This document discusses decision analysis techniques for evaluating decision problems involving uncertainty. It provides an example of a real estate development company (PDC) choosing the size of a new condominium project. The key decision alternatives and uncertain future states are identified. Techniques discussed include payoff tables, decision trees, and approaches like expected value analysis that incorporate probability estimates of future states. Sensitivity analysis is also covered to determine how changes to probabilities or payoffs might impact the recommended decision.
1) The Pittsburgh Development Corporation is deciding on the size of a new luxury condominium complex with three options - small (30 units), medium (60 units), or large (90 units).
2) There is uncertainty around the demand for the condominiums which could be strong or weak. This is represented as two states of nature - strong demand or weak demand.
3) Three decision making approaches are discussed to make a decision under uncertainty when probabilities of states of nature are unknown: optimistic, conservative, and minimax regret. The optimistic approach selects the option with the highest potential payoff, conservative takes the option with the highest minimum payoff, and minimax regret minimizes maximum regret.
This document discusses various optimization techniques used in pharmaceutical development. It begins with defining optimization and providing an outline of topics to be covered, including key terms, parameters, experimental designs, applied methods, and references. Experimental designs discussed include factorial, response surface, central composite, Box-Behnken, Plackett-Burman, and Taguchi designs. Applied optimization methods include classic optimization techniques using calculus as well as statistical methods like EVOP. The objective of pharmaceutical optimization is to develop the optimal formulation while reducing costs through fewer experiments.
A decision tree is a diagram that visually represents decisions, uncertainties, and outcomes of a complex decision-making process. It breaks down a complex problem into a step-by-step process. The document provides examples of how to construct a decision tree by defining decision points and possible outcomes as branches. It also explains how to evaluate a decision tree by assigning values and probabilities to outcomes and working backwards to calculate expected values at decision points in order to determine the optimal decision.
1. The document discusses quantitative analysis and decision making methods used in management. It describes modeling approaches such as linear programming that involve representing real-world problems mathematically.
2. Key steps in problem solving and decision making are identified, including defining the problem, determining alternatives, evaluating alternatives, and choosing a solution.
3. Quantitative models allow managers to systematically evaluate alternatives using factors like costs, revenues, profits, and constraints.
The document discusses key concepts in defining and structuring decision problems. It defines the three components of a problem statement as the current state, desired state, and central objective. Decision trees and influence diagrams are presented as tools to structure choices and uncertainties. Deterministic, stochastic, and simulation models are described based on their mathematical focus. Probability is discussed in terms of frequentist, subjective, and logical interpretations, and methods for forecasting and decomposing complex probabilities are outlined. Calibration and sensitivity analysis are introduced as ways to evaluate probability estimates and assumptions.
This technical paper discusses using a 2x2 Cartesian matrix framework to aid structured decision making in project management. The framework involves identifying decision areas, analyzing them to determine attributes, then designing a 2x2 matrix with the attributes on the axes to categorize scenarios into four quadrants. Each quadrant represents a unique decision making scenario requiring an identified action. The paper provides examples of decision matrices for stakeholder management, benefit realization, and governance. It also presents a case study where a company used the framework to help achieve the technology modernization project vision of lower ownership costs through consolidating technology.
1) The Pittsburgh Development Corporation is deciding on the size of a new luxury condominium complex with three options - small (30 units), medium (60 units), or large (90 units).
2) There is uncertainty around the demand for the condominiums which could be strong or weak. This is represented as two states of nature - strong demand or weak demand.
3) Three decision making approaches are discussed to make a decision under uncertainty when probabilities of states of nature are unknown: optimistic, conservative, and minimax regret. The optimistic approach selects the option with the highest potential payoff, conservative takes the option with the highest minimum payoff, and minimax regret minimizes maximum regret.
This document discusses various optimization techniques used in pharmaceutical development. It begins with defining optimization and providing an outline of topics to be covered, including key terms, parameters, experimental designs, applied methods, and references. Experimental designs discussed include factorial, response surface, central composite, Box-Behnken, Plackett-Burman, and Taguchi designs. Applied optimization methods include classic optimization techniques using calculus as well as statistical methods like EVOP. The objective of pharmaceutical optimization is to develop the optimal formulation while reducing costs through fewer experiments.
A decision tree is a diagram that visually represents decisions, uncertainties, and outcomes of a complex decision-making process. It breaks down a complex problem into a step-by-step process. The document provides examples of how to construct a decision tree by defining decision points and possible outcomes as branches. It also explains how to evaluate a decision tree by assigning values and probabilities to outcomes and working backwards to calculate expected values at decision points in order to determine the optimal decision.
1. The document discusses quantitative analysis and decision making methods used in management. It describes modeling approaches such as linear programming that involve representing real-world problems mathematically.
2. Key steps in problem solving and decision making are identified, including defining the problem, determining alternatives, evaluating alternatives, and choosing a solution.
3. Quantitative models allow managers to systematically evaluate alternatives using factors like costs, revenues, profits, and constraints.
The document discusses key concepts in defining and structuring decision problems. It defines the three components of a problem statement as the current state, desired state, and central objective. Decision trees and influence diagrams are presented as tools to structure choices and uncertainties. Deterministic, stochastic, and simulation models are described based on their mathematical focus. Probability is discussed in terms of frequentist, subjective, and logical interpretations, and methods for forecasting and decomposing complex probabilities are outlined. Calibration and sensitivity analysis are introduced as ways to evaluate probability estimates and assumptions.
This technical paper discusses using a 2x2 Cartesian matrix framework to aid structured decision making in project management. The framework involves identifying decision areas, analyzing them to determine attributes, then designing a 2x2 matrix with the attributes on the axes to categorize scenarios into four quadrants. Each quadrant represents a unique decision making scenario requiring an identified action. The paper provides examples of decision matrices for stakeholder management, benefit realization, and governance. It also presents a case study where a company used the framework to help achieve the technology modernization project vision of lower ownership costs through consolidating technology.
This technical paper discusses using a 2x2 Cartesian matrix framework to aid structured decision making in project management. The framework involves identifying decision areas, analyzing them to determine attributes, then designing a 2x2 matrix with the attributes on the axes to categorize scenarios into four quadrants. Each quadrant represents a unique decision making scenario requiring an identified action. The paper provides examples of decision matrices for stakeholder management, benefit realization, and governance. It also presents a case study where a company used the framework to help make decisions for a technology modernization project aimed at lowering costs while ensuring stakeholder engagement and benefits realization.
This document provides an overview of decision theory and decision making under uncertainty. It discusses structuring decision problems using decision trees and different types of decision making environments including uncertainty, risk, and certainty. It then covers various decision making criteria for uncertainty including optimistic, conservative, minimax regret, equally likely, and criterion of realism approaches. Expected values of perfect and sample information are also introduced. Examples are provided to illustrate key concepts such as calculating expected values and values of information.
