Department of Food, Agricultural and Resource Economics
Module E: Learning Curves
An important determinant of productivity (and production cost) is the learning curve effect which exhibits systematic increase in productivity (or decline in unit costs in real terms) as cumulative output increases. The phenomenon of the learning curve, sometimes also known as the experience curve, the improvement curve, the progress curve, was first reported in 1936 by Theodore Paul Wright that the number of labour hours required to produce an airplane declined systematically as the cumulative number of airplanes produced increased 3 .
Learning Objectives Define a learning curve
Compute learning curve effects with the logarithmic approach
Describe the strategic implications of learning curves
3 Yelle,
Louis, E, (1979), ”The Learning Curve: Historical Review and Comprehensive Survey”, Decision Sciences, 10:2, April, pp 302 - 328. 47 / 439
Learning Curves What is a learning curve?
Learning curves are based on the premise that people and organizations become better at their tasks as the tasks are repeated. Time to produce a unit decreases as more units are produced.
Learning curves typically follow a negative exponential distribution.
The rate of improvement decreases over time.
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Learning Curves The learning curve is based on a doubling of production: that is, when production doubles, the decrease in time per unit affects the rate of the learning curve. For example, if the learning curve is a 50% rate, the second unit takes 50% of the time of the first, the fourth unit takes 50% of the time of the second unit, the eighth unit takes 50% of the time of the fourth unit, etc. Time required for the n-th unit, Tn , is given by: Tn = T1 × LN
(4)
where T1 = unit cost or unit time of the first unit ; L = learning curve rate; N = number of times T is doubled Figure It Out: If the first unit of a particular product took 20 labourhours, how long will (a) the eighth unit and (b) the fourth unit take if you are on a 75% learning curve rate? Solution: (a) The 8-th unit requires doubling thrice 1 to 2 to 4 to 8.
= T ×L
N
3
= (20)(0.75)
= 20 × 0.422 = 8.438
labour − hours
Solution: (b) The 4-th unit requires doubling twice 1 to 2 to 4.
= T ×L
N
= (20)(0.75)
2
= 20 × 0.422 = 11.25
labour − hours 49 / 439
Learning Curves in Services and Manufacturing
Different organizations have different learning curves. The lower the learning curve rate, the steeper and the faster the the drop in costs. By tradition, learning curve rates, L, are defined in terms of the complements of their improvement rates, 1 − L. For example, a 75% learning curve implies a 25% decrease (i.e., 1-0.75=0.25) in time each time the number of repetitions is doubled.
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Examples of Learning Curve rates in Services and Manufacturing
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Learning Curves and Improvement Rates Question: When comparing a 70% learning curve rate versus a 90% learning curve rate, which one results in a more rapid reduction in labour requirements (i.e., higher progress rate)? Why? Answer: Learning curves are defined in terms of the complements of their improvement rates or progress rates. A 70% learning curve rate implies a 30% decrease in labour requirements each time the number of replications is doubled. A 90% learning curve rate implies a 10% decrease in labour required each time the number of replications is doubled. Therefore, the reduction in labor requirements is more rapid at 70% than at 90%.
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Application of the Learning Curve: Logarithmic Approach The logarithmic approach allows us to determine labour for any unit, TN , by the formulae: (5) TN = T1 (N b ) where TN = time for the N-th unit; T1 is hours to produce the first unit; b=(log of the learning rate)/log(2) = slope of the learning curve; C = N b is the learning curve coefficient.
Figure It Out: If Professor TQ takes 20 minutes to grade the first exam and follows an 75% learning curve, how long will it take her to grade: 1. the 25th exam? 2. the first four exams?
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Solutions Solution: b = log (.75)/log (2) = −0.415 1. For the 25th unit, at a 75% learning curve rate, the learning curve coefficient is C = N b = 25−0.415 = 0.263 T25 = T1 (N b ) = 20×(25−0.415 ) = 20×(0.263) = 5.26
minutes
2. For the first four exams: one need to calculate the learning curve coefficient C for C1 = N b = 1−0.415 = 1.000 ⇒ T1 = 20 × 1.000 = 20.00 C2 = N b = 2−0.415 = 0.750 ⇒ T2 = 20 × 0.750 = 15.00 C3 = N b = 3−0.415 = 0.634 ⇒ T3 = 20 × 0.634 = 12.68 C4 = N b = 4−0.415 = 0.563 ⇒ T4 = 20 × 0.563 = 11.26 The time for the first four exams is: = 20 × (1 + 0.75 + 0.634 + 0.563) = 58.94 minutes
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Figure It Out Suppose a student starts a term paper typing business. The student time himself on the first paper, then the second, and so on. The first time the student types up a 20 page term paper it takes 40 minutes. The second time the student types up a term paper it only takes 36 minutes. Calculate the learning curve rate, L, the progress rate, 1 − L, and the learning curve coefficient, C .
