How Many Suppliers Are Best For Managing Risk ? Xiaotian Geng, president of Shan

Question

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 hasmany 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 forecast, Xioatian 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 circle. She further estimates the “unique-event”

risk for any of the potential 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 , use of a decision tree seems appropriate, as Shanghai Manufacturing Corp. Has the

basis data: a choice of decisions , probabilities, and payoffs(costs).

solution: we draw a decision tree with a branch for each of the three decisions (one, two, three

suppliers,) assign the respective expected 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.

using equation , 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+0.006593, or 0.5064%

three suppliers: 0.005 + (1- 0.005)0.04 ^3=0.005+ 0.000064=0.005064, or 0.5064%

insight : 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.

Question: Suppose that the probability of a super-event increase to 50%. How many suppliers are

needed now? Using the 50% probability of a super-event , suppose that the financial ;loss of a

complete supplier shutdown drop to $500,000. Now how many suppliers are needed?

Explanation / Answer

1)

Probability of super-event, S = 50% = 0.5

Probability of unique-event, U = 4% = 0.04

Cost of managing each supplier, C = $ 10,000

Total disruption loss, L = $ 10,000,000

EMV with n suppliers = (S + (1-S)*Un)*L + n*C

EMV with one supplier = (0.5 + (1-0.5)*0.04)*10000000 + 1*10000 = $ 5,210,000

EMV with two suppliers = (0.5 + (1-0.5)*0.042)*10000000 + 2*10000 = $ 5,028,000

EMV with three suppliers = (0.5 + (1-0.5)*0.043)*10000000 + 3*10000 = $ 5,030,320

We see that the using two suppliers yields the lowest EMV. Therefore, two suppliers are needed.

2)

Total disruption loss, L = $ 500,000

EMV with one supplier = (0.5 + (1-0.5)*0.04)*500000 + 1*10000 = $ 270,000

EMV with two suppliers = (0.5 + (1-0.5)*0.042)*500000 + 2*10000 = $ 270,400

EMV with three suppliers = (0.5 + (1-0.5)*0.043)*500000 + 3*10000 = $ 280,016

We see that the using one supplier yields the lowest EMV. Therefore, one supplier is needed.

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