Decision making models help organizations and individuals make choices when facing uncertainty. There are different types of decision problems including decisions under certainty, uncertainty, probabilistic, and non-probabilistic situations. Key steps in decision making include identifying alternatives and possible outcomes, constructing payoff tables, and applying decision rules like maximizing, minimizing, or expected value to determine the optimal choice. Obtaining additional information can potentially improve decisions by reducing uncertainty and increasing expected value through perfect information.
The document describes decision analysis and provides examples of how decision trees and tables can be used to capture complex decision-making processes. It discusses five parts of a decision-making model: identify the problem, formulate options, model the problem, analyze the model, and implement and test the solution. Anchoring and framing errors in judgment are explained with examples. Finally, the use of decision trees and tables is demonstrated on examples involving business policies and rules.
The document describes decision analysis and decision making. It discusses identifying the problem, formulating a model, analyzing the model, testing results, and implementing solutions. It also discusses anchoring and framing biases that can influence decisions. Anchoring occurs when a trivial factor serves as a starting point for estimates. Framing affects how alternatives are perceived in terms of wins and losses. The way a problem is framed can influence choices made. Decision trees and tables are described as ways to represent complex decisions and business logic involving multiple conditions. Creating decision models allows for a more rigorous analysis of problems compared to using only narrative descriptions.
The document describes decision analysis and decision making. It discusses identifying the problem, formulating a model, analyzing the model, testing results, and implementing solutions. It also discusses sources of errors like anchoring and framing biases. Anchoring occurs when people rely too heavily on the first piece of information when making decisions. Framing refers to how the options are presented, which can influence choices. The document provides examples to illustrate these concepts and emphasizes the importance of focusing on the consequences of choices rather than how problems are framed.
The document describes decision analysis and decision making. It discusses identifying the problem, formulating a model, analyzing the model, testing results, and implementing solutions. It also discusses anchoring and framing biases that can influence decisions. Anchoring occurs when a trivial factor serves as a starting point for estimates. Framing affects how alternatives are perceived in terms of wins and losses. The way a problem is framed can influence choices. Decision trees and tables are described as ways to represent complex decisions involving multiple conditions. Creating decision models allows for a more rigorous analysis of problems compared to using narratives alone.
The document describes decision analysis and provides examples of how decision trees and tables can be used to analyze complex decisions. It discusses five parts of a decision-making model: identify the problem, formulate options, model the problem, analyze the model, and implement and test the solution. Anchoring and framing errors in judgment are described. Examples are provided to illustrate anchoring biases and how framing a problem as a sure win versus sure loss can influence choices. The use of decision trees to represent sequential decisions and incorporate uncertainty is demonstrated. Creating decision tables to systematically capture complex business rules is also illustrated.
The document describes decision analysis and decision making. It discusses identifying the problem, formulating a model, analyzing the model, testing results, and implementing solutions. It also discusses anchoring and framing biases that can influence decisions. Anchoring occurs when people rely too heavily on an irrelevant starting value. Framing means how a decision is perceived, such as in terms of gains or losses, can influence choices. The document provides an example where how a coin flip problem is framed affects whether people prefer a sure outcome or chance of gain/loss. Effective decision making requires understanding values, objectives, uncertainties, and consequences of options.
1) A decision tree can model sequential decision problems involving uncertainty through nodes and branches. It shows decisions, possible events, and outcomes.
2) The decision tree for DriveTek Research considers whether to prepare a proposal for a new storage device contract. It also models choices for development approaches if they win.
3) Terminal values, probabilities, and the rollback method are used to determine the optimal strategy for DriveTek, which is to prepare a proposal and use the electronic approach if awarded the contract.
Business decision, resource mgt and cost benefit analysisMohammed Jasir PV
The document provides information on decision making under conditions of certainty, risk, and uncertainty. It discusses three main types of decision making environments - certainty, where all outcomes are known; risk, where probabilities of outcomes are known; and uncertainty, where little is known about outcomes. Modern approaches to decision making under uncertainty include risk analysis, decision trees, and preference theory. Cost-benefit analysis is also summarized as a technique to evaluate the costs and benefits of potential decisions.
The document discusses various concepts in decision analysis including problem formulation, decision making without and with probabilities, and expected value analysis. In problem formulation, the key steps are to identify the decision alternatives, states of nature/uncertain events, and payoffs for each combination. When probabilities are unknown, the optimistic, conservative, and minimax regret approaches can be used. With probabilities, expected values are calculated for each alternative by weighting payoffs by their probabilities, and the alternative with the highest expected value is optimal. The expected value of perfect information is the increase in expected value if the uncertain state was known for certain.
Understanding the impact of certain uncertain event using bayesian networkKobi Vider
The document discusses using Bayesian networks and other methods to understand the impact of uncertain events and make decisions with limited information. It provides an agenda for presenting on a process that used these methods to address challenges in complex product development initiatives. The process identified goals, aligned them with modeling approaches, and predicted outcomes to help stakeholders understand tradeoffs and impacts of decisions. Factors in a performance model and challenges/successes of the approach are also mentioned.
This document describes using decision trees and linear regression for a statistical learning project on housing data. It discusses building decision trees and regression trees on latitude, longitude and other variables to predict housing prices. Linear regression performs poorly with an R-squared of 0.24, while regression trees more accurately identify areas with above-median home values. Further optimizing the regression tree with additional variables like income and population improves the model fit and predictions.
SMI SHAS4542 n4_Decision Making _ Organizing 0922.pdfssuser6d321e
This document discusses decision making and organizing for engineers. It covers various topics related to decision making processes and models, including rational choice models, risk assessment, and common decision making biases. It also discusses organizing topics such as the purposes of organizing, work specialization, departmentalization, centralization vs decentralization, and mechanistic vs organic structures. Traditional organizational design options like functional, divisional, and matrix structures are also covered.
Decision Theory LEARNING OBJECTIVES SUPPLEMENT OUTLINE 5S.5.docxsimonithomas47935
Decision Theory
LEARNING OBJECTIVES SUPPLEMENT OUTLINE 5S.5 Decision Making under Uncertainty, 219
After completing this supplement, you 5S.6 Decision Making under Risk, 220 5S.1 Introduction, 216
should be able to: 5S.7 Decision Trees, 2215S.2 The Decision Process and Causes of
L05S.1 Outline the steps in the decision Poor Decisions, 217 5S.8 Expected Value of Perfect
process. Information, 2235S.3 Decision Environments, 218
L05S.2 Name some causes of poor 5S.9 Sensitivity Analysis, 224
decisions. 5S.4 Decision Making under Certainty, 218
L05S.3 Describe and use techniques that
apply to decision making under
uncertainty.
L05S.4 Describe and use the expected-
value approach.
L05S.5 Construct a decision tree and use
it to analyze a problem.
