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 33 %.

Such a total shutdown would cost the company approximately $450,000.He estimates the "unique-event" risk for any of the suppliers to be 55 %.

Assuming that the marginal cost of managing an additional supplier is $15,500 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.

Which one has the best EMV

Answer 1

The probability of disruption in case of 1,2 or 3 suppliers = Probability of super event + (1-probability of super event) * Probability of unique event risk

One supplier, P1 = 0.33 + (1-0.33) * 0.55 = 0.6985

Two supplier , P2 = 0.33 + (1-0.33) * 0.55^2 = 0.532675

Three supplier , P3 = 0.33 + (1-0.33) * 0.55^3 = 0.44147

EMV 1 supplier = Probability of no disrupiton * Total cost of managing supplier + Probability of disruption * (Total cost of managing supplier + Total cost of risk)

Total cost of managing supplier 1 supplier = 15500 , | 2 suppliers = 15500*2 = 31000 | 3 suppliers = 15500*3 = 46500

= (1-P1) * 15500 + P1 * (15500 + 450000) =0.3015*15500 + 0.6985* 465500 = $ 329825

EMV 2 suppliers =  (1-P2) * 31000 + P2 * (31000 + 450000) = $ 270704

EMV 3 suppliers =  (1-P3) * 46500 + P3 * (46500+ 450000) = $ 245162

We can go with three supplier as it is least cost.