Learning Curve

Learning Curve

A presentation by

Ahmad Tariq BhattiFCMA, FPA, MA (Economics), BSc

04/10/2023 Learning Curve Phenomenon 2

OriginIt 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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Defi nitionThe mathematical expression of the phenomenon

that, when complex and labor–intensive procedures are repeated, unit labor time tend to decrease at a constant

rate. LC models mathematically this reduction in unit

production time.

– Cima Official TerminologyThe 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 ConceptIt 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 I l lustrat ive Model

Order #

No. of UnitsTotal Time

@LR of 80%

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

1 2 3 4 5 60

500

1000

1500

2000

2500

1 2 4 8 16 32

2,000

1,600

1,280

1,024

819655

Learning Curve W. 80% LR

Cumulative Quantity in Units (Col. 3)Avge. Hrs./Unit of Cumulative Production (Col. 4)

(Data used from table given at slide 5)

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The Formula

𝑌 𝑥=𝑎 𝑋 𝑏

Where,Y = the cumulative average time required to produce X

unitsa = 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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CalculationThe cumulative average time taken to produce 10

and 20 units is calculated as follows:

Y= 2000x0.476431

Y= 953 hours

Y = 2000 x 0.381126

Y = 762 hours(Data used from table given at slide 5)

𝒀 𝟐𝟎=𝟐𝟎𝟎𝟎 𝐱𝟐𝟎−𝟎 .𝟑𝟐𝟐

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Calculating Incremental HoursTo 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)

04/10/2023 Learning Curve Phenomenon 10

Calculating LR by Using LogsIllustration 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 hoursCumulative 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 hoursX = 12

b = Rate of learning = Log of learning rate/ Log2 ……(a)

𝒀 𝒙=𝒂𝑿𝒃

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CalculationTo calculate b:6.75 = 15 x

= 6.75/15 = 0.45b log12 = log 0.45

b = Log 0.45/Log 12 = (- 0.3468/1.0792) = - 0.3213

Now putting value of b in formula (a) at slide10

b = Log of learning rate/Log2

-0.3213= Log of learning rate / 0.3010Log of learning rate = 0.3010 x (-0.3213) = -

0.09671Log of learning rate = -0.09671

Find the value (-0.09671) in anti-log table. The value -0.09671 converts to 80% i.e.

the learning rate.

04/10/2023 Learning Curve Phenomenon 12

Calculating Total Time - Tabular MethodIllustration 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

04/10/2023 Learning Curve Phenomenon 13

Calculating Total Time by Using Formula

Illustration 3Sigma company has noted a learning rate of 85% while launching test for its product ET. It takes 100 hours to

produce the first unit in a batch. Requirement: Calculate total time for 14 unit batch???

SolutionY = average time per unit

a = time taken for the first unitb = 85% = - 0.2345

Y = 100 x = 53.856

Average time per unit for a batch containing 14 units = 53.856 hours

Total time for a batch containing 14 units = 14 x 53.856 = 753.984 hours

04/10/2023 Learning Curve Phenomenon 14

Pricing a Contract by Using LCIllustration 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 @ AED. 20 each)

1,000

Labor & related cost:

-- Direct Labor (100 hours @ AED.8 each)

800

-- Variable Overheads (100 hours @ AED. 2 each)

200

Total cost of 1st 50 units 2,000

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Calculation

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%)

Solution

Calculation of Contract Price:

Amount

D e s c r i p t i o n o f C o s t & P r i c e C o m p o n e n t s :

AED.

Materials (50 units @ AED. 20 each) 1,000

Direct labor (60 hours @ AED. 8 each) 480

Variable Overhead (60 hours @ AED. 2 each) 120

To t a l c o s t f o r a d d i t i o n a l 5 0 u n i t s 1,600

A d d : M a r k u p 5 0 % 800

Contract Pr ice for 50 un i ts 2,400

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Important NoteThe 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 Pr ic ing Dec is ionsIt 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 Schedul ingUseful in the management of delivery orders and related schedules. Scheduling labor work requirements.

Standard Sett ing & Budget ingPlays meaningful role in standard costing and applying budgetary controls. Standard costs should reflect the point that has been reached on LC.

Pr ic ing ContractsThe 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.

Sett ing Incent ive Wage RatesThe LC concept is applied in determining incentive wage rates across the industries.

Inventory ManagementThe LC concept can be used in the planning, budgeting and purchasing of inventory.

04/10/2023 Learning Curve Phenomenon 18

Abbreviat ions Used#

Abbrev iation Descr ipt ion

1 AED Emirati Dirham

2 LC Learning Curve

3 LR Learning Rate

4 WW-II World War Two

04/10/2023 Learning Curve Phenomenon 19

References

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

W. Hartman

04/10/2023 Learning Curve Phenomenon 20

The End.

A presentation by

Ahmad Tariq BhattiFCMA, FPA, MA (Economics), BSc

Dubai, United Arab Emirates.Contact:

[email protected]

T h a n k y o u !