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## Q. 11.S1

HOW MANY SUPPLIERS ARE BEST FOR MANAGING RISK? Xiaotian Geng, president of Shanghai Manufacturing Corp., wants to create a portfolio of suppliers for the motors used in her company’s products that will represent a reasonable balance between costs and risks. While she knows that the single-supplier approach has many potential benefits with respect to quality management and just-in-time production, she also worries about the risk of fires, natural disasters, or other catastrophes at supplier plants disrupting her firm’s performance. Based on historical data and climate and geological forecasts, Xiaotian estimates the probability of a “super-event” that would negatively impact all suppliers simultaneously to be 0.5% (i.e., probability = 0.005) during the supply cycle. She further estimates the “unique-event” risk for any of the potential suppliers to be 4% (probability = .04). Assuming that the marginal cost of managing an additional supplier is $10,000, and the financial loss incurred if a disaster caused all suppliers to be down simultaneously is$10,000,000, how many suppliers should Xiaotian use? Assume that up to three nearly identical suppliers are available.
APPROACH $\blacktriangleright$ Use of a decision tree seems appropriate, as Shanghai Manufacturing Corp. has the basic data: a choice of decisions, probabilities, and payoffs (costs).

## Verified Solution

SOLUTION $\blacktriangleright$ We draw a decision tree (Figure S11.1) with a branch for each of the three decisions (one, two, or three suppliers), assign the respective probabilities [using Equation (S11-1)] and payoffs for each branch, and then compute the respective expected monetary values (EMVs). The EMVs have been identified at each step of the decision tree.

P(n) = S + (1 – S)$U^n$              (S11-1)

Using Equation (S11-1), the probability of a total disruption equals:
One supplier: 0.005 + (1 – 0.005)0.04 = 0.005 + 0.0398 = 0.044800, or 4.4800%
Two suppliers: 0.005 + (1 – 0.005)$0.04^2$ = 0.005 + 0.001592 = 0.006592, or 0.6592%
Three suppliers: 0.005 + (1 – 0.005)$0.04^3$ = 0.005 + 0.000064 = 0.005064, or 0.5064%

INSIGHT $\blacktriangleright$ Even with significant supplier management costs and unlikely probabilities of disaster, a large enough financial loss incurred during a total supplier shutdown will suggest that multiple suppliers may be needed.

LEARNING EXERCISE $\blacktriangleright$ Suppose that the probability of a super-event increases to 50%. How many suppliers are needed now? [Answer: 2.] Using the 50% probability of a super-event, suppose that the financial loss of a complete supplier shutdown drops to \$500,000. Now how many suppliers are needed? [Answer: 1.]

RELATED PROBLEMS $\blacktriangleright$ S11.1, S11.2, S11.3, S11.4, S11.5