Learning Curve

1
Learning Curve

• A presentation by
• Ahmad Tariq Bhatti
• FCMA, FPA, MA (Economics), BSc

2
Origin
It was found at Boeing, the aircraft
manufacturing company, during WW-II period, that
the time taken to assemble an individual aircraft
declined as the number of aircrafts assembled
increased. It was noted that the rate of
improvement (known as rate of learning) was so
regular that it was presented in the form of a
mathematical formula. Thus, the labor hours
required for the assembly of aircrafts could be
predicted with reasonable precision. The name
given to this effect of increased efficiency was
Learning Curve (LC) phenomenon. The phenomenon
was tested in a number of manufacturing setups
across the industries and it was found invariably
everywhere. However, the learning rate of
laborers differed from one industry to another.
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Definition
The mathematical expression of the phenomenon
that, when complex and laborintensive
procedures are repeated, unit labor time tend to
decrease at a constant rate. LC models
mathematically this reduction in unit production
time. Cima Official Terminology The LC is based
on the idea that labor hours decrease in a
definite pattern as labor operations are
repeated. More specifically, it is derived from
statistical findings that as cumulative
production doubles, cumulative average time
required per unit will be reduced by some
constant percentage, say 10 to 20.
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The Concept
It was found that the cumulative average time per
unit decreased by a fixed percentage each time
the cumulative production doubled. In aircraft
industry, the percentage by which cumulative
average time per unit decreased was typically
80. Similarly different learning rates were
noted for different industries. Let us examine an
example of production where learning rate is
noted at 90
Units Avg. time/unit (hrs.) Cumulative production time (hrs.)
1 100.00 100.00
2 90.00 (100x90) 190.00
4 81.00 (90x90) 271.00
8 72.90 (81x90) 343.90
16 65.61 (72.90x90) 409.51
32 59.05 (65.61x90) 568.56
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An Illustrative Model
Order No. of Units No. of Units Total Time _at_LR of 80 Total Time _at_LR of 80
Order Per order Cumulative Production Per Unit (Hours) All Units (Hours)
1 2 3 4 5 3 x 4

1 1 1 2,000 2,000
2 1 2 1,600 (2,000 x 80) 3,200
3 2 4 1,280 (1,600 x 80) 5,120
4 4 8 1,024 (1,280 x 80) 8,192
5 8 16 819 (1,024 x 80) 13,104
6 16 32 655 (819 x 80) 20,960
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The Shape of LC
(Data used from table given at slide 5)
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The Formula
 
Where, Y the cumulative average time required
to produce X units a the time required to
produce the first unit of output b the
learning /improvement rate/index of learning X
number of units to be produced Important Note
, This formula calculates only direct labor time
against given number of units. The direct labor
cost shall be calculated, thereafter, by
multiplying the time calculated by this formula
with standard labor rate.
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Calculation
 
 
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Calculating Incremental Hours
To calculate incremental hours, we need to
examine the differences between total hours for
various combinations of cumulative hours. For
instance, in our foregoing illustrative model ,
the company has completed an order for 4 units
and an enquiry has been received for 6 units
later. The calculation for the time required
for the production of additional 6 units shall
proceed in the manner given as below Total
hours if an additional 6 units are produced (10 x
953) 9530 ..(a) Total hours for the first four
units (4 x 1280)
5120..(b) Hours required for 6 units after
completion of 4 units 4410 (a-b)
(Data used from table given at slide 5)
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Calculating LR by Using Logs
Illustration 1 Data relating to the production
of first 12 batches of Product X are given as
follows Time taken to produce the first unit
15 hours Cumulative time taken to produce first
12 batches 81 hours. Requirement Calculate the
learning rate??? Solution Where Y Average
time/batch 81/12 6.75 hours a 15 hours X
12 b Rate of learning Log of learning rate/
Log2 (a)
 
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Calculation
 
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Calculating Total Time - Tabular Method
Illustration 2 XYZ Ltd is calculating the time
taken for product Y and found that a 90 LC
applies to the behavior of labor working on its
production. The time taken for the first unit
produced is 4 hours. Requirement Calculate
total time taken for 8 units to be produced of
product Y??? Solution
of units Average Time/ Unit Cumulative Time
Hours Hours
1 4.000 4
2 3.600 (4.00 x 90) 7.2
4 3.240 (3.60 x 90) 12.960
8 2.916 (3.24 x 90) 23.328
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Calculating Total Time by Using Formula
 
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Pricing a Contract by Using LC
Illustration 4 ABC Company, finds that product
M has 80 learning effect. The company has just
produced 50 units at 100 hours per unit. Detail
of cost incurred is given in the table given
below. The company has just received a contract
calling for another 50 units. The company has
decided to have a 50 markup on the cost.
Requirement Determine price for the contract
for the 50 units????
Description Amount in AED.
Materials (50 units _at_ AED. 20 each) 1,000
Labor related cost
-- Direct Labor (100 hours _at_ AED.8 each) 800
-- Variable Overheads (100 hours _at_ AED. 2 each) 200
Total cost of 1st 50 units 2,000
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Calculation
Solution
Quantity Total Time Average Time /Unit
Units Hours Hours
50 100 2
100 160 (1.6 x 2 x 100) 1.6 (2hrs x 80)
Calculation of Contract Price Amount
Description of Cost Price Components AED.
Materials (50 units _at_ AED. 20 each) 1,000
Direct labor (60 hours _at_ AED. 8 each) 480
Variable Overhead (60 hours _at_ AED. 2 each) 120
Total cost for additional 50 units 1,600
Add Markup 50 800
Contract Price for 50 units 2,400
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Important Note
The LC formula is used to estimate direct labor
time for a given number of units and thus is
helpful in the calculation of direct labor cost
estimates. Further, the learning effect is
applied to those variables also that are
dependent upon direct labor time for their time
and cost estimation. The concept of LC is not
applied to direct material costs or overhead
costs relating to production. The concept of LC
is applicable where operations are complex and
carried out manually by labor. Where operations
are so simple that apply very low level of
intelligence, there shall be little scope for
learning effect. Hence, there shall be no LC.
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Applications

• Pricing Decisions
• It requires the ability of the management to use
  the learning effect to forecast and make the cost
  reductions and obtain a considerable lead over
  the competitors by giving better prices.
• Work Scheduling
• Useful in the management of delivery orders and
  related schedules. Scheduling labor work
  requirements.
• Standard Setting Budgeting
• Plays meaningful role in standard costing and
  applying budgetary controls. Standard costs
  should reflect the point that has been reached on
  LC.
• Pricing Contracts
• The LC has been quite useful in determining the
  likely costs relating to various contracts. It
  provides a rational basis for price negotiation
  and cost control.
• Setting Incentive Wage Rates
• The LC concept is applied in determining
  incentive wage rates across the industries.
• Inventory Management
• The LC concept can be used in the planning,
  budgeting and purchasing of inventory.

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Abbreviations Used
Abbreviation Description
1 AED Emirati Dirham
2 LC Learning Curve
3 LR Learning Rate
4 WW-II World War Two
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References

• Management Cost Accounting by Colin Drury 5/e
• Cima Official Terminology
• Business Finance by Joel G. Siegel, Jae K. Shim,
  Stephan W. Hartman

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Thank you!

• The End.

• A presentation by
• Ahmad Tariq Bhatti
• FCMA, FPA, MA (Economics), BSc
• Dubai, United Arab Emirates.
• Contact
• at.bhatty_at_gmail.com