 unit and the average time for 4 units is

80 percent of the time for 2 units, etc.

Effect of Learning on Cost Behavior

4

AverageNumber Labor Time Total Time:of Units per Unit Average x Units

1 1 × 10 = 10 1 × 10 = 102 .80 × 10 = 8 2 × 8 = 164 .80 × 8 = 6.4 4 × 6.4 = 25.68 .80 × 6.4 = 5.12 8 × 5.12 = 40.96

16 .80 × 5.12 = 4.096 16 × 4.096 = 65.536

The graphic presentation of the learning phenomenon is called the learning curve.

Cumulative Average-Time Learning Model

5

Learning Curve

Cumulative Production Output

Ave

rag

e L

abo

rT

ime

per

Un

it

Learning effectsare large initially.

Learning effectsbecome smaller, eventually reaching expected final time.

6

Cumulative Production Output

Ave

rag

e L

abo

rT

ime

per

Un

it

This is used to help determine investment required.

This is used to estimate ongoing results.

7

Learning Curve Formula

2ln

form decimalin % rate learningln factor Learning

produced units of no. Cumulative

1unit produce toDLH

unitper labor time average Cumulative

factor learning

8

Question for Discussion 2

•Time to produce the first unit = 100 minutes•Learning factor = ln(0.80)/ln2 = -0.32193

.1What is the cumulative average time to produce 5 units?

.2What is the total time to produce 5 units?

.3What is the time it took to produce the 5th unit?

9

Cum.Number Individual Unit Time Cumulative Ave. Timeof Units for X-th Unit Total Time Per Unit

1 1 × 10 = 10 10 102 0.80 × 10 = 8 10 + 8 = 18 93 7.02 18 + 7.02 = 25.02 8.344 0.80 × 8 = 6.40 25.02 + 6.40 = 31.42 7.865 5.96 31.42 + 5.96 = 37.38 7.48

Incremental Unit-Time Learning Model

Using the example of Berry Co. and using the incremental unit-time learning model