Learning Curve Analysis Supplement G 2007 Pearson Education

Learning Curves Process time per unit (hr) 0. 30 – 0. 25 – 0.

Learning Curves Process time per unit (hr) 0. 30 – Showing the learning period

Learning Curves Process time per unit (hr) 0. 30 – 0. 25 – Showing

Developing Learning Curves Ø In developing learning curves we make the following assumptions: Ø

80% Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit

90% Conversion Factors for the Cumulative Average Number of Direct Labor Hours per Unit

Example G. 1 Direct labor hours per locomotive (thousands) Developing the 80% Learning Curve

Example G. 1 Direct labor hours per locomotive (thousands) Estimating Direct Labor Requirements 50

Example G. 1 Direct labor hours per locomotive (thousands) using the formula 50 –

Example G. 1 Direct labor hours per locomotive (thousands) using Conversion Factors 80% Learning

Example G. 1 Direct labor hours per locomotive (thousands) using Unit-doublings 50 – Labor

Direct labor hours per locomotive (thousands) The 80% Learning Curve for Example G. 1

Application G. 1 Estimating Direct Labor Requirements The 1 st unit of a new

Example G. 2 Estimating Labor Requirements Month 1 2 3 4 5 Units per

Example G. 2 Estimating Labor Requirements Units per Cumulative Month Units 1 2 2

Example G. 2 Estimating Labor Requirements Units per Cumulative Month 1: Month Units 1

Example G. 2 Estimating Labor Requirements Units per Cumulative Month 1: 57, 000 0

Application G. 2 Estimating Cumulative Labor Hours An example of using the learning model

Application G. 2 First 38 -unit Job © 2007 Pearson Education

Application G. 2 Second additional 26 -unit Job © 2007 Pearson Education

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Learning Curves Process time per unit (hr) 0. 30 – Showing the learning period 0. 25 – 0. 20 – 0. 15 – Learning curve 0. 10 – Learning period 0. 05 – | | | 0 – 50 100 150 200 250 300 Cumulative units produced © 2007 Pearson Education

Learning Curves Process time per unit (hr) 0. 30 – 0. 25 – Showing the learning period and the time when standards are calculated 0. 20 – 0. 15 – Learning curve 0. 10 – Learning 0. 05 – period 0– © 2007 Pearson Education Standard time | | | 50 100 150 200 250 300 Cumulative units produced

Developing Learning Curves Ø In developing learning curves we make the following assumptions: Ø The direct labor required to produce the n + 1 st unit will always be less than the direct time of labor required for the nth unit. Ø Direct labor requirements will decrease at a declining rate as cumulative production increases. Ø The reduction in time will follow an exponential curve. kn = k 1 nb where k 1 = direct labor hours for the 1 st unit © 2007 Pearson Education n = cumulative number of units produced b = log r / log 2 r = learning rate

Example G. 1 Direct labor hours per locomotive (thousands) Developing the 80% Learning Curve 50 – Manufacturer of diesel locomotives: 40 – 30 – Labor hours required for first unit = 50, 000 20 – Learning rate = 80% 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) Estimating Direct Labor Requirements 50 – Labor hours required for first unit = 50, 000 40 – Learning rate = 80% 30 – 20 – 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using the formula 50 – Labor hours required for first unit = 50, 000 40 – Learning rate = 80% 30 – Labor hours required for 40 th unit 20 – k 40 = 50, 000(40)(log 0. 8)/(log 2) 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using the formula 50 – Labor hours required for first unit = 50, 000 40 – Learning rate = 80% 30 – k 40 = 50, 000(40)-0. 322 20 – 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using the formula 50 – Labor hours required for first unit = 50, 000 40 – Learning rate = 80% 30 – k 40 = 50, 000(0. 30488) 20 – 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using the formula 50 – Labor hours required for first unit = 50, 000 40 – Learning rate = 80% 30 – k 40 = 15, 244 hours 20 – 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using Conversion Factors 80% Learning Rate (n = cumulative production) 50 – n 40 – 1 230 – 3. . . 20 – 38 39 4010 – 64 128 0 – © 2007 Pearson Education 1. 00000 0. 90000 0. 83403. . . 0. 43634 0. 43304 0. 42984 0. 37382 | 0. 30269 | | Labor hours required for first unit = 50, 000 Learning rate = 80% Cumulative average labor hours = | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using Conversion Factors 80% Learning Rate 50 – (n = cumulative production) n 40 – 1 230 – 3. . . 20 – 38 39 4010 – 64 128 0 – © 2007 Pearson Education 1. 00000 0. 90000 0. 83403. . . 0. 43634 0. 43304 0. 42984 0. 37382 | 0. 30269 | | Labor hours required for first unit = 50, 000 Learning rate = 80% Cumulative average labor hours = 50, 000(0. 42984) | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using Conversion Factors 80% Learning Rate 50 – (n = cumulative production) n 40 – 1 230 – 3. . . 20 – 38 39 4010 – 64 128 0 – © 2007 Pearson Education 1. 00000 0. 90000 0. 83403. . . 0. 43634 0. 43304 0. 42984 0. 37382 | 0. 30269 | | Labor hours required for first unit = 50, 000 Learning rate = 80% Cumulative average labor hours = 21, 492 hours | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using Unit-doublings 50 – Labor hours required for first unit = 50, 000 40 – Learning rate = 80% 30 – 20 – 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using Unit-doublings 50 – Labor hours required for first unit = 50, 000 40 – Learning rate = 80% 30 – Second unit = 50, 000(80%) 20 – 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using Unit-doublings 50 – Labor hours required for first unit = 50, 000 40 – Learning rate = 80% 30 – Second unit = 40, 000 hours 20 – 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using Unit-doublings 50 – Labor hours required for first unit = 50, 000 40 – Learning rate = 80% 30 – Fourth unit = 40, 000(80%) 20 – 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Example G. 1 Direct labor hours per locomotive (thousands) using Unit-doublings 50 – Labor hours required for first unit = 50, 000 40 – Learning rate = 80% 30 – Fourth unit = 32, 000 hours 20 – 10 – 0– © 2007 Pearson Education | | | | 40 80 120 160 200 240 280 Cumulative units produced

