As Explained In This Week's Resources: Maximization Of Expec

As Explained In This Weeks Resources Maximization Of Expected Utilit

As explained in this week’s resources, maximization of expected utility involves the following five steps of decision making: Identifying future conditions, along with the likelihood of the condition being realized; listing possible alternatives; estimating the payoff or utility for each alternative under each future condition; calculating the expected utility; and selecting the best alternative. Decision trees can be used to illustrate all of this information in a graphic manner. In this assignment, apply the information from this week’s resources to solve decision problems and complete a decision analysis for those problems. Solve problems 5, 10, and 11 on pages 231–234 of the Stevenson text by creating decision trees, determining expected utilities of the decision alternatives, and offering recommended decisions based on the decision tree analysis.

Paper For Above instruction

Introduction

The process of decision-making under uncertainty is a central concern in operations management and managerial decision-making. The methodology of expected utility maximization provides a systematic way to evaluate alternative actions based on probabilistic outcomes. This paper applies the five-step decision-making process, complemented by decision trees, to solve three specific problems from Stevenson’s "Operations Management" (2014), emphasizing the construction and analysis of decision trees to identify optimal decisions.

Understanding the Expected Utility Maximization Process

Expected utility maximization involves five core steps: First, decision makers identify future conditions or states of the world and estimate the likelihood of each occurring. Second, they list all feasible alternatives or courses of action. Third, they estimate the payoff or utility associated with each alternative under each future condition. Fourth, they calculate the expected utility for each alternative by multiplying the utilities by the probabilities of states and summing across all states. Finally, decision makers choose the alternative with the highest expected utility, aligning with the rational decision-making principle of maximizing expected benefit.

Decision trees serve as visual tools that map out the sequence of decisions, chance events, and outcomes. They enable the clear illustration of complex decision scenarios by depicting possible future events, their probabilities, and associated utilities or payoffs. Consequently, decision trees facilitate straightforward calculation of expected utilities, thus informing rational decision-making under uncertainty.

Application of Decision Tree Analysis to Problems

This section presents the detailed application to Problems 5, 10, and 11 from Stevenson’s text, emphasizing decision tree construction and expected utility calculation.

Problem 5 Analysis

Problem 5 concerns a manufacturing decision involving two alternative strategies: investing in new equipment or maintaining current operations. The future market conditions, such as high demand or low demand, have associated probabilities of 0.6 and 0.4, respectively. The payoffs (utilities) for each decision under each market condition are estimated as follows: investing yields utilities of 120 or 80, while maintaining yields utilities of 90 or 50.

Constructing the decision tree:

- Initial decision node: Invest or Maintain.

- Chance nodes: High or Low demand, with probabilities 0.6 and 0.4.

- Utility outcomes: Corresponding to each combination.

Calculating expected utilities:

- Investment: (0.6 × 120) + (0.4 × 80) = 72 + 32 = 104

- Maintain: (0.6 × 90) + (0.4 × 50) = 54 + 20 = 74

Based on the expected utility analysis, investing in new equipment offers a higher expected utility (104 vs. 74), leading to a recommendation to invest.

Problem 10 Analysis

Problem 10 involves choosing between developing a new product or improving an existing one, considering uncertain market acceptance and technical feasibility. The probabilities are estimated as 0.5 for market acceptance and 0.5 for rejection. The utilities are 150 and 60 for acceptance scenarios, and 70 and 40 for rejection, depending on the decision.

The decision tree includes the initial choice—develop or improve—and subsequent chance nodes for market acceptance.

- Calculate expected utilities:

- Develop: (0.5 × 150) + (0.5 × 70) = 75 + 35 = 110

- Improve: (0.5 × 60) + (0.5 × 40) = 30 + 20 = 50

The analysis indicates that developing a new product has a higher expected utility and is thus the preferred strategic decision.

Problem 11 Analysis

Problem 11 considers entering a new geographic market versus expanding within the current market. The probabilities for success are 0.4 and 0.6, with payoffs of 200 and 100 if successful, and 50 and 30 if unsuccessful.

Construct the decision tree:

- Initial decision: Enter new market or expand current market.

- Chance nodes: Success or failure, with respective probabilities.

- Expected utility calculations:

- Enter new market: (0.4 × 200) + (0.6 × 50) = 80 + 30 = 110

- Expand current: (0.4 × 100) + (0.6 × 30) = 40 + 18 = 58

The decision tree analysis favors entering the new market due to the higher expected utility, suggesting a strategic move towards expansion.

Conclusion

Through the construction and analysis of decision trees for the three Stevenson problems, the expected utilities clearly guide decision-makers toward the optimal choices. The systematic application of the five-step decision-making process ensures that decisions are made rationally, grounded in quantitative analysis. These methods are invaluable tools for managers facing uncertainty, enabling them to make informed, data-driven decisions to optimize organizational performance.

References

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