# Learning Curve Essay

LEARNING CURVE CONCEPT AND ITS USEFULNESS IN MANAGEMENT DECISIONS Presented ByKriti Agarwal (A002) Aniket Rane(A046) Nitin Gupta(A024) Eshan Singh(A057) Mayank Bhatia(A013) HISTORY Introduced to the aircraft industry in 1936 by T. P. Wright in his article Journal of the Aeronautical Science He found that per unit production time reduced at an unvarying rate Since then, learning curves (also known as progress functions) have been applied to all types of work INTRODUCTION

A graphical representation of the changing rate of learning (in the average person) for a given activity or tool The underlying hypothesis is that the direct labor man-hours necessary to complete a unit of production will decrease by a constant percentage each time the production quantity is doubled EXAMPLE FUNDAMENTAL PROPERTIES As the number of completed tasks increases: time taken to complete a task decreases time savings from one task to another decreases amount of improvement decreases ASSUMPTIONs That the task is repetitive That only manual labour is involved and there is no automation of processes.

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That staff are fully motivated and there are no constraints.

That no labour turnovers occurred for a long time That the products and processes are standardised, no midway modification. There must be continuous production- no stoppage That repetitive process will increase production FACTS ABOUT LEARNING CURVE… • Learning applies to people, machinery, systems • Learning Curve is similar to Experience curve but former applies more to whole organisation. • Learning Curve is based on empirical evidences. • 80% learning curve usually assumed WHERE CAN WE APPLY learning curve? • • • • • • • • • • • •

New Product Production Costs Make or Buy Decisions Suppliers Progress Payments Analyze Pricing Practices of Suppliers Cost-Volume-Profit (CVP) Analysis Evaluation of Production Employees Multi-Year Procurement Analysis Production Rate Evaluation Production Improvement Cycle Times Costs versus Prices Over Time Competitive Bidding Technology Forecasting ARITHMETIC APPROACH Empirical evidence shows that doubling of repetition results in constant percentage decrease in time per repetition. Unit 1ST 2ND 4TH 8TH 16TH 32ND Man hours 1000 800 640 512 410 328 1000 X . 80 800 X . 80 640 X . 0 512 X . 80 410 X . 80 LIMITATIONS OF BASIC APPROACH It’s very difficult to calculate or predict the Man Hrs for anything other than that at the DOUBLING POINT: 1, 2, 4, 8, 16 … 128 … Now it gets mathematical! 1. Use of Formula 2. Use Of Table of Coefficients LEARNING THEORY Two variations: Cumulative Average Theory Unit Theory 17 – 11 CUMULATIVE AVERAGE THEORY “If there is learning in the production process, the cumulative average cost of some doubled unit equals the cumulative average cost of the undoubled unit times the slope of the learning curve” Described by T. P.

Wright in 1936 based on examination of WW I aircraft production costs CUMULATIVE AVERAGE LEARNING THEORY Defined by the equation YN = AN b where YN = the average cost of N units A = the theoretical cost of unit 1 N = the cumulative number of units produced b = a constant representing the slope UNIT THEORY “If there is learning in the production process, the cost of some doubled unit equals the cost of the undoubled unit times the slope of the learning curve” Credited to J. R. Crawford in 1947 led a study of WWII airframe production commissioned by USAF to validate learning curve theory

CONCEPT OF UNIT THEORY As the quantity of units produced doubles, the cost to produce a unit is decreased by a constant percentage 80% Unit Learning Curve $120. 00 $100. 00 $80. 00 $60. 00 $40. 00 $0. 50 $20. 00 $0. 00 0 2 4 6 8 10 12 14 16 $0. 00 0 0. 5 1 1. 5 100 80 66. 92 54. 98 44. 638 $2. 50 $2. 00 $1. 50 $1. 00 UNIT THEORY Defined by the equation Yx = Axb ,where Yx = the cost of unit x (dependent variable) A = the theoretical cost of unit 1 (a. k. a. T1) x = the unit number (independent variable b = ln(slope)/in(2) In practice, -0. 5 < b < -0. 5 corresponds roughly with learning curves between 70% and 96% learning parameter largely determined by the type of industry and the degree of automation for b = 0, the equation simplifies to Y = A which means any unit costs the same as the first unit. In this case, the learning curve is a horizontal line and there is no learning. DIFFERENCE BETWEEN TWO MODELS Over the first few units, an operation following the cumulative average curve will experience a much greater reduction in cost (hours or dollars) than an operation following a unit curve with the same slope.