L05S.6 Compute the expected value of
perfect information.
L05S.7 Conduct sensitivity analysis on a
simple decision problem.
55.1 INTRODUCTION
-
Decision theory represents a general approach to decision making. It is suitable for a wide
range of operations management decisions. Among them are capacity planning, product and
service design, equipment selection, and location planning. Decisions that lend themselves to
a decision theory approach tend to be characterized by the following elements:
1. A set of possible future conditions that will have a bearing on the results of the decision.
2. A list of alternatives for the manager to choose from.
3. A known payoff for each alternative under each possible future condition.
To use this approach, a decision maker would employ this process:
1. Identify the possible future conditions (e.g., demand will be low, medium, or high; the
competitor will or will not introduce a new product). These are called states of nature.
2. Develop a list of possible alternatives, one of which may be to do nothing.
t
3. Determine or estimate the payoff associated with each alternative for every possible
future condition.
---- ----------------------------------------~--
216
217 Supplement to Chapter Five Decision Theory
If possible, estimate the likelihood of each possible future condition.
5. Evaluate alternatives according to some decision criterion (e.g., maximize expected
profit), and select the best alternative.
The information for a decision is often summarized in a payoff table, which shows the
expected payoffs for each alternative under the various possible states of nature. These tables
are helpful in choosing among alternatives because they facilitate comparison of alternatives.
Consider the following payoff table, which illustrates a capacity planning problem.
POSSIBLE FUTURE DEMAND
Alternatives Low Moderate High
Small facility $10* $10 $10
Medium facility 7 12 12
Large facil ity (4) 2 16
'Present value in $ millions.
The payoffs are shown in the body of the table. In this instance, the payoffs are in terms
of present values, which represent equivalent current dollar values of expected .
Decision Theory LEARNING OBJECTIVES SUPPLEMENT OUTLINE 5S..docxtheodorelove43763
Decision Theory
LEARNING OBJECTIVES SUPPLEMENT OUTLINE 5S.5 Decision Making under Uncertainty, 219
After completing this supplement, you 5S.6 Decision Making under Risk, 220 5S.1 Introduction, 216
should be able to: 5S.7 Decision Trees, 2215S.2 The Decision Process and Causes of
L05S.1 Outline the steps in the decision Poor Decisions, 217 5S.8 Expected Value of Perfect
process. Information, 2235S.3 Decision Environments, 218
L05S.2 Name some causes of poor 5S.9 Sensitivity Analysis, 224
decisions. 5S.4 Decision Making under Certainty, 218
L05S.3 Describe and use techniques that
apply to decision making under
uncertainty.
L05S.4 Describe and use the expected-
value approach.
L05S.5 Construct a decision tree and use
it to analyze a problem.
L05S.6 Compute the expected value of
perfect information.
L05S.7 Conduct sensitivity analysis on a
simple decision problem.
55.1 INTRODUCTION
-
Decision theory represents a general approach to decision making. It is suitable for a wide
range of operations management decisions. Among them are capacity planning, product and
service design, equipment selection, and location planning. Decisions that lend themselves to
a decision theory approach tend to be characterized by the following elements:
1. A set of possible future conditions that will have a bearing on the results of the decision.
2. A list of alternatives for the manager to choose from.
3. A known payoff for each alternative under each possible future condition.
To use this approach, a decision maker would employ this process:
1. Identify the possible future conditions (e.g., demand will be low, medium, or high; the
competitor will or will not introduce a new product). These are called states of nature.
2. Develop a list of possible alternatives, one of which may be to do nothing.
t
3. Determine or estimate the payoff associated with each alternative for every possible
future condition.
---- ----------------------------------------~--
216
217 Supplement to Chapter Five Decision Theory
If possible, estimate the likelihood of each possible future condition.
5. Evaluate alternatives according to some decision criterion (e.g., maximize expected
profit), and select the best alternative.
The information for a decision is often summarized in a payoff table, which shows the
expected payoffs for each alternative under the various possible states of nature. These tables
are helpful in choosing among alternatives because they facilitate comparison of alternatives.
Consider the following payoff table, which illustrates a capacity planning problem.
POSSIBLE FUTURE DEMAND
Alternatives Low Moderate High
Small facility $10* $10 $10
Medium facility 7 12 12
Large facil ity (4) 2 16
'Present value in $ millions.
The payoffs are shown in the body of the table. In this instance, the payoffs are in terms
of present values, which represent equivalent current dollar values of expected future income.
This paper is highlighted as the agile tasking simulations mitigation scenario that determines the handling method of various scenarios and the splicing
effect of certain developmental requirements primarily in the emulation of Ark Sciences and glass systems concepts. This paper has very good counsel for
risk mitigation techniques universally
Decision Tree Analysis for statistical tool. The deck provides understanding on the Decision Analysis.
It provides practical application and limited theory. Will be useful for MBA students.
This technical paper discusses using a 2x2 Cartesian matrix framework to aid structured decision making in project management. The framework involves identifying decision areas, analyzing them to determine attributes, then designing a 2x2 matrix with the attributes on the axes to categorize scenarios into four quadrants. Each quadrant represents a unique decision making scenario requiring an identified action. The paper provides examples of decision matrices for stakeholder management, benefit realization, and governance. It also presents a case study where a company used the framework to help make decisions for a technology modernization project aimed at lowering costs while ensuring stakeholder engagement and benefits realization.
This document provides an overview of decision theory and decision making under uncertainty. It discusses structuring decision problems using decision trees and different types of decision making environments including uncertainty, risk, and certainty. It then covers various decision making criteria for uncertainty including optimistic, conservative, minimax regret, equally likely, and criterion of realism approaches. Expected values of perfect and sample information are also introduced. Examples are provided to illustrate key concepts such as calculating expected values and values of information.
Decision making models help organizations and individuals make choices when facing uncertainty. There are different types of decision problems including decisions under certainty, uncertainty, probabilistic, and non-probabilistic situations. Key steps in decision making include identifying alternatives and possible outcomes, constructing payoff tables, and applying decision rules like maximizing, minimizing, or expected value to determine the optimal choice. Obtaining additional information can potentially improve decisions by reducing uncertainty and increasing expected value through perfect information.
The document describes decision analysis and provides examples of how decision trees and tables can be used to capture complex decision-making processes. It discusses five parts of a decision-making model: identify the problem, formulate options, model the problem, analyze the model, and implement and test the solution. Anchoring and framing errors in judgment are explained with examples. Finally, the use of decision trees and tables is demonstrated on examples involving business policies and rules.
The document describes decision analysis and decision making. It discusses identifying the problem, formulating a model, analyzing the model, testing results, and implementing solutions. It also discusses anchoring and framing biases that can influence decisions. Anchoring occurs when a trivial factor serves as a starting point for estimates. Framing affects how alternatives are perceived in terms of wins and losses. The way a problem is framed can influence choices made. Decision trees and tables are described as ways to represent complex decisions and business logic involving multiple conditions. Creating decision models allows for a more rigorous analysis of problems compared to using only narrative descriptions.
