Question

Phillip Witt, president of Witt Input Devices, wishes to create a portfolio of local suppliers for his new line of keyboards. As the suppliers all reside in a location prone to hurricanes, tornadoes, flooding, and earthquakes, Phillip believes that the probability in any year of a super-event that might shut down all suppliers at the same time at least 2 weeks is 4%. Such a total shutdown would cost the company approximately $520,000. He estimates the unique-event risk for any of the suppliers to be 7%. Assuming that the marginal cost of managing an additional supplier is $14, 800 per year, how many suppliers should Witt Input Devices use? Assume that up to three nearly identical local suppliers are available.

Find the EMV for alternatives using 1, 2, or 3 suppliers.
EMV(1) = $ _______ (Enter your response rounded to the nearest whole number.)
EMV(2) = $ _______ (Enter your response rounded to the nearest whole number.)
EMV(3) = $ _______ (Enter your response rounded to the nearest whole number.)
Based on the EMV value, the best choice is to use (1). _______.
a. one supplier
b. two suppliers
c. three suppliers

Answer 1

To determine the optimal number of suppliers, Phillip Witt must calculate the EMV for each scenario. The calculations for 1, 2, and 3 suppliers result in the lowest EMV when using three suppliers, thus it is the best choice to minimize potential monetary losses due to supplier-related shutdowns.

Step-by-step explanation:

Phillip Witt, president of Witt Input Devices, is evaluating the number of suppliers to use for his new line of keyboards, considering the probabilities of super-events that could shut down his suppliers and the marginal costs of managing additional suppliers. To calculate the expected monetary value (EMV) for using 1, 2, or 3 suppliers, we use the formula EMV = (Probability of shutdown × Cost of shutdown) + (Marginal cost of managing suppliers). The probability of a super-event shutting down all suppliers is 4%, and the cost incurred from such an event is $520,000. Additionally, the marginal cost of managing an additional supplier is $14,800 per year.

EMV(1) supplier: The EMV for using one supplier considers the full 4% risk of a super-event shutdown and the marginal cost of one supplier. EMV(1) = (0.04 × 520,000) + (1 × 14,800) = $34,800.

EMV(2) suppliers: With two suppliers, the risk of both being shut down is the probability of a super-event and a unique-event happening to the other (assumed to be independent). EMV(2) = (0.04 × 0.07 × 520,000) + (2 × 14,800) = $11,248.

EMV(3) suppliers: For three suppliers, we assume independence of events and calculate EMV(3) = (0.04 × 0.07 × 0.07 × 520,000) + (3 × 14,800) = $10,253.

Based on the EMV values calculated, the best choice to minimize expected losses due to supplier shutdowns would be using three suppliers (c), as it has the lowest EMV.