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Jon Jackson Manufacturing is searching for suppliers for its new line of equipment. Jon has narrowed his choices to two sets of suppliers. Believing in diversification of risk, Jon would select two suppliers under each choice. However, he is still concerned about the risk of both suppliers failing at the same time. The “San Francisco option” uses both suppliers in San Francisco. Both are stable, reliable, and profitable firms, so Jon calculates the “unique-event” risk for either of them to be 0.5%. However, because San Francisco is in an earthquake zone, he estimates the probability of an event that would knock out both suppliers to be 2%. The “North American option” uses one supplier in Canada and another in Mexico. These are upstart firms; John calculates the “unique-event” risk for either of them to be 10%. But he estimates the “super-event” probability that would knock out both of these suppliers to be only 0.1%. Purchasing costs would be $500,000 per year using the San Francisco option and$510,000 per year using the North American option. A total disruption would create an annualized loss of $800,000. Which option seems best? ## Step-by-Step ## Report Solution ## Verified Solution Using Equation (S11-1), the probability of a total disruption (i.e., the probability of incurring the$800,000 loss) equals:

P(n) = S + (1 – S)$U^n$                        (S11-1)
San Francisco option: 0.02 + (1 – 0.02)$0.005^2$ = 0.02 + 0.0000245 = 0.0200245, or 2.00245%
North American option: 0.001 + (1 – 0.001)$0.1^2$ = 0.001 + 0.0099 = 0.01099, or 1.099%
Total annual expected costs = Annual purchasing costs + Expected annualized disruption costs
San Francisco option: $500,000 +$800,000(0.0200245) = $500,000 +$16,020 = $516,020 North American option:$510,000 + $800,000(0.01099) =$510,000 + $8,792 =$518,792
In this case, the San Francisco option appears to be slightly cheaper.