Purpose To Assess Your Ability To Make Decisions Under Uncer

Purposeto Assess Your Ability To Make Decisions Under Uncertainty An

Purpose To assess your ability to: · make decisions under uncertainty and risk using decision trees · apply the utility theory to make a decision Action Items · Complete the following case making certain that you address all the questions in the case. · Case Study: Waldo Books . If you have any difficulty completing the case, you should work through the problems at the end of Chapter 3 in Quantitative Analysis for practice. · Place the problem in an Excel worksheet. Submission Instructions · Complete and submit this assignment per your professor's instructions. Grading Criteria · Documentation : thorough documentation with clarity of thought and process: 0 – 2 points · Problem solving and analysis: · Solution is accurate (0 – 1 point) · Calculations are accurate and valid (0 – 1 point) · Responses are detailed and accurate (0 – 1 point) Purpose To assess your ability to use decision trees and probability to identify various possible solutions.

Paper For Above instruction

This paper addresses the core concepts of decision-making under uncertainty, focusing on the application of decision trees, utility theory, and risk analysis through a set of practical case studies. The overarching goal is to examine how individuals and organizations can make optimal decisions in conditions of incomplete information, considering probabilities and potential payoffs. Two prominent problems are explored: an investment decision involving market risks and returns, and a retail inventory problem confronting Waldo Books. These cases illustrate fundamental decision-making principles and quantitative methods used in modern management science.

Decision-Making Under Uncertainty: An Introduction

Decision-making under uncertainty involves selecting the best course of action when outcomes are uncertain and probabilistic. Traditional decision models include decision trees, expected monetary value (EMV), expected opportunity loss (EOL), and criteria such as maximax, maximin, equal likelihood, and minimax regret. Complementing these models, utility theory helps account for risk preferences, enabling a decision maker to incorporate subjective attitudes towards risk into the analysis. This integrative approach combines quantitative analysis with behavioral insights, providing more comprehensive decision support.

Case Study 1: Investment Decision for Allen Young

The first case involves Allen Young’s investment options between the stock market and a certificate of deposit (CD) over a year. The decision hinges on market conditions categorized as good, fair, and bad, each associated with specific returns and probabilities. The analysis aims to determine the optimal choice using decision trees and probability-weighted expected returns. Additionally, the scenario extends to assessing the worth of predictive market newsletters that could improve decision accuracy.

Part A: Developing a Decision Table

To model Allen’s decision problem, a decision tree or decision table can be created, comparing the initial choices—invest in stocks or CDs—and their respective outcomes under different market conditions. The key parameters include the investment amount, possible rates of return, and their associated probabilities:

• Stock investment: Initial amount of $10,000
• Favorite returns: Good market (14%), Fair market (8%), Bad market (0%)
• Probabilities: Good (0.4), Fair (0.4), Bad (0.2)
• CD investment: Fixed return of 9% (less uncertain)

The decision table aggregates these data, illustrating the expected payoffs for each decision in different market conditions. Calculations involve multiplying each return by its probability to derive the expected value (EV) for each choice, leading to a rational decision based on maximizing expected return.

Part B: Optimal Decision

Analyzing the expected values, the decision with the highest EV reflects the optimal choice. If, for example, the EV of investing in stocks exceeds that of investing in a CD, then stock investment is advisable. The calculations incorporate the weighted risks, ensuring that the strategy aligns with the decision maker’s risk appetite and financial goals.

Case Study 2: The Value of Market Prediction and Utility

The second problem extends the analysis to estimating the maximum price Allen should pay for a newsletter that provides market predictions. The newsletter’s accuracy influences the expected payoffs through better-informed decision-making. The question involves calculating the maximum worth of this predictive tool by comparing the expected monetary value with and without the newsletter, considering the potential improvement in decision quality.

Part A: Maximum Willingness to Pay

This calculation involves the concept of expected value with perfect or imperfect information. The value of perfect information (VPI) quantifies how much Allen would pay to eliminate uncertainty. By modeling the decision tree with and without the newsletter, alongside the corresponding probabilities, the maximum premium Allen would accept indicates the worth of the predicted insights.

Part B: Effect of Updated Market Returns

Changing the expected return in a good market from 14% to 11% impacts the valuation of the newsletter. The revised expected values are recalculated, and the maximum willingness to pay is adjusted accordingly. This dynamic analysis highlights how risk-return trade-offs influence decision-making valuations and the importance of accurate probability estimates.

Practical Applications: Inventory Management at Waldo Books

Transitioning from individual investment decisions, this case studies Waldo Books' inventory management problem. The store must determine optimal order quantity considering demand scenarios with assigned probabilities. A decision criterion framework—maximax, maximin, equal likelihood, minimax regret, and the criterion of realism—guides the selection process based on different risk preferences.

Scenario Analysis using Decision Criteria

Waldo’s demand scenarios: 50, 100, 150, or 200 books, with their associated costs and revenues. Using the decision criteria:

• Maximax: choosing the maximum possible payoff
• Maximin: choosing the decision with the best worst-case payoff
• Equal likelihood: averaging payoffs assuming equal probability
• Minimax regret: minimizing the maximum regret across scenarios
• Realism with _=0.7: blending optimism and pessimism with weighted criteria

Expected monetary value (EMV) analysis considers demand probabilities (20%, 35%, 25%, 20%), providing optimal order quantities based on expected profits. Moreover, calculations of opportunity costs and willingness to pay for additional market insights further enhance decision quality.

Conclusion: Integrating Quantitative Decision Tools

This comprehensive analysis demonstrates the importance of decision trees, utility theory, and risk analysis in managerial decision-making. Quantitative models assist in balancing risks and returns, optimizing resource allocation, and assessing the value of information. Critical to these processes is understanding probability distributions, decision criteria, and subjective preferences, which collectively serve as powerful tools for navigating uncertainty in complex environments.

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