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1. Session 1 Learning Curves Dr. Mahamaya Mohanty

2. Principle of learning effect Learning curve is based on the premise that the organization and individuals get better (more efficient) at their task as the task is repeated over time. Phenomenon is exhibited in many facets of life. Your driving skill improves after repeated trials at driving. You practise mathematics problems before the exam to solve the examination problem in reasonably less time. You take less time to cook a dish after you have cooked it several times in the past. And so on…

3. Genesis of learning curve T.P. Wright in 1936 used learning curves to mathematically represent this relationship. In his report, he described how direct labour cost of making a particular airplane decreases with learning. This relationship was represented by negative exponential curve. Later, several aircraft manufacturer confirmed the relationship to be applicable in their organization too. However, it was noticed that the learning rate varied across organization, different product, etc. An academic interest arose to base strategic decision making on this theory and how to improve the learning rate.

4. Typical learning curve

5. Mathematical representation : arithmetic Approach Each time production volumes doubles, labour-hours/per unit declines by a constant factor called learning rate. For example: if learning rate is 80% and the first unit took 100 hours to produce then values in the following table are valid - Obviously, this approach cannot be used to calculate the hours required to produce, say 3, 7, 10 units. Nth Unit Produced Hours for Nth Unit 1 100.0 2 80 = (0.8*100) 4 64.0 = (0.8*80) 8 51.2 = (0.8*64) 16 41.0 = (0.8*51.2)

6. Mathematical representation : logarithmic Approach If Then Obviously it enables us to calculate the hours required at any unit produced.  

7. Logarithmic approach : worked example Learning rate for a particular operation is 80%, and the first unit of production took 100 hours. The hours required to produce the third unit may be computed as below Solution: = 100* = 70.2 labour-hours. (Answer) This method requires some computations. There is a also much simpler approach available.   Example E1

8. Example E2

9. Table E.3 also shows cumulative values . These allow us to compute the total number of hours needed to complete a specified number of units. Again , the computation is straightforward. Just multiply the table value times the time required for the first unit. Example E3 illustrates this concept. Example E3

10. Learning curve coefficient approach If then Tn=T1*C  

11. Worked Example A shipyard takes 125000 labour hours to produce first of many boats. 2 nd and the 3 rd boats have been produced with the learning rate of 85%. At 40$ per labour-hour, how much you expect to pay for the fourth unit? Solution: we know that Tn = T1C Hence, T4 = 125000*0.723 = 90,375 hours. Cost incurred is 90,375*40 = $3,615,000

12. Managerial considerations in using learning curves A good representative estimate of learning rate is very crucial. Using industry average is not advisable, as competitive niches and type of work differs. Learning rate depends upon process complexity, rate of capital additions (might hamper repeatability). Any change in the process can negatively effect learning rate. Too frequent changes in the process must be avoided. Learning rate reduces with higher level of automation. Learning effect is most pronounced in the initial phases, hence technology adoption should be accordingly. Product life cycle also effects the benefit the organization can yield from learning. For a team, learning rate may be restricted by the bottleneck. Total quality management, continual improvement program have large effect on learning rate.

13. Uses of learning curves in industry Some of the uses include Internal: Labour forecasting, Scheduling, Establishing cost and budgets. External: Supply chain negotiations (Bid preparation). Strategic: Evaluation of company performance, including cost and pricing.

14. Digicomp produces a new telephone system with built-in TV screens . Its learning rate is 80%. (a) If the first one took 56 hours, how long will it take Digicomp to make the eleventh system? (b) How long will the first 11 systems take in total? (c) As a purchasing agent, you expect to buy units 12 through 15 of the new phone system. What would be your expected cost for the units if Digicomp charges $30 for each labor -hour?

15. Strategic Example Company must follow an aggressive pricing policy It should focus on continuing productivity improvement and cost reduction Keep capacity growing according to the demand.

16. Other examples The Minnesota Coach Company has just been given the following production schedule for ski-lift gondola cars. This product is considerably different from any others the company has produced. Historically, the company‘s learning rate has been 80 percent on large projects. The first unit took 1,000 hours to produce. 1) Estimate how many hours would be required to complete the 38th unit. 2) If the budget only provides for a maximum of 30 direct labor employees in any month and a total of 15,000 direct labor hours for the entire schedule, will the budget be adequate? Assume that each direct labor employee is productive for 150 work hours each month.