LEARNING CURVE

Learning curve shows the rate of improvement in performing a task as a function of time.

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. 11/23/2012 Learning Curve Phenomenon 2

3. Definition The 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 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%. 11/23/2012 Learning Curve Phenomenon 3

4. 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 11/23/2012 Learning Curve Phenomenon 4

5. An Illustrative Model 11/23/2012 Learning Curve Phenomenon 5 Order # No. of Units Total 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

6. The Shape of LC 11/23/2012 Learning Curve Phenomenon 6 (Data used from table given at slide 5)

7. The Formula 11/23/2012 Learning Curve Phenomenon 7   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.

8. Calculation 11/23/2012 Learning Curve Phenomenon 8 The 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)    

9. Calculating Incremental Hours 11/23/2012 Learning Curve Phenomenon 9 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)

10. Calculating LR by Using Logs 11/23/2012 Learning Curve Phenomenon 10 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/ Log 2 …… ( a )  

11. Calculation 11/23/2012 Learning Curve Phenomenon 11 To calculate b: 6.75 = 15 x = 6.75/15 = 0.45 b 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/Log 2 -0.3213= Log of learning rate / 0.3010 Log of learning rate = 0.3010 x (-0.3213) = - 0.09671 Log 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 .  

12. Calculating Total Time - Tabular Method 11/23/2012 Learning Curve Phenomenon 12 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

13. 11/23/2012 Learning Curve Phenomenon 13 Calculating Total Time by Using Formula Illustration 3 Sigma 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??? Solution Y = average time per unit a = time taken for the first unit b = 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  

14. Pricing a Contract by Using LC 11/23/2012 Learning Curve Phenomenon 14 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 @ 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 1 st 50 units 2,000

15. Calculation 11/23/2012 Learning Curve Phenomenon 15 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 Description of Cost & Price Components: 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 Total cost for additional 50 units 1,600 Add: Markup 50% 800 Contract Price for 50 units 2,400

16. Important Note 11/23/2012 Learning Curve Phenomenon 16 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.

17. Applications 11/23/2012 Learning Curve Phenomenon 17 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.

18. Abbreviations Used 11/23/2012 Learning Curve Phenomenon 18 # Abbreviation Description 1 AED Emirati Dirham 2 LC Learning Curve 3 LR Learning Rate 4 WW-II World War Two

19. References 11/23/2012 Learning Curve Phenomenon 19 Management & Cost Accounting by Colin Drury 5/e Cima Official Terminology Business Finance by Joel G. Siegel, Jae K. Shim, Stephan W. Hartman

20. T h e E n d . A presentation by Ahmad Tariq Bhatti FCMA, FPA, MA (Economics), BSc Dubai, United Arab Emirates. Contact: [email protected] 11/23/2012 Learning Curve Phenomenon 20 T h a n k y o u !