The document describes decision analysis and decision making. It discusses identifying the problem, formulating a model, analyzing the model, testing results, and implementing solutions. It also discusses sources of errors like anchoring and framing biases. Anchoring occurs when people rely too heavily on the first piece of information when making decisions. Framing refers to how the options are presented, which can influence choices. The document provides examples to illustrate these concepts and emphasizes the importance of focusing on the consequences of choices rather than how problems are framed.
The document describes decision analysis and decision making. It discusses identifying the problem, formulating a model, analyzing the model, testing results, and implementing solutions. It also discusses anchoring and framing biases that can influence decisions. Anchoring occurs when a trivial factor serves as a starting point for estimates. Framing affects how alternatives are perceived in terms of wins and losses. The way a problem is framed can influence choices. Decision trees and tables are described as ways to represent complex decisions involving multiple conditions. Creating decision models allows for a more rigorous analysis of problems compared to using narratives alone.
The document describes decision analysis and provides examples of how decision trees and tables can be used to analyze complex decisions. It discusses five parts of a decision-making model: identify the problem, formulate options, model the problem, analyze the model, and implement and test the solution. Anchoring and framing errors in judgment are described. Examples are provided to illustrate anchoring biases and how framing a problem as a sure win versus sure loss can influence choices. The use of decision trees to represent sequential decisions and incorporate uncertainty is demonstrated. Creating decision tables to systematically capture complex business rules is also illustrated.
The document describes decision analysis and decision making. It discusses identifying the problem, formulating a model, analyzing the model, testing results, and implementing solutions. It also discusses anchoring and framing biases that can influence decisions. Anchoring occurs when people rely too heavily on an irrelevant starting value. Framing means how a decision is perceived, such as in terms of gains or losses, can influence choices. The document provides an example where how a coin flip problem is framed affects whether people prefer a sure outcome or chance of gain/loss. Effective decision making requires understanding values, objectives, uncertainties, and consequences of options.
1) A decision tree can model sequential decision problems involving uncertainty through nodes and branches. It shows decisions, possible events, and outcomes.
2) The decision tree for DriveTek Research considers whether to prepare a proposal for a new storage device contract. It also models choices for development approaches if they win.
3) Terminal values, probabilities, and the rollback method are used to determine the optimal strategy for DriveTek, which is to prepare a proposal and use the electronic approach if awarded the contract.
Business decision, resource mgt and cost benefit analysisMohammed Jasir PV
The document provides information on decision making under conditions of certainty, risk, and uncertainty. It discusses three main types of decision making environments - certainty, where all outcomes are known; risk, where probabilities of outcomes are known; and uncertainty, where little is known about outcomes. Modern approaches to decision making under uncertainty include risk analysis, decision trees, and preference theory. Cost-benefit analysis is also summarized as a technique to evaluate the costs and benefits of potential decisions.
The document discusses various concepts in decision analysis including problem formulation, decision making without and with probabilities, and expected value analysis. In problem formulation, the key steps are to identify the decision alternatives, states of nature/uncertain events, and payoffs for each combination. When probabilities are unknown, the optimistic, conservative, and minimax regret approaches can be used. With probabilities, expected values are calculated for each alternative by weighting payoffs by their probabilities, and the alternative with the highest expected value is optimal. The expected value of perfect information is the increase in expected value if the uncertain state was known for certain.
Understanding the impact of certain uncertain event using bayesian networkKobi Vider
The document discusses using Bayesian networks and other methods to understand the impact of uncertain events and make decisions with limited information. It provides an agenda for presenting on a process that used these methods to address challenges in complex product development initiatives. The process identified goals, aligned them with modeling approaches, and predicted outcomes to help stakeholders understand tradeoffs and impacts of decisions. Factors in a performance model and challenges/successes of the approach are also mentioned.
This document describes using decision trees and linear regression for a statistical learning project on housing data. It discusses building decision trees and regression trees on latitude, longitude and other variables to predict housing prices. Linear regression performs poorly with an R-squared of 0.24, while regression trees more accurately identify areas with above-median home values. Further optimizing the regression tree with additional variables like income and population improves the model fit and predictions.
SMI SHAS4542 n4_Decision Making _ Organizing 0922.pdfssuser6d321e
This document discusses decision making and organizing for engineers. It covers various topics related to decision making processes and models, including rational choice models, risk assessment, and common decision making biases. It also discusses organizing topics such as the purposes of organizing, work specialization, departmentalization, centralization vs decentralization, and mechanistic vs organic structures. Traditional organizational design options like functional, divisional, and matrix structures are also covered.
Decision Theory LEARNING OBJECTIVES SUPPLEMENT OUTLINE 5S.5.docxsimonithomas47935
Decision Theory
LEARNING OBJECTIVES SUPPLEMENT OUTLINE 5S.5 Decision Making under Uncertainty, 219
After completing this supplement, you 5S.6 Decision Making under Risk, 220 5S.1 Introduction, 216
should be able to: 5S.7 Decision Trees, 2215S.2 The Decision Process and Causes of
L05S.1 Outline the steps in the decision Poor Decisions, 217 5S.8 Expected Value of Perfect
process. Information, 2235S.3 Decision Environments, 218
L05S.2 Name some causes of poor 5S.9 Sensitivity Analysis, 224
decisions. 5S.4 Decision Making under Certainty, 218
L05S.3 Describe and use techniques that
apply to decision making under
uncertainty.
L05S.4 Describe and use the expected-
value approach.
L05S.5 Construct a decision tree and use
it to analyze a problem.
L05S.6 Compute the expected value of
perfect information.
L05S.7 Conduct sensitivity analysis on a
simple decision problem.
55.1 INTRODUCTION
-
Decision theory represents a general approach to decision making. It is suitable for a wide
range of operations management decisions. Among them are capacity planning, product and
service design, equipment selection, and location planning. Decisions that lend themselves to
a decision theory approach tend to be characterized by the following elements:
1. A set of possible future conditions that will have a bearing on the results of the decision.
2. A list of alternatives for the manager to choose from.
3. A known payoff for each alternative under each possible future condition.
To use this approach, a decision maker would employ this process:
1. Identify the possible future conditions (e.g., demand will be low, medium, or high; the
competitor will or will not introduce a new product). These are called states of nature.
2. Develop a list of possible alternatives, one of which may be to do nothing.
t
3. Determine or estimate the payoff associated with each alternative for every possible
future condition.
---- ----------------------------------------~--
216
217 Supplement to Chapter Five Decision Theory
If possible, estimate the likelihood of each possible future condition.
