In the case "NORTH STAR CONCERT", Lucinda Ramirez is getting ready to manufacture T-shirts for a rock concert. The main concern is figuring out the best quantity of shirts to produce for maximizing profits. This decision falls under the category of "Decision under uncertainty" as no probabilities regarding potential outcomes are given in the case, and they cannot be deduced from the provided information.
To assist in making a decision, I require a decision table incorporating potential states of nature and their corresponding pay-offs. The key factors influencing the central problem include stadium attendance, percentage of attendees purchasing shirts, possible cancellation of the North Star band's rock concert, Lucinda's risk attitude, and decision-making criteria. As per Lucinda's estimates, there is a low likelihood that the 100,000-capacity stadium will reach 90% capacity. Conversely, there is a high probability of it bei
...ng only 50% full. Additionally, she wishes to consider the scenario where the stadium is merely 25% full due to inclement weather.
Thus, the potential attendance of the stadium could vary from 25,000 to 90,000, resulting in possible states of nature of 2,500, 5,000, and 9,000, considering that an average of 10% of attendees purchases shirts. Lucinda's concern about the rock band canceling the show adds another possible state of nature. Therefore, the decision table would include four potential states of nature: 2,500, 5,000, 9,000 (number of people purchasing shirts from Lucinda). The critical aspect lies in selecting the criteria for decision-making amidst uncertainty.
The text highlights five criteria used for decision-making, which include Laplace, pessimism, optimism, Hurwicz criterion, and Savage criterion. However, the Laplace criterion is not applicable in this case due to varying probabilities associated with eac
state of nature. The case facts indicate that Lucinda does not demonstrate complete optimism or pessimism regarding pay-offs. Additionally, the Savage criteria are not appropriate as Lucinda acknowledges the possibility of business losses as a risk. Hence, the only suitable criteria for the given scenario are the Hurwitz criteria with an assumption that the coefficient of optimism is equal to 0.
8. The coefficient of optimism is high because Lucinder is optimistic about the pay-offs and concerned only about the show's cancellation. According to the decision table below, ordering 4000 shirts will yield the maximum monetary value. The biggest risk factor is the cancellation of a rock band concert. By analyzing various factors and using the Hurwitz criteria, it is recommended that Lucinder orders 4000 shirts for better profits.
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