Application G. 1 Estimating Direct Labor Requirements The 1 st unit of a new product is expected to take 1, 000 hours. The learning rate is 80%, how much time should the 50 th unit take? © 2007 Pearson Education

Example G. 2 Estimating Labor Requirements Units per Cumulative Month Units 1 2 2 2 3 5 10 4 8 Cumulative 18 5 12 Average Time 30 Month per Unit © 2007 Pearson Education 90% Learning Rate (n = cumulative production) n 1 Cumulative 1. 00000 2 Total Hours 0. 95000 3 for All Units 0. 91540 4 0. 88905 5 0. 86784. . . 30 0. 69090 64 0. 62043 128 0. 56069

Example G. 2 Estimating Labor Requirements Units per Cumulative Month Units 1 2 2 2 3 5 10 4 8 Cumulative 18 5 12 Average Time 30 Month per Unit 1 © 2007 Pearson Education 30, 000(0. 95000) = 28, 500 90% Learning Rate (n = cumulative production) n 1 Cumulative 1. 00000 2 Total Hours 0. 95000 3 for All Units 0. 91540 4 0. 88905 5 0. 86784. . . 30 0. 69090 64 0. 62043 128 0. 56069

Example G. 2 Estimating Labor Requirements Units per Cumulative Month Units 1 2 2 2 3 5 10 4 8 Cumulative 18 5 12 Average Time 30 Month per Unit 1 2 © 2007 Pearson Education 30, 000(0. 95000) = 28, 500 30, 000(0. 86784) = 26, 035 90% Learning Rate (n = cumulative production) n 1 Cumulative 1. 00000 2 Total Hours 0. 95000 3 for All Units 0. 91540 4 0. 88905 28, 500(2) = 57, 000 5 0. 86784. . . 30 0. 69090 64 0. 62043 128 0. 56069

Example G. 2 Estimating Labor Requirements Units per Cumulative Month Units 1 2 2 2 3 5 10 4 8 Cumulative 18 5 12 Average Time 30 Month per Unit 1 2 3 4 5 © 2007 Pearson Education 30, 000(0. 95000) = 28, 500 30, 000(0. 86784) = 26, 035 30, 000(0. 79945) = 23, 983 30, 000(0. 74080) = 22, 224 30, 000(0. 69090) = 20, 727 90% Learning Rate (n = cumulative production) n 1 Cumulative 1. 00000 2 Total Hours 0. 95000 3 for All Units 0. 91540 4 0. 88905 28, 500(2) = 57, 000 5 0. 86784. . 26, 035(5) = 130, 175. . 23, 983(10) = 239, 830 30 0. 69090 22, 224(18) = 400, 032 64 0. 62043 20, 727(30) = 621, 810 128 0. 56069

Example G. 2 Estimating Labor Requirements Units per Cumulative Month Units 1 2 2 2 3 5 10 4 8 Cumulative 18 5 12 Average Time 30 Month per Unit 1 2 3 4 5 © 2007 Pearson Education 30, 000(0. 95000) = 28, 500 30, 000(0. 86784) = 26, 035 30, 000(0. 79945) = 23, 983 30, 000(0. 74080) = 22, 224 30, 000(0. 69090) = 20, 727 Cumulative Total Hours for All Units 28, 500(2) 26, 035(5) 23, 983(10) 22, 224(18) 20, 727(30) = = = 57, 000 130, 175 239, 830 400, 032 621, 810