Given: T1 = 40, T2 = 36, Unknowns: C1 =?, L =? 1. The learning curve rate Tn = T1 × LN
⇒ 36 = 40L1
⇒ L = 36/40 = 0.90 = 90%
2. The progress rate, 1 − L 1 − L = 1 − 0.9 = 0.1 = 10% 3. The learning curve coefficient, C2 First calculate b, b = log (0.9)/log (2) = −0.152. Then, calculate C2 = 2−0.152 = 0.90. 55 / 439
Strategic Implications of Learning Curves To pursue a strategy of a steeper curve than the rest of the industry, a firm can: 1. Follow an aggressive pricing policy 2. Focus on continuing productivity improvement and cost reduction 3. Build on shared experience 4. Keep capacity ahead of demand
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Limitations of Learning Curves To pursue a strategy of a steeper curve than the rest of the industry, a firm can: 1. Learning curves differ from company to company as well as industry to industry so estimates should be developed for each organization 2. Learning curves are often based on time estimates which must be accurate and should be reevaluated when appropriate 3. Any changes in personnel, design, or procedure can be expected to alter the learning curve 4. Learning curves do not always apply to indirect labor or material 5. The culture of the workplace, resource availability, and changes in the process may alter the learning curve
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True or False4 1. Experience curves may be valid for industrial applications, but have no role in services such as health care procedures. 2. Experience curves are the opposite of learning curves-as one rises, the other falls. 3. Learning curves are based on the premise that people and organizations become better at their tasks as the tasks are repeated. 4. The earliest application of learning curves appears in the work of architect Frank Lloyd Wright. 5. Learning curves can only be applied to labor. 6. If the learning curve for a process is 100 percent, then each unit in a series of units will have the same labor requirements. 7. If the first unit in a series of units takes 200 days to complete, and the learning curve is 80%, then the second unit will take 160 days. 8. An 80% learning curve means that with each unit increase in production, labor requirements fall by 20%. 9. A 90% learning curve implies that each time the production volume is doubled the direct time per unit is reduced to 90% of its previous value. 10. The logarithmic approach to learning curve calculations allows us to determine the hours required for any unit. 4 1)
F, 2) F, 3) T, 4) F, 5) F, 6) T, 7) T, 8) F, 9) T, 10) T
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An important determinant of productivity (and production cost) is the learning curve effect which exhibits systematic increase in productivity (or decline in unit costs in real terms) as cumulative output increases. The phenomenon of the learning curve, sometimes also known as the experience curve, the improvement curve, the progress curve, was first reported in 1936 by Theodore Paul Wright that the number of labour hours required to produce an airplane declined systematically as the cumulative number of airplanes produced increased 3 .
Learning Objectives Define a learning curve
Compute learning curve effects with the logarithmic approach
Describe the strategic implications of learning curves
3 Yelle,
Louis, E, (1979), ”The Learning Curve: Historical Review and Comprehensive Survey”, Decision Sciences, 10:2, April, pp 302 - 328. 47 / 439
Learning Curves What is a learning curve?
Learning curves are based on the premise that people and organizations become better at their tasks as the tasks are repeated. Time to produce a unit decreases as more units are produced.
Learning curves typically follow a negative exponential distribution.
The rate of improvement decreases over time.
48 / 439
Learning Curves The learning curve is based on a doubling of production: that is, when production doubles, the decrease in time per unit affects the rate of the learning curve. For example, if the learning curve is a 50% rate, the second unit takes 50% of the time of the first, the fourth unit takes 50% of the time of the second unit, the eighth unit takes 50% of the time of the fourth unit, etc. Time required for the n-th unit, Tn , is given by: Tn = T1 × LN
(4)
where T1 = unit cost or unit time of the first unit ; L = learning curve rate; N = number of times T is doubled Figure It Out: If the first unit of a particular product took 20 labourhours, how long will (a) the eighth unit and (b) the fourth unit take if you are on a 75% learning curve rate? Solution: (a) The 8-th unit requires doubling thrice 1 to 2 to 4 to 8.
= T ×L
N
3
= (20)(0.75)
= 20 × 0.422 = 8.438
labour − hours
Solution: (b) The 4-th unit requires doubling twice 1 to 2 to 4.
= T ×L
N
= (20)(0.75)
2
= 20 × 0.422 = 11.25
labour − hours 49 / 439
Learning Curves in Services and Manufacturing
Different organizations have different learning curves. The lower the learning curve rate, the steeper and the faster the the drop in costs. By tradition, learning curve rates, L, are defined in terms of the complements of their improvement rates, 1 − L. For example, a 75% learning curve implies a 25% decrease (i.e., 1-0.75=0.25) in time each time the number of repetitions is doubled.
