1. Learning Curve Analysis
For Operations Management, 9e by Krajewski/Ritzman/Malhotra © 2010 Pearson Education
PowerPoint Slides by Jeff Heyl
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The Learning Effect
Organizational learning
Automation
Productivity improvements
Learning effect
Relationship between total direct labor per unit and the cumulative quantity produced
Sometimes called manufacturing progress function or experience curve
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The Learning Effect
Background
First developed in aircraft industry
Rate may be different for different products and different companies
Learning curves and competitive strategy
Project the manufacturing cost per unit
Product design changes disrupt the learning effect
Costs decrease as products move down the learning curve
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Learning Curve
0.30 –
0.25 –
0.20 –
0.15 –
0.10 –
0.05 –
0 –
| | | | | |
Cumulative units produced
Process time per unit (hr)
Learning curve
Learning period
Standard time
Figure I.1 – Learning Curve, Showing the Learning Period and the Time When Standards Are Calculated
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5. Developing Learning Curves
In developing learning curves we make the following assumptions
The direct labor required to produce the n + 1st unit will always be less than the direct time of labor required for the nth unit
Direct labor requirements will decrease at a declining rate as cumulative production increases
The reduction in time will follow an exponential curve
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6. Developing Learning Curves
Using a logarithmic model to draw a learning curve, the direct labor required for the nth unit, kn, is
kn = k1nb
where
k1 = direct labor hours for the first unit
n = cumulative numbers of units produced
r = learning rate (as decimal)
Doubling of the quantity reduces the time per unit by (1 – r)
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7. Developing Learning Curves
TABLE I.1 | CONVERSION FACTORS FOR THE CUMULATIVE AVERAGE | NUMBER OF DIRECT LABOR HOURS PER UNIT
80% Learning Rate
(n = cumulative production) n 1 11 21 2 12 22 3 13 23 4 14 24 5 15 25 6 16 26 7 17 27 8 18 28 9 19 29 10 20 30
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8. Developing Learning Curves
TABLE I.1 | CONVERSION FACTORS FOR THE CUMULATIVE AVERAGE | NUMBER OF DIRECT LABOR HOURS PER UNIT
90% Learning Rate
(n = cumulative production) n 1 11 21 2 12 22 3 13 23 4 14 24 5 15 25 6 16 26 7 17 27 8 18 28 9 19 29 10 20 30
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Using Learning Curves
EXAMPLE I.1
A manufacturer of diesel locomotives needs 50,000 hours to produce the first unit. Based on past experience with similar products, you know that the rate of learning is 80 percent.
a. Use the logarithmic model to estimate the direct labor required for the 40th diesel locomotive and the cumulative average number of labor hours per unit for the first 40 units.
b. Draw a learning curve for this situation.
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Using Learning Curves
SOLUTION
a. The estimated number of direct labor hours required to produce the 40th unit is
k40 =
50,000(40)(log 0.8)/(log 2) = 50,000(40)–0.322 = 50,000( )
= 15,248 hours
We calculate the cumulative average number of direct labor hours per unit for the first 40 units with the help of Table I.1. For a cumulative production of 40 units and an 80 percent learning rate, the factor is The cumulative average direct labor hours per unit is 50,000( ) = 21,492 hours.
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11. Direct labor hours per locomotive (thousands)
Using Learning Curves
b. Plot the first point at (1, 50,000). The second unit‘s labor time is 80 percent of the first, so multiply 50,000(0.80) = 40,000 hours. Plot the second point at (2, 40,000). The fourth is 80 percent of the second, so multiply 40,000(0.80) = 32,000 hours. Plot the point (4, 32,000). The result is shown in Figure I.2.
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Figure I.2 – The 80 Percent Learning Curve
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Application I.1
The first unit of a new product is expected to take 1000 hours to complete. If the rate of learning is 80 percent, how much time should the 50th unit take?
SOLUTION
Given
k1 = 1,000 n = 50 r = 0.80
kn = k1nb
k50 = 1000(50)(log 0.8/log 2)
= 1000(50)–
= 1000( )
k50 = hours
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Using Learning Curves
Bid preparation
Use learning curves to estimate labor cost
Add materials costs and desired profit to obtain total bid amount
Financial planning
Use learning curves to estimate cash needed to finance operations
Estimating cumulative labor requirements, such as for training requirements and hiring plans
Based on doublings, given rate of learning
Based on conversion factors tables
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Using Learning Curves
EXAMPLE I.2
The manager of a custom manufacturer has just received a production schedule for an order for 30 large turbines. Over the next 5 months, the company is to produce 2, 3, 5, 8, and 12 turbines, respectively. The first unit took 30,000 direct labor hours, and experience on past projects indicates that a 90 percent learning curve is appropriate; therefore, the second unit will require only 27,000 hours. Each employee works an average of 150 hours per month. Estimate the total number of full-time employees needed each month for the next 5 months.
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Using Learning Curves
SOLUTION
The following table shows the production schedule and cumulative number of units scheduled for production through each month:
Month
Units per Month
Cumulative Units 1 2 3 5 10 4 8 18 12 30
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16. Cumulative Average Time per Unit Cumulative Total Hours for All Units
Using Learning Curves
We first need to find the cumulative average time per unit using Table I.1 and the cumulative total hours through each month. We then can determine the number of labor hours needed each month. The calculations for months 1 – 5 follow.