The unit curve should be used in situations where the firm is fully prepared for production; and the cumulative average curve should be used in situations where the firm is not completely ready for production. Most firms in the airframe industry use the cumulative average curve. Most firms in other industries use the unit curve. EXAMPLE to Understand Formula y = axb b = log (Learning Rate) / log 2 For 80% LC, (Learning Rate) = . 80 b = log . 80 / log 2 = -. 3219 Assume k = 1000 y1 = 1000 (1)-. 3219 = 1000 (1) = 1000 y2 = 1000 (2)-. 3219 = 1000 (. 80) = 800 y3 = 1000 (3)-. 219 = 1000 (. 7021) = 702 y4 = 1000 (4)-. 3219 = 1000 (. 6400) = 640 y100 = 1000 (100)-. 3219 = 1000 (. 2270) = 227 LEARNING CURVE Coefficients 70% Unit Number (N) 1 2 3 4 5 10 15 20 85% Unit Time(C) 1. 000 . 700 . 568 . 490 . 437 . 306 . 248 . 214 Total Time 1. 000 1. 700 2. 268 2. 758 3. 195 4. 932 6. 274 7. 407 Unit Time(C) 1. 000 . 850 . 773 . 723 . 686 . 583 . 530 . 495 Total Time 1. 000 1. 850 2. 623 3. 345 4. 031 7. 116 9. 861 12. 402 TN = T1C where T1 is Time required for 1st Unit ESTIMATING LEARNING curve parameters must estimate far in advance Aggregation rather than to individual operations •First unit hours rarely known in time to develop curve – •Slope can be estimated by least-squares regression •Comparisons should always be made to similar products/processes – industry data usually available •Extensive pre-production planning should result in lower, flatter curve STRATEGY FORMULATION To pursue a strategy of a steeper curve than the rest of the industry, a firm can: 1. Follow an aggressive pricing policy 2. Focus on continuing cost reduction and productivity improvement 3. Build on shared experience 4. Keep capacity ahead of demand

STRATEGY FORMULATION … Price per unit (log scale) Loss Gross profit margin (c) (b) (a) Accumulated volume (log scale) In general terms, the following guidelines might be useful for us 75% hand assembly/25% machining = 80% learning 50% hand assembly/50% machining = 85% learning 25% hand assembly/75% machining = 90% learning Alternatively, industry averages: Aerospace Shipbuilding Raw materials Purchased parts 85% 80 – 85% 93 – 96% 85 – 88% APPLICATIONS & USES Three general areas – 1. Strategic o Volume-cost changes, o Estimating new product start-up costs, and oPricing of new products 2.

Internal oDeveloping labour standards, oScheduling, oBudgeting, and oMake-or-buy decisions 3. External oSupplier scheduling, oCash flow budgeting, and oEstimating purchase costs The usefulness of learning curves depends on a number of factors; oThe frequency of product innovation, oThe amount of direct labour versus machine-paced output, and oThe amount of advanced planning of methods and tooling All lead to a predictable rate of reduction in throughput time BATCH ACCUMULATION Suppose a batch of 20 units has just been made and it has taken 200 hours –i. . an average of 10 hours per unit. A 90 per cent learning curve is expected to apply. We are required to estimate the following: a. The cumulative average time for the first two batches. b. The total time to produce 40 units. c. The incremental time for 41 to 60 units – ie, a third batch of 20 units. Solution : a)A learning curve is geometric with the general form Y =axb This is a batch situation, so the Y value will be the cumulative average time per batch for two batches of 20 units a = 20 x 10 = 200 hours (ie, the time for the first batch). = log 0. 9 ? log 2 = – 0. 152. X = 40 ? 20 = 2 (ie, two cumulative batches). Y = 200(2– 0. 152) = 180 hours per batch. b) Total time to make 2 batches : 2 batches x 180 hours per batch = 360 hours c) We already have the total time for 40, so we need the total time for 60 (ie, X = 3): Y = 200(3 – 0. 152) = 169. 24 hours per batch. Total time for 60 units = 169. 24 x 3 = 507. 72 hours Incremental time = 507. 72 – 360 = 147. 72 hours Amount of Time 205 200 195 190 185 180 175 170 165 0 20 40 60 80 169. 24 180 Amount of Time 200 Aviation Industry

Learning curves were first used by the aircraft industry in the 1930s The Boeing Co. pioneered the discipline when it discovered that the cost to build new airplanes was highly predictable The planes get cheaper to build as the company learns how to do it more efficiently Workers work faster, make fewer mistakes and waste less material The steeper it is, the faster the person, project team or company is learning to produce that item or service. Total Cost Of Production 120 100 80 60 40 20 0 0 1 2 3 4 5 100 80 64 51 Total Cost Of Production

VARIED APPLICATIONS Cost Estimation Error analysis What you can estimate Interruption of production Fitting learning curves to production data Tradeoff analysis with learning curves Standard Costing COST ESTIMATION You use marginal costing system. You have been asked to provide calculations of total variable costs for a contract for one of your products, based on the following alternative situations: 1. A contract for one order of 600 units. 2. Contracts for a sequence of individual orders of 200, 100, 100 and 200 units. Four separate costings are required.