5. Evaluate alternatives according to some decision criterion (e.g., maximize expected
profit), and select the best alternative.
The information for a decision is often summarized in a payoff table, which shows the
expected payoffs for each alternative under the various possible states of nature. These tables
are helpful in choosing among alternatives because they facilitate comparison of alternatives.
Consider the following payoff table, which illustrates a capacity planning problem.
POSSIBLE FUTURE DEMAND
Alternatives Low Moderate High
Small facility $10* $10 $10
Medium facility 7 12 12
Large facil ity (4) 2 16
'Present value in $ millions.
The payoffs are shown in the body of the table. In this instance, the payoffs are in terms
of present values, which represent equivalent current dollar values of expected .
Decision Theory LEARNING OBJECTIVES SUPPLEMENT OUTLINE 5S..docxtheodorelove43763
Decision Theory
LEARNING OBJECTIVES SUPPLEMENT OUTLINE 5S.5 Decision Making under Uncertainty, 219
After completing this supplement, you 5S.6 Decision Making under Risk, 220 5S.1 Introduction, 216
should be able to: 5S.7 Decision Trees, 2215S.2 The Decision Process and Causes of
L05S.1 Outline the steps in the decision Poor Decisions, 217 5S.8 Expected Value of Perfect
process. Information, 2235S.3 Decision Environments, 218
L05S.2 Name some causes of poor 5S.9 Sensitivity Analysis, 224
decisions. 5S.4 Decision Making under Certainty, 218
L05S.3 Describe and use techniques that
apply to decision making under
uncertainty.
L05S.4 Describe and use the expected-
value approach.
L05S.5 Construct a decision tree and use
it to analyze a problem.
L05S.6 Compute the expected value of
perfect information.
L05S.7 Conduct sensitivity analysis on a
simple decision problem.
55.1 INTRODUCTION
-
Decision theory represents a general approach to decision making. It is suitable for a wide
range of operations management decisions. Among them are capacity planning, product and
service design, equipment selection, and location planning. Decisions that lend themselves to
a decision theory approach tend to be characterized by the following elements:
1. A set of possible future conditions that will have a bearing on the results of the decision.
2. A list of alternatives for the manager to choose from.
3. A known payoff for each alternative under each possible future condition.
To use this approach, a decision maker would employ this process:
1. Identify the possible future conditions (e.g., demand will be low, medium, or high; the
competitor will or will not introduce a new product). These are called states of nature.
2. Develop a list of possible alternatives, one of which may be to do nothing.
t
3. Determine or estimate the payoff associated with each alternative for every possible
future condition.
---- ----------------------------------------~--
216
217 Supplement to Chapter Five Decision Theory
If possible, estimate the likelihood of each possible future condition.
5. Evaluate alternatives according to some decision criterion (e.g., maximize expected
profit), and select the best alternative.
The information for a decision is often summarized in a payoff table, which shows the
expected payoffs for each alternative under the various possible states of nature. These tables
are helpful in choosing among alternatives because they facilitate comparison of alternatives.
Consider the following payoff table, which illustrates a capacity planning problem.
POSSIBLE FUTURE DEMAND
Alternatives Low Moderate High
Small facility $10* $10 $10
Medium facility 7 12 12
Large facil ity (4) 2 16
'Present value in $ millions.
The payoffs are shown in the body of the table. In this instance, the payoffs are in terms
of present values, which represent equivalent current dollar values of expected future income.
This paper is highlighted as the agile tasking simulations mitigation scenario that determines the handling method of various scenarios and the splicing
effect of certain developmental requirements primarily in the emulation of Ark Sciences and glass systems concepts. This paper has very good counsel for
risk mitigation techniques universally
Decision Tree Analysis for statistical tool. The deck provides understanding on the Decision Analysis.
It provides practical application and limited theory. Will be useful for MBA students.
We are pleased to share with you the latest VCOSA statistical report on the cotton and yarn industry for the month of March 2024.
Starting from January 2024, the full weekly and monthly reports will only be available for free to VCOSA members. To access the complete weekly report with figures, charts, and detailed analysis of the cotton fiber market in the past week, interested parties are kindly requested to contact VCOSA to subscribe to the newsletter.
06-20-2024-AI Camp Meetup-Unstructured Data and Vector DatabasesTimothy Spann
Tech Talk: Unstructured Data and Vector Databases
Speaker: Tim Spann (Zilliz)
Abstract: In this session, I will discuss the unstructured data and the world of vector databases, we will see how they different from traditional databases. In which cases you need one and in which you probably don’t. I will also go over Similarity Search, where do you get vectors from and an example of a Vector Database Architecture. Wrapping up with an overview of Milvus.
Introduction
Unstructured data, vector databases, traditional databases, similarity search
Vectors
Where, What, How, Why Vectors? We’ll cover a Vector Database Architecture
Introducing Milvus
What drives Milvus' Emergence as the most widely adopted vector database
Hi Unstructured Data Friends!
I hope this video had all the unstructured data processing, AI and Vector Database demo you needed for now. If not, there’s a ton more linked below.
My source code is available here
https://github.com/tspannhw/
Let me know in the comments if you liked what you saw, how I can improve and what should I show next? Thanks, hope to see you soon at a Meetup in Princeton, Philadelphia, New York City or here in the Youtube Matrix.
Get Milvused!
https://milvus.io/
Read my Newsletter every week!
https://github.com/tspannhw/FLiPStackWeekly/blob/main/141-10June2024.md
For more cool Unstructured Data, AI and Vector Database videos check out the Milvus vector database videos here
https://www.youtube.com/@MilvusVectorDatabase/videos
Unstructured Data Meetups -
https://www.meetup.com/unstructured-data-meetup-new-york/
https://lu.ma/calendar/manage/cal-VNT79trvj0jS8S7
https://www.meetup.com/pro/unstructureddata/
https://zilliz.com/community/unstructured-data-meetup
https://zilliz.com/event
Twitter/X: https://x.com/milvusio https://x.com/paasdev
LinkedIn: https://www.linkedin.com/company/zilliz/ https://www.linkedin.com/in/timothyspann/
GitHub: https://github.com/milvus-io/milvus https://github.com/tspannhw
Invitation to join Discord: https://discord.com/invite/FjCMmaJng6
Blogs: https://milvusio.medium.com/ https://www.opensourcevectordb.cloud/ https://medium.com/@tspann
https://www.meetup.com/unstructured-data-meetup-new-york/events/301383476/?slug=unstructured-data-meetup-new-york&eventId=301383476
https://www.aicamp.ai/event/eventdetails/W2024062014
PyData London 2024: Mistakes were made (Dr. Rebecca Bilbro)Rebecca Bilbro
To honor ten years of PyData London, join Dr. Rebecca Bilbro as she takes us back in time to reflect on a little over ten years working as a data scientist. One of the many renegade PhDs who joined the fledgling field of data science of the 2010's, Rebecca will share lessons learned the hard way, often from watching data science projects go sideways and learning to fix broken things. Through the lens of these canon events, she'll identify some of the anti-patterns and red flags she's learned to steer around.
