Problem 6-4 You’ve just completed a pilot run of 10 units of a major product and

Question

Problem 6-4

You’ve just completed a pilot run of 10 units of a major product and found the processing time for each unit was as follows: Use Exhibit 6.4 and Exhibit 6.5.

According to the pilot run, what would you estimate the learning rate to be? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Based on (a), how much time would it take for the next 190 units, assuming no loss of learning? (Round your answer to the nearest whole number.)

How much time would it take to make the 1,000th unit? (Round your answer to the nearest whole number.)

You’ve just completed a pilot run of 10 units of a major product and found the processing time for each unit was as follows: Use Exhibit 6.4 and Exhibit 6.5.

Explanation / Answer

a. According to the pilot run, what would you estimate the learning rate to be? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Estimated learning rate      85 %

Explanation

Learning rate - Every time the production volume is doubled, the labor per unit decreases at a constant rate

Units 1 to 2 = 800/970 = 82.47% ( ie second unit is produced in 82.47% of the time taken by first unit)

Units 2 to 4 = 680/800 = 85.00% (i.e. fourth unit is produced in 85.00% of the time taken by second unit)

Units 4 to 8 =600/680 = 88.24%

Average learning rate = (82.47+85+88.24)/ 3= 85.24%.

b. Based on (a), how much time would it take for the next 190 units, assuming no loss of learning? (Round your answer to the nearest whole number.)

Time taken 65641            hours

Explanation:

Cumulative improvement factor for 200 units at 85% is 74.79

For 10 units it's 7.116

So for 190 units it is = 74.79-7.119= 67.671

So time for 190 more units is = 970(67.671)=65640.87

Another example

Consider a production. It takes 10 minutes for producing the first unit. The learning rate is 60%.

Then producing two units will take 10(first unit) + 6 (second unit) =16 minutes.

Similarly, for 4 units it will take 24.05 minutes

Cumulative improvement factor shows the time taken to produce n units for a learning rate.

(This answers the question.’ how much time will it take to take to produce the n units)

Time is taken to produce n units = time taken for the first unit * cumulative improvement factor

e.g in the above production,

Cumulative improvement factor 10 units for a learning rate of 60% = 3.813

time taken to produce to produce 10 units = 10 * 3.813= 38.13 minutes

c. How much time would it take to make the 1,000th unit? (Round your answer to the nearest whole number.)

Time took         192 hours

Explanation:

Unit improvement factor for 1000th unit at 85% learning rate is 0.1980

Time taken to produce 1000th unit= 970(0.1980) =192.06

Another example

Unit improvement factor

Consider a production. It takes 1 minute for producing first unit. The learning rate is 60%.

Then the second unit will take 0.6% of the time taken by the first unit.

The 4th unit will take 0.36 % of the time taken by the first unit

This percent is expressed as unit improvement factor.

Time is taken to produce nth unit= time taken for first unit * unit improvement factor

E.g. Unit improvement factor for 4 units at learning rate 80% is 0.6400 (from table)

Time taken to produce 4th unit= 1* 0.6400 = 0.64 minutes

This answers the question.’ how much time will it take to take to produce the nth unit)

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