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A business has developed a new product. The first batch of 100 units takes 1500 labour hours to produce. The business has estimated that there will be an 85% learning curve that will continue until 6400 units have been produced. Batches after this level will each take the same amount of time as the 64th batch. The batch size is 100 units.
Note. The learning index for an 85% learning curve is -0.2345
What is the cumulative average time per batch for the first 64 batches?
I calculated the answer to be 665.5579688 using the doubling rule. I don’t understand where I went wrong.There is another part of the same question, and it is the following:
The total time for the first 16 batches of 100 units was 9000 hours.
What was the actual learning rate closest to (to the nearest %)?
I think that the 85% learning curve given in the question is the same thing as the learning rate. So the answer should be 85% which is already given in the question. Is it correct?
Another alternative answer that I thought is that the learning rate should be the average time for 16 batches divided by the average time for the first batch, and then the figure that comes should be square rooted to the power of 4. So, it should be 562.5 divided by 1500 and then the square root to the power of 4 which comes to 2.45 and as a percentage it is 245%. I don’t understand where I went wrong in this alternative approach as well.
First question:
Making 64 batches means doubling 6 times.
Therefore the average time per batch is 1,500 x 0.85^6 = 566 hours
Second question:
Just because they have estimated a learning rate of 85% does not mean that it will actually be 85%.
The average time per batch when they make 16 batches is 9,000/16 = 562.5 hours
16 batches means doubling 4 times.
Therefore the learning rate is the fourth root of (562.5/1500) = 0.7825 (or 78.25%)
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