06-18-2024-Princeton Meetup-Introduction to MilvusTimothy Spann
06-18-2024-Princeton Meetup-Introduction to Milvus
tim.spann@zilliz.com
https://www.linkedin.com/in/timothyspann/
https://x.com/paasdev
https://github.com/tspannhw
https://github.com/milvus-io/milvus
Get Milvused!
https://milvus.io/
Read my Newsletter every week!
https://github.com/tspannhw/FLiPStackWeekly/blob/main/142-17June2024.md
For more cool Unstructured Data, AI and Vector Database videos check out the Milvus vector database videos here
https://www.youtube.com/@MilvusVectorDatabase/videos
Unstructured Data Meetups -
https://www.meetup.com/unstructured-data-meetup-new-york/
https://lu.ma/calendar/manage/cal-VNT79trvj0jS8S7
https://www.meetup.com/pro/unstructureddata/
https://zilliz.com/community/unstructured-data-meetup
https://zilliz.com/event
Twitter/X: https://x.com/milvusio https://x.com/paasdev
LinkedIn: https://www.linkedin.com/company/zilliz/ https://www.linkedin.com/in/timothyspann/
GitHub: https://github.com/milvus-io/milvus https://github.com/tspannhw
Invitation to join Discord: https://discord.com/invite/FjCMmaJng6
Blogs: https://milvusio.medium.com/ https://www.opensourcevectordb.cloud/ https://medium.com/@tspann
Expand LLMs' knowledge by incorporating external data sources into LLMs and your AI applications.
2. Introduction
• Business analytics is about making better decisions.
• Decision analysis can be used to develop an optimal strategy:
• When a decision maker is faced with several decision alternatives
and an uncertain or risk-filled pattern of future events.
• E.g. The State of North Carolina used decision analysis in
evaluating whether to implement a medical screening test to
detect metabolic disorders in newborns.
• A good decision analysis includes careful consideration of risk.
2
3. Introduction
• Risk analysis helps to provide the probability information about the
favourable as well as the unfavourable outcomes that may occur.
• Decision analysis considers problems that involve reasonably few
decision alternatives and reasonably few possible future events.
• Topics to be discussed under decision analysis:
• Payoff tables and decision trees
• Sensitivity analysis
• Use of Bayes’ Theorem
3
5. Problem Formulation
• The steps in the decision analysis process are as follows:
• Problem formulation
• Create verbal statement of the problem
• Identify the decision alternatives:
• The uncertain future events, referred to as chance events.
• The outcomes associated with each combination of decision
alternative and chance event outcome.
5
6. Problem Formulation
• Example:
PDC commissioned preliminary architectural drawings for three different
projects: one with 30 condominiums, one with 60 condominiums, and one
with 90 condominiums. The financial success of the project depends on the
size of the condominium complex and the chance event concerning the
demand for the condominiums. The statement of the PDC decision
problem is to select the size of the new luxury condominium project that
will lead to the largest profit given the uncertainty concerning the demand
for the condominiums. Given the statement of the problem, it is
6
7. Problem Formulation
clear that the decision is to select the best size for the condominium complex.
PDC has the following three decision alternatives:
d1 = a small complex with 30 condominiums
d2 = a medium complex with 60 condominiums
d3 = a large complex with 90 condominiums
7
8. Problem Formulation
• In decision analysis, the possible outcomes for a chance event are
the states of nature.
• The states of nature are mutually exclusive (no more than one can
occur) and collectively exhaustive (at least one must occur).
• Thus one and only one of the possible states of nature will occur.
8
9. Problem Formulation
• For PDC Example: The chance event concerning the demand for
the condominiums has two states of nature:
• s1 = strong demand for the condominiums
• s2 = weak demand for the condominiums
9
10. Problem Formulation
• Payoff Tables
• Payoff is the outcome resulting from a specific combination of a decision
alternative and a state of nature.
• Payoff table is a table showing payoffs for all combinations of decision
alternatives and states of nature.
10
11. Table 12.1 - Payoff Table For The PDC
Condominium Project ($ Millions)
11
12. Problem Formulation
• Example:
We will use the notation Vij to denote the payoff associated
with decision alternative i and state of nature j. Using Table
12.1, V31 = 20 indicates that a payoff of $20 million occurs if
the decision is to build a large complex (d3) and the strong
demand state of nature (s1) occurs.
12
13. Problem Formulation
• Decision Tree
• Provides a graphical representation of the decision-making
process
• It shows the natural or logical progression that will occur over time
• Example:
The topmost payoff of 8 indicates that an $8 million profit is
anticipated if PDC constructs a small condominium complex (d1) and
demand turns out to be strong (s1).
13
14. Figure 12.1 - Decision Tree For The PDC Condominium Project ($
Millions)
14
15. Problem Formulation
• The decision tree in Figure 12.1 shows:
• Four nodes, numbered 1–4.
• Nodes: They are used to represent decisions and chance events.
• Squares are used to depict decision nodes, circles are used to
depict chance nodes.
• Thus, node 1 is a decision node, and nodes 2, 3, and 4 are chance
nodes.
15
16. Problem Formulation
• The branches connect the nodes; those leaving the decision node
correspond to the decision alternatives.
• The branches leaving each chance node correspond to the states
of nature.
• The outcomes (payoffs) are shown at the end of the states-of-
nature branches.
16
18. 18
Decision Analysis Without Probabilities
• Decision analysis without probabilities is appropriate in
situations:
• In which a simple best-case and worst-case analysis is sufficient
• Where the decision maker has little confidence in his or her ability
to assess the probabilities.
19. 19
Decision Analysis Without Probabilities
• Optimistic Approach
• Evaluates each decision alternative in terms of the best payoff that
can occur.
• The decision alternative that is recommended is the one that
provides the best possible payoff.
20. 20
Decision Analysis Without Probabilities
• In the PDC problem,
• the optimistic approach would lead the decision maker to choose the
alternative corresponding to the largest profit.
• for minimization problems, this approach leads to choosing the
alternative with the smallest payoff.
21. 21
Table 12.2 - Maximum Payoff For Each PDC
Decision Alternative
22. • Conservative Approach
• Evaluates each decision alternative in terms of the worst payoff
that can occur.
• The decision alternative recommended is the one that provides
the best of the worst possible payoffs.
Decision Analysis Without Probabilities
22
23. • In the PDC problem,
• The conservative approach would lead the decision maker to choose
the alternative that maximizes the minimum possible profit that could
be obtained.
• For problems involving minimization (for example, when the output
measure is cost), this approach identifies the alternative that will
minimize the maximum payoff.
