Readcase 63 Electronic Timing System For Olympics Pages 27

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Read Case 6.3: Electronic Timing System for Olympics on pages of the textbook. For this assignment, you will assess and use the correct support tool to develop a decision tree as described in Part “a” of Case 6.3. Analyze and apply the best decision making process to provide answers and brief explanations for parts “a”, “b”, “c”, and “d”. The answers and explanations can be placed in the same Excel document as the decision tree.

a. Develop a decision tree that can be used to solve Chang’s problem. You can assume in this part of the problem that she is using EMV (of her net profit) as a decision criterion. Build the tree so that she can enter any values for p1, p2, and p3 (in input cells) and automatically see her optimal EMV and optimal strategy from the tree.

b. If p2 = 0.8 and p3 = 0.1, what value of p1 makes Chang indifferent between abandoning the project and going ahead with it? Calculate this value.

c. How much would Chang benefit if she knew for certain that the Olympic organization would guarantee her the contract? (This guarantee would be in force only if she were successful in developing the product.) Assume p1 = 0.4, p2 = 0.8, and p3 = 0.1. Show calculations.

d. Suppose now that this is a relatively big project for Chang. Therefore, she decides to use expected utility as her criterion, with an exponential utility function. Using some trial and error, see which risk tolerance changes her initial decision from “go ahead” to “abandon” when p1 = 0.4, p2 = 0.8, and p3 = 0.1. In your Excel document,:

1. Develop a decision tree using the most appropriate support tool as described in Part a.
2. Calculate the value of p1 as described in Part b.
3. Calculate the possible profit using the most appropriate support tool as described in Part c.
4. Calculate risk tolerance as described in Part d.

Paper For Above instruction

The case of the electronic timing system for the Olympics presents a complex decision-making problem that involves assessing potential profits, probabilities, and risk preferences. Utilizing decision trees and advanced utility analysis can guide Chang in making informed choices about her project. This paper comprehensively examines the decision-making steps outlined in the case, including the development of a decision tree for maximizing expected monetary value (EMV), determining critical probabilities, and applying utility-based approaches to account for risk preferences.

Development of a Decision Tree for EMV Optimization

In addressing part “a,” the first step involves constructing a decision tree that encapsulates all possible choices and uncertain outcomes relevant to Chang’s project. The decision node represents the initial choice to pursue or abandon the project. Subsequent chance nodes embody the probabilities p1, p2, and p3 which characterize the likelihood of success, partial success, or failure respectively. The decision tree articulates potential profits associated with each outcome, allowing Chang to compute the EMV for each strategy based on these probabilities.

The decision tree's utility lies in its flexibility; it permits input of variable probabilities into designated cells (p1, p2, p3) and instantly recalculates the EMV for each decision branch. Using a support tool like Excel’s data tables or specialized decision analysis add-ins, Chang can determine the optimal strategy by selecting the branch with the highest EMV. The framework ensures that decision makers can evaluate diverse scenarios efficiently without manual recalculation for each set of probabilities.

Critical Probability Threshold for Indifference

Part “b” analyses the scenario where p2 = 0.8 and p3 = 0.1, seeking the value of p1 that makes Chang indifferent between abandoning or proceeding with the project. Indifference occurs when the expected monetary values of both options are equal, leading to the equation: EMV(continue) = EMV(abandon). Calculating this involves setting the EMV formulas equal and solving for p1. The mathematical formulation demonstrates how changes in success probabilities influence the decision boundary and informs Chang about the sensitivity of her decision to initial estimates.

Value of Certainty - Benefits of Guaranteed Contract

Part “c” evaluates the benefit Chang gains if she is assured of a guaranteed contract from the Olympic organization, assuming her initial probabilities: p1=0.4, p2=0.8, p3=0.1. This involves comparing the EMV with and without the guarantee, where the guaranteed contract assures a certain profit in the event of success. The calculation quantifies the premium Chang would be willing to pay for certainty, which directly relates to her expected gain from eliminating risk and variance associated with the project’s uncertain outcomes.

Expected Utility and Risk Tolerance

Part “d” introduces the utility-based approach, recognizing that Chang’s risk preferences significantly impact her decision. By adopting an exponential utility function, which characterizes her risk tolerance, she can determine at what level of risk aversion she would switch her choice from “go ahead” to “abandon.” This analysis involves trial-and-error adjustments of the utility function’s risk tolerance parameter and observing the resulting decision changes.

This process demonstrates the importance of individual risk preferences in complex project evaluations. The calculation entails assessing the expected utility across various risk tolerances and identifying the point where utility-based decision support favors risk-averse or risk-seeking behavior.

Conclusions

In summary, the application of decision trees and utility analysis provides a robust framework for Chang to navigate her project’s uncertainties. Constructing a dynamic decision model allows for flexible scenario testing, sensitivity analysis, and risk management. These tools enable her to quantify the value of information and risk premiums, leading to more informed and strategic decision-making in high-stakes technological projects like the Olympic electronic timing system.

References

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