Learning Curves

Overview

• The resources required to produce the given amounts of a product tend to decline as output accumulates
• Cause of decline -- > learning curve. Workers become more adept at a task the more they perform it. This is measured mathematically
• Cumulative average time per unit/batch decreases by a fixed percentage each time the cumulative production doubles
• Learning rate = %

When does learning curve theory apply?

• Labor intensive - product made largely by labor effort
• New - brand new or relativity short-lived product
• Complex - product made in small quantities for special orders

Example 1

A firm with a learning rate of 80% takes 50 hours to make its first unit. It has now made a total of 16 units. How long will the next 16 units take?

Formula Approach

Example 2

• Derive the formula for the 80% learning rate and apply it to confirm the cumulative average time per unit for 16 batches in the previous illustration
• Using the same formula, calculate the cumulative average time per unit for 20 batches
• The formula is calculated as follows:
• b = log 0.8/log 2 = -0.322
• y = ax -0.322
• At 16 batches: 50 x 16 -0.322 = 20.48
• At 20 batches: 50 x 20 -0.322 = 19.06

Uses of the learning curve

• Price setting
• Budget setting
• Production scheduling

Limitations of learning curve theory

• Not always present
• Assumes stable conditions which allow learning to take place
• Assumes certain degree of motivation among employees
• Breaks between repeating production of an item must not be too long or workers will forget and learning will have to begin again
• Maybe difficult to obtain enough accurate data to decide what learning factor is
• Learning is eventually cease

Practice Test

36 Batch Processing (10 Marks)

• Standard direct labor cost of one batch of 100 units of product is $50.40
• Standard time of 4.2 hours @ $12 per hour, with average time expected per batch based on product life of 12,800 units or 128 batches
• Expected time for the first batch was 20 hours and an 80% learning curve
• Company already completed 32 batches with total actual direct labor cost of $3,493
• Direct labor variances:
• Direct labor rate = $85 adverse
• Direct labor efficiency = $891 adverse

• Required:
• Actual rate of learning
• Total direct labor cost

• Answers:

a) Y = axb

• Standard cost of actual labor hours worked is actual cost less the adverse direct labor rate variance
• $3,493 - $85 = $3,408
• Actual labor hours worked is $3,408/$12 = 284 labor hours
• Hours per batch = 284/32 = 8.875 hours per batch
• Learning rate = 5√(8.875/20) = 0.85 = 85% --> 32 batches represents 5 doublings of output

b) Total direct labor cost

• Actual labor rate is $3,493/284 = $12.30 per hour
• b = log .85/log 2 = -0.2345
• Average time: Y = axb
• 20 X 128 -0.2345 = 6.41 hours
• Total cost = average time x no. of batches x actual labor rate
• 6.41 x 128 x $12.30
• $10,092

37 The Learning curve effect

• Actual output is 560 units, 3500 hours at a cost of $57,750
• Standard time of 8 hours @ $15 per hour
• Expected time for the first 600 units was 8 hours and an 90% learning curve
• Direct labor variances:
• Direct labor rate = $5,250 adverse
• Direct labor efficiency = $14,700 Favourable

• Required:
• Planning and Operating variances
• Importance of learning curves in the context of Target costing
• 90% learning index of -0.1520

• Answers:

a) Y = axb

• Y = 8 X 560 -0.1520 = 3.057 hours
• Total time for 560 units (560 X 3.057 hours) = 1,712 hours