Example G. 2 Estimating Labor Requirements Units per Cumulative Month 1: Month Units 1 2 2 2 3 5 10 4 8 Cumulative 18 5 12 Average Time 30 Month per Unit 1 2 3 4 5 © 2007 Pearson Education 30, 000(0. 95000) = 28, 500 30, 000(0. 86784) = 26, 035 30, 000(0. 79945) = 23, 983 30, 000(0. 74080) = 22, 224 30, 000(0. 69090) = 20, 727 Cumulative Total Hours for All Units 28, 500(2) 26, 035(5) 23, 983(10) 22, 224(18) 20, 727(30) = = = 57, 000 130, 175 239, 830 400, 032 621, 810

Example G. 2 Estimating Labor Requirements Units per Cumulative Month 1: 57, 000 0 = 57, 000 hours Month– Units 1 2 2 2 3 5 10 4 8 Cumulative 18 Cumulative 5 12 Average Time 30 Total Hours Month per Unit for All Units 1 2 3 4 5 © 2007 Pearson Education 30, 000(0. 95000) = 28, 500 30, 000(0. 86784) = 26, 035 30, 000(0. 79945) = 23, 983 30, 000(0. 74080) = 22, 224 30, 000(0. 69090) = 20, 727 28, 500(2) 26, 035(5) 23, 983(10) 22, 224(18) 20, 727(30) = = = 57, 000 130, 175 239, 830 400, 032 621, 810

Example G. 2 Estimating Labor Requirements Units per Cumulative Month 1: 57, 000 0 = 57, 000 hours Month– Units Month 1 2: 130, 175 2 – 57, 000 2= 73, 175 hours 2 3 5 10 4 8 Cumulative 18 Cumulative 5 12 Average Time 30 Total Hours Month per Unit for All Units 1 2 3 4 5 © 2007 Pearson Education 30, 000(0. 95000) = 28, 500 30, 000(0. 86784) = 26, 035 30, 000(0. 79945) = 23, 983 30, 000(0. 74080) = 22, 224 30, 000(0. 69090) = 20, 727 28, 500(2) 26, 035(5) 23, 983(10) 22, 224(18) 20, 727(30) = = = 57, 000 130, 175 239, 830 400, 032 621, 810

Example G. 2 Estimating Labor Requirements Units per Cumulative Month 1: 57, 000 0 = 57, 000 hours Month– Units Month 1 2: 130, 175 2 – 57, 000 2= 73, 175 hours Month 2 3: 239, 830 3 – 130, 175 5= 109, 655 hours Month 3 4: 400, 032 5 – 239, 83010= 160, 202 hours Month – 400, 03218= 221, 778 hours. Cumulative 4 5: 621, 810 8 Cumulative 5 12 Average Time 30 Total Hours Month per Unit for All Units 1 2 3 4 5 © 2007 Pearson Education 30, 000(0. 95000) = 28, 500 30, 000(0. 86784) = 26, 035 30, 000(0. 79945) = 23, 983 30, 000(0. 74080) = 22, 224 30, 000(0. 69090) = 20, 727 28, 500(2) 26, 035(5) 23, 983(10) 22, 224(18) 20, 727(30) = = = 57, 000 130, 175 239, 830 400, 032 621, 810

Example G. 2 Estimating Labor Requirements Units per Cumulative Month 1: 57, 000 0 = 57, 000 /150 Month– Units Month 1 2: 130, 175 2 – 57, 000 2= 73, 175 /150 Month 2 3: 239, 830 3 – 130, 175 5= 109, 655 /150 Month 3 4: 400, 032 5 – 239, 83010= 160, 202 /150 Month – 400, 03218= 221, 778 /150 4 5: 621, 810 8 Cumulative 5 12 Average Time 30 Month per Unit 1 2 3 4 5 © 2007 Pearson Education 30, 000(0. 95000) = 28, 500 30, 000(0. 86784) = 26, 035 30, 000(0. 79945) = 23, 983 30, 000(0. 74080) = 22, 224 30, 000(0. 69090) = 20, 727 = 380 employees = 488 employees = 731 employees = 1068 employees =Cumulative 1479 employees Total Hours for All Units 28, 500(2) 26, 035(5) 23, 983(10) 22, 224(18) 20, 727(30) = = = 57, 000 130, 175 239, 830 400, 032 621, 810

Application G. 2 Estimating Cumulative Labor Hours An example of using the learning model to test budget constraints: 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. Do you think the 38 -unit job can be completed within the 15, 000 -hour budget? How many additional hours would you need for a second job of an 26 additional units? © 2007 Pearson Education