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請問一題 learning curve 的計算

今天在做練習的時候

有一題一模一樣的題目, 在 Gleim and Hock 的答案不一樣

讓我很困惑 不知有沒有高手可以幫我解答一下

Q.

A learning curve of 80% assumes that direct labor costs are reduced by 20% for each doubling of output. What is the cost of the sixteenth unit produced as an approximate percentage of thefirst unit produced?

a. 51%

b. 32%

c. 40%

d.64%

Hock's answer: c

-> In a learning curve situation in which the labor costs are reduced by 20% each time that production is doubles, this means that if the first unit requires 100% of the labor cost, the second unit will require only 80% of the labor. The 4th unit will require only 80% of the 80%, or 64%. the eighthunit will require 80% of 64%, or 51%. The 16th unit will require 80% of 51%, or 41% of the original direct labor cost.

Gleim's answer: B

-> With an 80% learning curve, the average cost after 8 units is 51.2% of the cost of the first unit (100%x80%x80%x80%). After 16 units, the average cost is 40.96% (51.2%x80%). Thus, the average cost of units in the last batch (units 9 through 16)must have been 30.72%. (40.96%x2-51.2%)

正好刚考完part1还有些印象,hock用的是Incremental Unit-Time Learning Model 而gleim用的是Cumulative Average-Time Learning Model

There are two learning-curve models:

Cumulative Average-Time Learning Model - evaluates the average time per unit required to produce a given number of units

80% learning curve, and if the time required to build the first automobile is 10 hrs, then the total time required to manufacture the first 2 autos will be 80% * 10 * 2=16 hrs, or an average of 8 hrs for each automobile for first 2 autos.

Incremental Unit-Time Learning Model - evaluates the time needed to produce the last unit in a quantity of units.

80% learning curve rate and requires 10 hours to build the first automobile. The time required to manufacture the second auto will be 80% *10=8 hrs. Thus, the total time required to produce first 2 autos is 10+ 8=18 hrs. And the average time per unit will be 18 ÷ 2=9 hrs.

这个题并没有确切指出用哪种model。

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