It’s expected that the average unit variable cost data for an initial batch of 200 units will be as follows: Direct material: 15m2 at ? 8 per m2. Direct labour: department A: 8 hours at ? 8 per hour; and department B: 100 hours at ? 10 per hour. Variable overhead: 25 per cent of labour. Labour times in department A are expected to follow an 80 per cent learning curve. Department B labour times are expected to follow a 70 percent learning curve. The cost estimates are as follows: For one order for 600 units, we first need to define the appropriate values of a.

We are dealing with a batch situation, so we need to define a as the time for the first batch of 200 units: Department A: 200 x 8 = 1,600 hours. Department B: 200 x 100 = 20,000 hours. Next, we calculate the values of b: Department A: log 0. 8 ? log 2 = – 0. 322. Department B: log 0. 7 ? log 2 = – 0. 515. The appropriate formulas are, therefore: Department A: Y = 1,600(X– 0. 322). Department B: Y = 20,000(X– 0. 515). We can now proceed with the calculation of the total variable cost for a contract for 600 units: Direct material: 600 x ? 120 per unit = ? 72,000.

Direct labour: we use the curve formulas to ascertain the labour times and then convert to cost. The cumulative quantity is 600 units, so X = 3 (ie, 600 ? 200). Department A: Y = 1,600(3– 0. 322) = 1,123. 28 hours per batch. This is the cumulative average time per batch for the cumulative three batches, so the total time is 1,123. 28 x 3 = 3,370 hours. The cost is, therefore, 3,370 x ? 8 = ? 26,960 Department B: Y = 20,000(3– 0. 515) = 11,358. 28 hours per batch. The total time is, therefore, 11,358. 28 x 3 = 34,075 hours. The cost is, therefore, 34,075 x 10 = ? 340,750.

Variable overhead: 0. 25 x (26,960 + 340,750) = ? 91,928. The total variable cost for the 600 units is as follows: Direct materials: ? 72,000 Direct labour: ? 367,710 Variable overhead: ? 91,928 Total: ? 531,638 For sequential individual orders of 200, 100, 100 and 200 units, four separate costings are required. The costing for the first batch of 200 will be straightforward as we will simply use the average unit cost data initially given. So the total variable cost for the first batch of 200 units is: Direct material: 200 x 120 = ? 24,000 Direct labour: Department A: 200 x 64 = ? 2,800 Department B: 200 x 1,000 = ? 200,000 Variable overhead: 0. 25 x 212,800 = ? 53,200 Total: ? 290,000 For the next three batch orders we need to work out the incremental costs. Direct material cost is constant per Unit, so it’s not a problem. The variable overhead is 25 per cent of labour cost. Direct labour cost is affected by learning curves, so we need to calculate the incremental times using the learning curve formulas and then convert to cost. Then we can complete the costings for the second, third and fourth orders. LIMITATIONS LIMITATIONS(1)

Unplanned changes in production techniques or labour turnover will cause problems and affect the learning rate Employees need to be motivated, agree to the plan and keep to the learning schedule Accurate and appropriate learning curve data may be difficult to estimate. Inaccuracy in estimating the initial labour requirement for the first unit. LIMITATIONS(2) Assumes a constant rate learning factor Learning curves do not always apply to indirect labor or material Culture of the workplace, resource availability, and changes in the process may alter the learning curve LIMITATIONS(3)

Learning curves differ from company to company as well as industry to industry so estimates should be developed for each organization LIMITATIONS Learning curves are often based on time estimates which must be accurate and should be reevaluated when appropriate CONCLUSION Learning curve models are an important technique for predicting how long it will take to undertake future tasks. Management accountants must consequently take account of the impact of learning for planning, control and decision-making While very few use the learning curve for management accounting, only a small minority consider it to be inappropriate for their organisation.

Learning curve users make extensive use of this technique for management accounting. Learning curve can be applied to a wide range of business sectors, including sectors not normally associated with its use. Almost half of learning curve users work in the service sector. Key obstacle to implementation by non-users is a lack of understanding of learning curve theory. However, procedural and cultural barriers are also a major impediment to the introduction of techniques at some organisations THANK YOU