# Solved problems of the curve

## Solved problems of the curve

In this article I plan to share with you some solved exercises of the learning curve.

So, if you are interested, keep reading and I hope you find it useful.

A good way for you to really learn the theoretical concepts that you read is without a doubt through practice.

Therefore, I would like you to put into practice what you learned about the learning curve.

In this way, you will be able to apply the theory to real life situations in which it is possible to use said knowledge.

Captain Nemo, owner of the Suboptimum Underwater Boat Company (SUB), is very intrigued.

He has a contract to genera 11 boats and has finished 4 of them.

He has observed that his production manager, the young Mr.

Overick, has been reassigning more and more people to speed up assembly after the first four ships were built.

For example, the first ship required 225 workers, each working a 40-hour week, while the second ship required 45 fewer workers.

Overick has told them that it is “just the beginning” and that he will finish the last ship on the current contract with just 100 workers.

Overick is riding on the learning curve, but is he overreacting?

### Solution

#### Step 1​

As we already saw in the example, there is a decrease in the number of workers needed to craft the ships.

We have the data of the first ship and the second.

Now, with these data we are going to obtain the percentage of learning.

To obtain the percentage of learning we only have to divide 180 by 225 (because 225 – 45 = 180).

Therefore, the learning percentage is 80%.

#### Step 2​

Since we have the percentage of learning, what we have to do is find the rate of improvement for 80%.

For that, we are going to use the following table taken from the book Operations Management by Richard B.

Chase.

Remember that we are looking for 80% for 11 units.

Since the table does not espectáculo us for 11 units, what we will do is take the average (taking 10 and 12 units into account).

Which gives us an improvement index of 0.4629.

#### Step 3​

Finally, we are going to multiply the upgrade rate by the number of workers needed to build the first ship (225).

Which gives us a value of 104.15 workers.

Which means that it would take 104 workers to make ship number 11 and therefore Overick would need 4 more workers.

A person is put through some tests because he has applied for a position on the assembly line.

Management thinks that a steady state is reached, more or less, after performing a task 1,000 times.

Regular assembly line workers are expected to complete the task within four minutes.

a) If the job applicant performed the first operation of the test in 10 minutes and the second in 9 minutes, should he be hired?

b) What is the expected time the applicant would take to complete unit 10?

### Solution

a) As in the previous example, the first step is to obtain the learning rate.

Therefore, what we have to do is divide 9 minutes by 10 minutes.

Which gives us a value of 90%.

The second step is to use the table to obtain the rate of improvement of 1000 units with 90%.

Which gives us a value of 0.3499.

Finally, the third step consists of multiplying the improvement index obtained by the 10 minutes.

Which gives us a value of 3,499 minutes.

That is, we would hire the person because it falls within 4 minutes.

b) Following the above, we are going to obtain the improvement index of 10 units for 90%.

Which gives us a value of 0.7047.

Finally, we are going to multiply the rate of improvement by the 10 units, which gives us a value of 7,047 minutes.

So it would take you 7,047 minutes on unit 10.

A time estándar was established at 0.20 hours per unit based on the 50 unit produced.

If Task 1 has a 90% learning curve, what would be the expected time for Unit 100, Unit 200, and Unit 400?

### Solution

for unit 100

The first step would be to obtain the improvement index of 100 units with 90%.

Which gives us a value of 0.4966.

Finally, we are going to multiply the rate of improvement by 12 minutes (0.20 hours) and it gives us a value of 5.9592 minutes.

That is, in unit 100, it would take 5.9592 minutes to complete the task.

For unit 200

As in the previous case, we are going to obtain the improvement index of 200 units with 90%.

The value we get is 0.4469.

What we have to do now is multiply the rate of improvement by 12 and it gives us a value of 5.3628 minutes.

For unit 400

We are going to obtain the improvement index of 400 units with 90%.

It gives us a value of 0.4022.

Finally, we multiply the index by 12 minutes and it gives us a value of 4.8264 minutes.

We hope you liked our article Solved problems of the curve
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