Question

Phillip? Witt, president of Witt Input? Devices, wishes to create a portfolio of local suppliers for his new line of keyboards. As the suppliers all reside in a location prone to? hurricanes, tornadoes,? flooding, and? earthquakes, Phillip believes that the probability in any year of a? "super-event" that might shut down all suppliers at the same time at least 2 weeks is 2?%.

Such a total shutdown would cost the company approximately

?$450,000.

He estimates the? "unique-event" risk for any of the suppliers to be 5?%.

Assuming that the marginal cost of managing an additional supplier is

?$16,000

per? year, how many suppliers should Witt Input Devices? use? Assume that up to three nearly identical local suppliers are available.

Find the EMV for alternatives using? 1, 2, or 3 suppliers.

?EMV(1)=? EMV(2)= EMV(3)=

?(Enter your response rounded to the nearest whole? number.)

Answer 1

All suppliers would be disrupted simultaneously if the super event occurs or the super event does not occur however the unique event happens to all the suppliers. As we know that the probability of a particular supplier being disrupted is independent of anybody else the probability of “n” number of suppliers being disrupted is given by the formula:-

Where S = Probability of Super Event and U = Probability of Unique Event

Hence , We find

P(1) = 0.02 + (1 - 0.02) * 0.04 = 0.0592 = 5.92 %

P(2) = 0.02 + (1 - 0.02) * 0.04^2 = 0.0215 = 2.15 %

P(3) = 0.02 + (1 - 0.02) * 0.04^3 = 0.0200 = 2 %

Using decision tree we get

Therefore ,

EMV (1) = 16,000 * 0.9408 + 466000 * 0.0592 = $ 42, 640

EMV (2) = 32000 * 0.9785 + 482000 * 0.0215 = $ 41,675

EMV (3) = 48000 * 0.98 + 478000 * 0.02 = $ 56, 600

Hence, the company must go with two suppliers.

PS:-Please rate the answer if you find the answer helpful and comment in case of clarifications.