Month
Cumulative Average Time per Unit
Cumulative Total Hours for All Units 1
30,000( ) = 28,500.0
(2)28,500.0 = 57,000 2
30,000( ) = 26,035.2
(5)26,035.2 = 130,176 3
30,000( ) = 23,983.5
(10)23,983.5 = 239,835 4
30,000( ) = 22,224.0
(18)22,224.0 = 400,032 5
30,000( ) = 20,727.0
(30)20,727.0 = 621,810
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Using Learning Curves
Calculate the number of hours needed for a particular month by subtracting its cumulative total hours from that of the previous month.
Month 1:
Month 2:
Month 3:
Month 4:
Month 5:
57,000 – 0 = 57,000 hours
130,176 – 57,000 = 73,176 hours
239,835 – 130,176 = 109,659 hours
400,032 – 239,835 = 160,197 hours
621,810 – 400,032 = 221,778 hours
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Using Learning Curves
The required number of employees equals the number of hours needed each month divided by 150, the number of hours each employee can work.
Month 1:
Month 2:
Month 3:
Month 4:
Month 5:
57,000/150 = 380 employees
73,176/150 = 488 employees
109,659/150 = 731 employees
160,197/150 = 1,068 employees
221,778/150 = 1,479 employees
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Application I.2
A company has a contract to make a product for the first time. The total budget for the 38-unit job is 15,000 hours. The first unit took 1000 hours, and the rate of learning is expected to be 80 percent.
a. Do you think the 38-unit job can be completed within the 15,000-hour budget?
b. How many additional hours would you need for a second job of 26 additional units?
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Application I.2
SOLUTION a.
Average38 =
Total38 =
1000( ) =
436.34(38) = 16,581 hours
They will have trouble meeting the 15,000 hour budget b.
Average64 =
Total64 =
Total64 – Total38 = =
1000( ) =
373.82(64) = 23,924 hours
23,924 – 16,581
7,343 additional hours required
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21. Managerial Considerations
Good estimates of the learning rate may be difficult to obtain
The simpler the service or product, the less the learning rate
The entire learning curve is based on the time required for the first unit
Learning curves are used to greatest advantage in the early stages of new product or service production
Implementing a team approach can change organizational learning rates
Learning curves are only approximations
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Solved Problem
The Minnesota Coach Company has just been given the following production schedule for ski-lift gondola cars. This product is considerably different from any others the company has produced. Historically, the company‘s learning rate has been 80 percent on large projects. The first unit took 1,000 hours to produce.
Month
Units
Cumulative Units 1 3 2 7 10 20 4 12 32 5 36 6 38
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Solved Problem
a. Estimate how many hours would be required to complete the 38th unit.
b. If the budget only provides for a maximum of 30 direct labor employees in any month and a total of 15,000 direct labor hours for the entire schedule, will the budget be adequate? Assume that each direct labor employee is productive for 150 work hours each month.
SOLUTION
a. We use the learning curve formulas to calculate the time required for the 38th unit:
kn = k1nb =
(1,000 hours)(38)–0.322 = 310 hours
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24. Cumulative Average Time per Unit Cumulative Total Hours for All Units
Solved Problem
b. Table I.1 gives the data needed to calculate the cumulative number of hours through each month of the schedule. Table I.2 shows these calculations.
TABLE I.2 | CUMULATIVE TOTAL HOURS
Month
Cumulative Units
Cumulative Average Time per Unit
Cumulative Total Hours for All Units 1 3 2 10 20 4 32 5 36 6 38
1,000( ) = hr/u
( hr/u)(3 u) = 2,502.1 hr
1,000( ) = hr/u
( hr/u)(10 u) = 6,315.4 hr
1,000( ) = hr/u
( hr/u)(20 u) = 10,485.0 hr
1,000( ) = hr/u
( hr/u)(32 u) = 14,678.7 hr
1,000( ) = hr/u
( hr/u)(36 u) = 15,958.4 hr
1,000( ) = hr/u
( hr/u)(38 u) = 16,580.9 hr
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25. Cumulative Total Hours for Month Direct Labor Workers by Month
Solved Problem
The cumulative amount of time needed to produce the entire schedule of 38 units is 16,580.9 hours, which exceeds the 15,000 hours budgeted. By finding how much the cumulative total hours increased each month, we can break the total hours into monthly requirements. Finally, the number of employees required is simply the monthly hours divided by 150 hours per employee per month. The calculations are shown in Table I.3.
TABLE I.3 | DIRECT LABOR EMPLOYEES
Month
Cumulative Total Hours for Month
Direct Labor Workers by Month 1 2 3 4 5 6
2,502.1 – 0 = 2,502.1 hr
(2,502.1 hr)/(150 hr) = 16.7, or 17
6,315.4 – 2,502.1 = 3,813.3 hr
(3,813.3 hr)/(150 hr) = 25.4, or 26
10,485.0 – 6,315.4 = 4,169.6 hr
(4,169.6 hr)/(150 hr) = 27.8, or 28
14,678.7 – 10,485.0 = 4,193.7 hr
(4,193.7 hr)/(150 hr) = 27.9, or 28
15,958.4 – 14,678.7 = 1,279.7 hr
(1,279.7 hr)/(150 hr) = 8.5, or 9
16,580.9 – 15,958.4 = hr
(622.5 hr)/(150 hr) = 4.2, or 5
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Solved Problem
The schedule is feasible in terms of the maximum direct labor required in any month because it never exceeds 28 employees. However, the total cumulative hours are 16,581, which exceeds the budgeted amount by 1,581 hours. Therefore, the budget will not be adequate.
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