Still concerned about the risk in Problem S112 suppose that

Still concerned about the risk in Problem S11.2, suppose that Phillip is willing to use one local supplier and up to two more located in other territories within the country. This would reduce the probability of a “super-event” to .05%, but due to increased distance the annual costs for managing each of the distant suppliers would be $25,000 (still $15,000 for the local supplier). Assuming that the local supplier would be the first one chosen, how many suppliers should Witt Input Devices use now?

Solution

Data as per problem S11.2

Probability of Super-event, S = 0.5%

Probability of Unique event, U = 5%

Loss due to total shutdown, L = $ 400,000

Cost of local supplier, C1 = 15000

Marginal cost of each additional distant supplier, C2 = 25000

Expected cost with only 1 local supplier = (S + (1-S)*U¹)*L + C1

= (0.5% + (1-0.5%)*5%¹)*400000 + 15000

= $ 36,900

Expected cost with 1 local supplier and 1 distant supplier = (S + (1-S)*U²)*L + C1 + C2

= (0.5% + (1-0.5%)*5%²)*400000 + 15000 + 25000

= $ 42,995

Expected cost with 1 local supplier and 2 distant suppliers = (S + (1-S)*U³)*L + C1 + 2*C2

= (0.5% + (1-0.5%)*5%³)*400000 + 15000 + 2*25000

= $ 67,050

Total expected cost of only 1 local supplier is the lowest.

Therefore, Witt Input Devices should use only 1 local supplier.