50 / 439
Examples of Learning Curve rates in Services and Manufacturing
51 / 439
Learning Curves and Improvement Rates Question: When comparing a 70% learning curve rate versus a 90% learning curve rate, which one results in a more rapid reduction in labour requirements (i.e., higher progress rate)? Why? Answer: Learning curves are defined in terms of the complements of their improvement rates or progress rates. A 70% learning curve rate implies a 30% decrease in labour requirements each time the number of replications is doubled. A 90% learning curve rate implies a 10% decrease in labour required each time the number of replications is doubled. Therefore, the reduction in labor requirements is more rapid at 70% than at 90%.
52 / 439
Application of the Learning Curve: Logarithmic Approach The logarithmic approach allows us to determine labour for any unit, TN , by the formulae: (5) TN = T1 (N b ) where TN = time for the N-th unit; T1 is hours to produce the first unit; b=(log of the learning rate)/log(2) = slope of the learning curve; C = N b is the learning curve coefficient.
Figure It Out: If Professor TQ takes 20 minutes to grade the first exam and follows an 75% learning curve, how long will it take her to grade: 1. the 25th exam? 2. the first four exams?
53 / 439
Solutions Solution: b = log (.75)/log (2) = −0.415 1. For the 25th unit, at a 75% learning curve rate, the learning curve coefficient is C = N b = 25−0.415 = 0.263 T25 = T1 (N b ) = 20×(25−0.415 ) = 20×(0.263) = 5.26
minutes
2. For the first four exams: one need to calculate the learning curve coefficient C for C1 = N b = 1−0.415 = 1.000 ⇒ T1 = 20 × 1.000 = 20.00 C2 = N b = 2−0.415 = 0.750 ⇒ T2 = 20 × 0.750 = 15.00 C3 = N b = 3−0.415 = 0.634 ⇒ T3 = 20 × 0.634 = 12.68 C4 = N b = 4−0.415 = 0.563 ⇒ T4 = 20 × 0.563 = 11.26 The time for the first four exams is: = 20 × (1 + 0.75 + 0.634 + 0.563) = 58.94 minutes
54 / 439
Figure It Out Suppose a student starts a term paper typing business. The student time himself on the first paper, then the second, and so on. The first time the student types up a 20 page term paper it takes 40 minutes. The second time the student types up a term paper it only takes 36 minutes. Calculate the learning curve rate, L, the progress rate, 1 − L, and the learning curve coefficient, C .
Given: T1 = 40, T2 = 36, Unknowns: C1 =?, L =? 1. The learning curve rate Tn = T1 × LN
⇒ 36 = 40L1
⇒ L = 36/40 = 0.90 = 90%
2. The progress rate, 1 − L 1 − L = 1 − 0.9 = 0.1 = 10% 3. The learning curve coefficient, C2 First calculate b, b = log (0.9)/log (2) = −0.152. Then, calculate C2 = 2−0.152 = 0.90. 55 / 439
Strategic Implications of Learning Curves To pursue a strategy of a steeper curve than the rest of the industry, a firm can: 1. Follow an aggressive pricing policy 2. Focus on continuing productivity improvement and cost reduction 3. Build on shared experience 4. Keep capacity ahead of demand
56 / 439
Limitations of Learning Curves To pursue a strategy of a steeper curve than the rest of the industry, a firm can: 1. Learning curves differ from company to company as well as industry to industry so estimates should be developed for each organization 2. Learning curves are often based on time estimates which must be accurate and should be reevaluated when appropriate 3. Any changes in personnel, design, or procedure can be expected to alter the learning curve 4. Learning curves do not always apply to indirect labor or material 5. The culture of the workplace, resource availability, and changes in the process may alter the learning curve
57 / 439
True or False4 1. Experience curves may be valid for industrial applications, but have no role in services such as health care procedures. 2. Experience curves are the opposite of learning curves-as one rises, the other falls. 3. Learning curves are based on the premise that people and organizations become better at their tasks as the tasks are repeated. 4. The earliest application of learning curves appears in the work of architect Frank Lloyd Wright. 5. Learning curves can only be applied to labor. 6. If the learning curve for a process is 100 percent, then each unit in a series of units will have the same labor requirements. 7. If the first unit in a series of units takes 200 days to complete, and the learning curve is 80%, then the second unit will take 160 days. 8. An 80% learning curve means that with each unit increase in production, labor requirements fall by 20%. 9. A 90% learning curve implies that each time the production volume is doubled the direct time per unit is reduced to 90% of its previous value. 10. The logarithmic approach to learning curve calculations allows us to determine the hours required for any unit. 4 1)
F, 2) F, 3) T, 4) F, 5) F, 6) T, 7) T, 8) F, 9) T, 10) T
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