Decision Analysis Without Probabilities
23
24. 24
Table 12.3 - Minimum Payoff For Each PDC Decision
Alternative
25. • Minimax Regret Approach
• Regret is the difference between the payoff associated with a
particular decision alternative and the payoff associated with the
decision would yield the most desirable payoff for a given state of
nature.
• Regret is often referred to as opportunity loss.
• Under the minimax regret approach, one would choose the decision
alternative that minimizes the maximum state of regret that could
occur over all possible states of nature.
Decision Analysis Without Probabilities
25
27. 27
Decision Analysis Without Probabilities
• Using equation (12.1) and the payoffs in Table 12.1, the regret
associated with each combination of decision alternative di and
state of nature sj is computed.
• To compute the regret, subtract each entry in a column from the
largest entry in the column.
28. Table 12.4 - Opportunity Loss, Or Regret, Table For The PDC
Condominium Project ($ Millions)
28
29. Table 12.5 - Maximum Regret For Each PDC Decision
Alternative
29
30. 30
Decision Analysis Without Probabilities
• The next step in applying the minimax regret approach is to list the
maximum regret for each decision alternative;
• For the PDC problem, the alternative to construct the medium
condominium complex, with a corresponding maximum regret of
$6 million, is the recommended minimax regret decision.
32. • Expected Value Approach
• The expected value of a decision alternative is the sum of
weighted payoffs for the decision alternative.
• The weight for a payoff is the probability of the associated state of
nature and therefore the probability that the payoff will occur.
• Figure 12.2 shows the decision tree for the PDC problem with
state-of-nature branch probabilities.
Decision Analysis With Probabilities
32
33. Equation 12.2 - Expected Value of Decision Alternative Di
33
34. Figure 12.2 - PDC Decision Tree With State-of-nature
Branch Probabilities
34
35. Figure 12.3 - Applying The Expected Value Approach Using
A Decision Tree For The PDC Condominium Project
35
36. • Select the decision branch leading to the chance node with the
best expected value. The decision alternative associated with this
branch is the recommended decision.
• In practice, obtaining precise estimates of the probabilities for
each state of nature is often impossible so historical data is
preferred to use for estimating the probabilities for the different
states of nature.
Decision Analysis With Probabilities
36
37. • Risk Analysis
• Helps the decision maker recognize the difference between the
expected value of a decision alternative and the payoff that may
actually occur.
• Decision alternative and a state of nature combine to generate the
payoff associated with a decision.
• Risk profile for a decision alternative shows the possible payoffs
along with their associated probabilities.
Decision Analysis With Probabilities
37
38. Figure 12.4 - Risk Profile For The Large Complex Decision
Alternative For The PDC Condominium Project
38
39. • Sensitivity Analysis
• Determines how changes in the probabilities for the states of
nature or changes in the payoffs affect the recommended decision
alternative.
• In many cases, the probabilities for the states of nature and the
payoffs are based on subjective assessments.
Decision Analysis With Probabilities
39
40. • So sensitivity analysis helps the decision maker understand which
of these inputs are critical to the choice of the best decision
alternative.
• If a small change in the value of one of the inputs causes a change
in the recommended decision alternative, the solution to the
decision analysis problem is sensitive to that particular input.
Decision Analysis With Probabilities
40
41. • Example:
Suppose that in the PDC problem the probability for a strong
demand is revised to 0.2 and the probability for a weak demand is
revised to 0.8.
EV(d1 ) = 0.2 (8) + 0.8 (7) = 7.2
EV(d2 ) = 0.2 (14) + 0.8 (5) = 6.8
EV(d3 ) = 0.2 (20) + 0.8 (-9) = -3.2
Decision Analysis With Probabilities
41
42. 42
Decision Analysis With Probabilities
• With these probability assessments, the recommended decision
alternative is to construct a small condominium complex (d1), with
an expected value of $7.2 million.
• Thus, when the probability of strong demand is large, PDC should
build the large complex, when the probability of strong demand is
small, PDC should build the small complex.
44. • Decision makers have the ability to collect additional information
about the states of nature.
• Additional information is obtained through experiments designed
to provide sample information about the states of nature.
• The preliminary or prior probability assessments for the states of
nature that are the best probability values available prior to
obtaining additional information.
Decision Analysis with Sample Information
44
45. • Posterior probabilities are revised probabilities after obtaining
additional information.
Decision Analysis with Sample Information
45
46. • Example:
PDC management is considering a 6-month market research study
designed to learn more about potential market acceptance of the
PDC condominium project anticipating two results;
• Favorable report: A substantial number of the individuals
contacted express interest in purchasing a PDC condominium.
• Unfavorable report: Very few of the individuals contacted
express interest in purchasing a PDC condominium.
Decision Analysis with Sample Information
46
47. Figure 12.5 - The PDC Decision Tree Including The
Market Research Study
47
48. FIGURE 12.6 THE PDC DECISION TREE WITH
BRANCH PROBABILITIES
48
49. FIGURE 12.7 PDC DECISION TREE AFTER COMPUTING
EXPECTED VALUES AT CHANCE NODES 6–14
49
50. FIGURE 12.8 PDC DECISION TREE AFTER CHOOSING BEST
DECISIONS AT NODES 3, 4, AND 5
50
51. FIGURE 12.9 PDC DECISION TREE REDUCED TO TWO
DECISION BRANCHES
51
52. • If the market research is favorable, construct the large
condominium complex.
• If the market research is unfavorable, construct the medium
condominium complex.
Decision Analysis with Sample Information
52
53. • Expected Value of Sample Information
• From Figure 12.9 we can conclude that the difference, 15.93 -
14.20 = 1.73, is the expected value of sample information (EVSI).
Decision Analysis with Sample Information
53
54. • Expected Value of Perfect Information
• A special case of gaining additional information related to a
decision problem is when the sample information provides perfect
information on the states of nature.
• We can state PDC’s optimal decision strategy when the perfect
information becomes available as follows:
• If s1, select d3 and receive a payoff of $20 million.
Decision Analysis with Sample Information
54
55. • If s2, select d1 and receive a payoff of $7 million.
• The original probabilities for the states of nature:
• P(s1) = 0.8 and P(s2) = 0.2.
Decision Analysis with Sample Information
55
56. • From equation (12.2) the expected value of the decision strategy
that uses perfect information is 0.8(20) + 0.2(7) = 17.4. i.e.
expected value with perfect information (EVwPI).
• Earlier using the expected value approach is decision alternative d3
$14.2 million is referred to as the expected value without perfect
information (EVwoPI).
• So, Expected value of the perfect information (EVPI) is $17.4 -
$14.2 = $3.2 million.
Decision Analysis with Sample Information
56
57. TABLE 12.6 PAYOFF TABLE FOR THE PDC CONDOMINIUM PROJECT
($ MILLIONS)
57
59. • Baye’s Theorem
• Used to compute branch probabilities for decision trees.
