Question

Consider the disaster risk decision tree model given by P (n) = S + (1 - S) U^n,

where
S = the probability of a "super-event" that would disrupt all suppliers simultaneously
U = the probability of a "unique-event" that would disrupt only one supplier
L = the financial loss incurred in a supply cycle if all suppliers were disrupted and C = the marginal cost of managing a supplier
(a) Derive a formula to represent the amount that the probability of all suppliers being disrupted simultaneously, P (n), increases if the super-event probability S is doubled.
(b) Test your formula derived in part (a) by computing the amount of increase if the original S equals 1% and there are two suppliers, each with U = 4%.
(c) Using the notation from the model, determine the expected monetary value (cost) of choosing two suppliers?

Answer 1

a) The formula representing the increase in probability if the super-event probability S is doubled is P'(n) = 2S + (1 - 2S)U^n. b) The increase in probability when S is doubled for S = 1% and U = 4% is 0.0128. c) The expected monetary value of choosing two suppliers is (S + (1 - S)U^n)(L + C).

Step-by-step explanation:

a) To derive a formula representing the increase in the probability of all suppliers being disrupted simultaneously if the super-event probability S is doubled, we can compare the original probability P(n) with the probability when S is doubled, denoted as P'(n). From the given model, we have P(n) = S + (1 - S)U^n. Doubling S means the new probability becomes 2S. Plugging this into the model, we have P'(n) = 2S + (1 - 2S)U^n.

b) Given S = 1% and U = 4% for two suppliers, we can use the derived formula P'(n) = 2S + (1 - 2S)U^n to calculate the increase in probability if S is doubled. Plugging in the values, we have P'(n) = 2(0.01) + (1 - 2(0.01))(0.04)^2 = 0.02 + 0.992 = 0.0128.

c) To determine the expected monetary value (cost) of choosing two suppliers, we need to consider the financial loss incurred in a supply cycle and the marginal cost of managing a supplier. Let L be the financial loss and C be the marginal cost. The expected monetary value is given by P(n)(L + C) = (S + (1 - S)U^n)(L + C).