2 Indexes and Sizing Models Padre works for a trade magazine that publishes list

Question

2 Indexes and Sizing Models Padre works for a trade magazine that publishes lists of power-sizing exponents (PSE) that reflect economies of scale for developing engineering esti- mates of unable to find any published data on the VMIC machine and wants to list its PSE value in his next issue. Given the following data calculate the PSE value that Padre should publish. (Note: The VMIC- 100 can handle twice the volume of a VMIC-50.) various types of equipment. Padre has been Cost of VMIC-100 today $250,000 Cost of VMIC-50 5 years ago $95,000 VMIC equipment index today = 350 VMIC equipment index 5 years ago = 235 3 The Learning Curve The Mountain "M bike workshop can only sell exactly one customized bike every month, because the city only agrees to issue one plate for this type of modified bike per month. So they make exactly one every month. During the first year of business (12 bikes was made), on average they can make a bike in 100 labor hours. During the second year of business (another 12 was made), they improved a lot and were able to on average make the same bike in 75 labor hours. Unfortunately, we do not have records on how many labor hours they spent to make the bike in each month of the 24 months. Please estimate the learning-curve percentage/rate for their bike production. You may make any assumptions as you need, but please justify them so that they sound reasonable to other engineers in the room.

Explanation / Answer

Question 2

Cost of VMIC-100 today = $250,000

Cost of VMIC-50 5 years ago = $95,000

VMIC equipment index today = 350

VMIC equipment index 5 years ago = 235

Calculate the power-sizing exponents (PSE) -

Cost of VMIC-100 today = Cost of VMIC-50 5 years ago * (100/50)PSE * (Index today/Index 5 years ago)

$250,000 = $95,000 * (2)PSE * (350/235)

$250,000 = $95,000 * 1.49 * (2)PSE

$250,000 = $141,550 * (2)PSE

$250,000/$141,550 = (2)PSE

(2)PSE = 1.77

Taking log both sides

PSE log 2 = log 1.77

PSE = log1.77/log 2

PSE = 0.248/0.301 = 0.82

The PSE for VMIC machine is 0.82

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