Linear Programming

Technical Supplement 3

Learning Curves

Copyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Objectives Objectives

1. Explain the learning curve concept

2. Identify different uses of learning curves in operations management

3. Calculate the estimated time required to do a task for a given learning curve

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Concepts

• Learning curve is an equation that can be used to estimate a rate of improvement in tasks

• Resource needs are reduced as people learn through repetition

–Time to assemble a product

–Cost to fabricate an item

• Resource requirement is reduced by certain percentage each time cumulative output is doubled

Overview of Learning CurvesOverview of Learning Curves

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The Learning CurveThe Learning Curve

Tn = T1 (nb)

Where:• Tn = time required to complete the nth task• r = learning rate percentage • b = ln(r)/ln(2)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

Cumulative repetitionsT

ime

pe

r u

nit

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ExampleExample

T1 = 100 minutes

T2 = 80 minutes

T4 = 64 minutes

• What would be the time required to produce the eighth part?

T8 = (100)(8-0.322) = 51.2 minutes

since b= ln(0.80)/ln(2) = -0.322

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Learning Curve TableLearning Curve Table

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Factors that Impact Learning RateFactors that Impact Learning Rate

• Incentives and rewards• Supporting resources for experimentation• Training• Tools and technology• Culture

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How OM Managers Use Learning CurvesHow OM Managers Use Learning Curves

• Setting goals and expectations• Capacity planning• Costing• Changes to product and process designs

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SummarySummary

• Learning curve estimation is a powerful planning tool–Helps to identify resources needed to accomplish a

production program–Can be used to set goals and assess progress

• Wide application given that underlying drivers of learning are present

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