• The notation | in P(s1|F) and P(s2|F) is read as “given” and indicates
a conditional probability because we are interested in the
probability of a particular state of nature “conditioned” on the fact
that we receive a favorable market report.
Computing Branch probabilities with Bayes’
Theorem
59
60. • P(s1|F) and P(s2|F) are referred to as posterior probabilities
because they are conditional probabilities based on the outcome of
the sample information.
Computing Branch probabilities with Bayes’
Theorem
60
61. • The steps used to develop this table computations for the PDC
problem based on a favorable market research report (F) are as
follows:
• Step 1. In column 1, enter the states of nature
• Step 2. In column 2, enter the prior probabilities for the states of
nature
• Step 3. In column 3, enter the conditional probabilities of a favorable
market research
Computing Branch probabilities with Bayes’
Theorem
61
62. • report (F) given each state of nature
• Step 4. In column 4, compute the joint probabilities by multiplying
the prior probability
• values in column 2 by the corresponding conditional probability
values
• in column 3
• Step 5. Sum the joint probabilities in column 4 to obtain the
probability of a favorable
Computing Branch probabilities with Bayes’
Theorem
62
63. • market research report, P(F)
• Step 6. Divide each joint probability in column 4 by P(F) = 0.77 to
obtain the revised
• or posterior probabilities, P(s1 |F) and P(s2 |F)
Computing Branch probabilities with Bayes’
Theorem
63
64. TABLE 12.7 BRANCH PROBABILITIES FOR THE PDC CONDOMINIUM
PROJECT BASED
ON A FAVORABLE MARKET RESEARCH REPORT
64
65. TABLE 12.8 BRANCH PROBABILITIES FOR THE PDC CONDOMINIUM
PROJECT BASED ON AN UNFAVORABLE MARKET RESEARCH
REPORT
65
67. • When monetary value does not necessarily lead to the most
preferred decision, expressing the value (or worth) of a
consequence in terms of its utility will permit the use of expected
utility to identify the most desirable decision alternative.
Utility Theory
67
68. • Utility
• Measure of the total worth or relative desirability of a particular
outcome.
• Reflects the decision maker’s attitude toward a collection of
factors such as profit, loss, and risk.
• Example of a situation in which utility can help in selecting the best
decision alternative:
Utility Theory
68
69. • Swofford Inc. currently has two investment opportunities that
require approximately the same cash outlay. The cash
requirements necessary prohibit Swofford from making more than
one investment at this time. Consequently, three possible decision
alternatives may be considered.
Utility Theory
69
71. • Utility and Decision Analysis
• The following steps state in general terms the procedure used to
solve the Swofford, Inc., investment problem:
• Step 1. Develop a payoff table using monetary values
• Step 2. Identify the best and worst payoff values in the table and
assign each a utility,
• with u(best payoff)> u(worst payoff)
Utility Theory
71
72. • Step 3. For every other monetary value m in the original payoff table,
do the following to determine its utility:
• a. Define the lottery such that there is a probability p of the best
payoff and a probability (1 - p) of the worst payoff
• b. Determine the value of p such that the decision maker is indifferent
between a guaranteed payoff of m and the lottery defined in step 3(a)
• c. Calculate the utility of m as follows:
• U(M) = pU(best payoff) + (1 - p)U(worst payoff)
Utility Theory
72
73. • Step 4. Convert each monetary value in the payoff table to a utility
• Step 5. Apply the expected utility approach to the utility table
developed in step 4 and select the decision alternative with the
highest expected utility
Utility Theory
73
76. • Utility Functions
• We describe how different decision makers may approach risk in
terms of their assessment of utility.
• A risk taker is a decision maker who would choose a lottery over a
guaranteed payoff when the expected value of the lottery is
inferior to the guaranteed payoff.
Utility Theory
76
77. • We analyze the decision problem faced by Swofford from the point
of view of a decision maker who would be classified as a risk taker.
• Compare the conservative point of view of Swofford’s president (a
risk avoider) with the behavior of a decision maker who is a risk
taker.
Utility Theory
77
80. • Using the state-of-nature probabilities P(s1) = 0.3, P(s2) = 0.5, and
P(s3) = 0.2, the expected utility for decision alternative is
• EU(d2 ) = 0.3 (10) + 0.5 (1.5 ) + 0.2 (1.0 ) = 3.95
• EU(d1 ) = 3.50
• EU(d3 ) = 2.50
• The analysis recommends investment B, with the highest expected
utility of 3.95
Utility Theory
80
81. FIGURE 12.11 UTILITY FUNCTION FOR MONEY FOR RISK-
AVOIDER, RISK- TAKER, AND RISK-NEUTRAL DECISION
MAKERS
81
82. • Utility function for a risk avoider shows a diminishing marginal
return for money. For example, the increase in utility going from a
monetary value of -$30,000 to $0 is 7.5 - 4.0 = 3.5, whereas the
increase in utility in going from $0 to $30,000 is only 9.5 - 7.5 = 2.0.
• Utility function for a risk taker shows an increasing marginal
return. For example, the increase in utility for the risk taker in
going from -$30,000 to $0 is 2.5 - 1.0 = 1.5, whereas the increase
in utility in going from $0 to $30,000 for the risk taker is 5.0 - 2.5 =
2.5.
Utility Theory
82
83. • Utility function for a decision maker neutral to risk shows a
constant return.
• The following characteristics are associated with a risk-neutral
decision maker:
• The utility function can be drawn as a straight line connecting the
“best” and the “worst” points.
• The expected utility approach and the expected value approach
applied to monetary payoffs result in the same action.
Utility Theory
83
84. • Exponential Utility Function
• Used as an alternative to assume that the decision maker’s utility
is defined when decision maker provides enough indifference
values to create a utility function.
• All the exponential utility functions indicate that the decision
maker is risk averse.
Utility Theory
84
86. • The R parameter in equation (12.7) represents the decision
maker’s risk tolerance; it controls the shape of the exponential
utility function.
• Larger R values create flatter exponential functions, indicating that
the decision maker is less risk averse (closer to risk neutral).
Utility Theory
86
87. • Smaller R values indicate that the decision maker has less risk
tolerance (is more risk averse). For example:
• For instance, if the decision maker is comfortable accepting a
gamble with a 50 percent chance of winning $2,000 and a 50
percent chance of losing $1,000, but not with a gamble with a 50
percent chance of winning $3,000 and a 50 percent chance of
losing $1,500 then we would use R = $2,000 in equation (12.7).
Utility Theory
87
Editor's Notes
Reference from Chapter 8
Notes: The previously discussed process can also be used to develop a utility measure for nonmonetary consequences.
U(consequence) = pU(best consequence) + (1 - p)U(worst consequence)