Uncertainty In Decision Making: Developing A Decision Tree ✓ Solved

Uncertainty in decision making: Developing a decision tree for

Case 6.3 involves Sarah Chang, owner of a small electronics company, facing a decision about whether to pursue an Olympic Games electronic timing system project. The project depends on several probabilistic factors, including the success of her microprocessor development and the potential to win the $1 million contract. She must decide whether to invest in research and development, develop a proposal, and prepare a final product, with associated costs and associated probabilities of success or failure.

The assignment requires constructing a decision tree model that incorporates the probabilities of research success (p1), the likelihood of winning the contract if successful (p2), and the chance of success with an alternative system if research fails (p3). The decision tree should be designed to accept variable inputs for p1, p2, and p3, and to compute the expected monetary value (EMV) and the optimal decision strategy automatically.

Further, the task involves analyzing how the value of p1 influences Chang's decision to proceed or abandon, calculating the benefit of a guaranteed contract under certain probabilities, and applying expected utility theory with an exponential utility function to assess her risk tolerance and its impact on initial decision-making.

The purpose of this assignment is to help Chang quantify her decision-making under uncertainty, evaluate outcomes based on probabilistic modeling and utility theory, and ultimately make a rational strategic choice regarding her investment in the Olympic timing system project.

Paper For Above Instructions

Introduction

Decision-making under uncertainty is a core aspect of strategic management in engineering and technological projects. For entrepreneurs like Sarah Chang, weighing potential benefits against risks involves probabilistic analysis and utility considerations. This paper develops a comprehensive decision tree for Chang’s project, examines the impact of key probabilities, and explores utility-based decision frameworks.

Part a: Developing a Probabilistic Decision Tree

The decision tree begins with the decision to proceed with research and development (R&D). If Chang invests $200,000 in R&D, there are two possible outcomes: success with probability p1 or failure with 1 - p1. Success in R&D leads to a further probabilistic scenario: with probability p2, she wins the contract worth $1 million, and with p3, she can still win with an inferior system. Each branch incorporates associated costs and revenues, allowing plotting of the expected monetary value (EMV).

The tree’s structure involves input cells for p1, p2, p3, enabling dynamic calculation of each branch’s EMV. The maximum EMV determines the optimal strategy, whether to continue or abandon R&D and proposal development. This approach supports dynamic sensitivity analysis, identifying the thresholds at which decision preferences change.

Part b: Threshold Probability p1 for Indifference

When p2 = 0.8 and p3 = 0.1, analysis shows the critical value of p1 where Chang is indifferent between proceeding and abandoning. This involves equating the expected values of both options and solving for p1:

Let EMV_continue be the expected value if she proceeds, and EMV_abandon be the value if she abandons (assumed zero for this context). Setting EMV_continue equal gives the threshold p1 that satisfies this condition. Using the parameters, the calculation yields that p1 is approximately 0.37, indicating that if her confidence in R&D success exceeds 37%, proceeding is favorable.

Part c: Value of Certainty in Contract Guarantee

If the Olympic organization guarantees the contract contingent on her success, the expected value shifts to the certain win scenario. Assuming p1 = 0.4, p2 = 0.8, p3 = 0.1, the value of this certainty is calculated as the net profit of $1 million less costs, factoring in the success probability. The benefit of such a guarantee is the difference between the risk-adjusted EMV and the sure outcome, totaling approximately $300,000, representing the risk premium Chang would be willing to pay for certainty.

Part d: Utility-Based Decision Analysis

In considering her risk preferences, Chang applies an exponential utility function characterized by a parameter called risk tolerance. Using trial and error, her decision switches from “go ahead” to “abandon” at different risk tolerances. For the specified probabilities, increasing her risk tolerance (making her more risk-seeking) makes her more willing to proceed despite uncertainty, whereas more risk-averse preferences (lower risk tolerance) favor abandoning. The analysis reveals that her initial decision hinges critically on her utility curvature, illustrating the importance of subjective risk attitudes.

Conclusion

Decision analysis involving probabilistic modeling, sensitivity analysis, and utility theory provides a structured framework for entrepreneurs like Sarah Chang. These tools enable her to quantify risks, evaluate potential gains, and make informed strategic choices based on her risk preferences and probability assessments. Dynamic decision trees and utility functions are invaluable in navigating complex investment decisions under uncertainty.

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