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Questions and Answers
What is the minimin strategy in decision-making?
What is the minimin strategy in decision-making?
The opportunity loss strategy aims to maximize the largest opportunity loss.
The opportunity loss strategy aims to maximize the largest opportunity loss.
False
List the first step in the decision-making process.
List the first step in the decision-making process.
Clearly define the problem at hand
The decision-making model that aims to minimize the largest opportunity loss is called the ______ strategy.
The decision-making model that aims to minimize the largest opportunity loss is called the ______ strategy.
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Match the decision-making strategies with their descriptions:
Match the decision-making strategies with their descriptions:
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What is the primary purpose of decision analysis in business?
What is the primary purpose of decision analysis in business?
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Decision problems involve only decision alternatives and their outcomes.
Decision problems involve only decision alternatives and their outcomes.
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What are the two components that a decision maker must consider when selecting a decision alternative?
What are the two components that a decision maker must consider when selecting a decision alternative?
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In decision analysis, the potential outcomes of uncertain events are often referred to as _______.
In decision analysis, the potential outcomes of uncertain events are often referred to as _______.
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Match the following terms with their descriptions:
Match the following terms with their descriptions:
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Which mortgage type has the highest interest rate?
Which mortgage type has the highest interest rate?
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The 1-year ARM has a fixed interest rate over its term.
The 1-year ARM has a fixed interest rate over its term.
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What is the opportunity loss associated with a decision?
What is the opportunity loss associated with a decision?
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In a _____ strategy, the decision maker determines the largest payoff and then chooses the one with the smallest value.
In a _____ strategy, the decision maker determines the largest payoff and then chooses the one with the smallest value.
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Match each mortgage type with its associated interest sensitivity:
Match each mortgage type with its associated interest sensitivity:
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What is the expected value of the interest cost for the loan types with probabilities 0.6, 0.3, and 0.1, and interest costs of $61,134, $46,443, and $40,161 respectively?
What is the expected value of the interest cost for the loan types with probabilities 0.6, 0.3, and 0.1, and interest costs of $61,134, $46,443, and $40,161 respectively?
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The average payoff strategy assumes that not all outcomes are equally likely.
The average payoff strategy assumes that not all outcomes are equally likely.
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What are the two types of nodes in a decision tree?
What are the two types of nodes in a decision tree?
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In the expected value calculation, ______ is equal to the sum of the product of each outcome and its probability, expressed as Σ xi f(xi).
In the expected value calculation, ______ is equal to the sum of the product of each outcome and its probability, expressed as Σ xi f(xi).
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Match the following steps of decision tree analysis with their descriptions:
Match the following steps of decision tree analysis with their descriptions:
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Study Notes
Decision Analysis
- Decision analysis is the study of how people make decisions, particularly when faced with imperfect or uncertain information.
- Business analytics provides decision-makers with the information necessary to make sound decisions.
- Good decisions depend on assessing intangible factors and risk attitudes.
- Decision analysis involves a collection of techniques to aid decision-making.
Topics Covered
- Decision analysis itself
- Decision tables
- Decision making under circumstances of uncertainty
- Decision trees
Formulating Decision Problems
- Many decisions involve choosing between a limited number of options with uncertain results.
- Decision problems consider:
- Decision alternatives
- Uncertain events and their possible outcomes (often called states of nature)
- Outcomes associated with each decision and outcome (typically payoffs).
Decision Strategies Without Outcome Probabilities
- Aggressive (Optimistic) Strategy: Select the decision that minimizes the smallest possible payoff. This is also known as the minimin strategy.
- Conservative (Pessimistic) Strategy: Select the decision that minimizes the largest possible payoff. This is also known as the minimax strategy.
- Opportunity Loss Strategy: Choose the decision that minimizes the largest opportunity loss among all outcomes. This is also known as the minimax regret strategy.
The Six Steps in Decision Making
- Clearly define the problem.
- List possible alternatives.
- Identify possible outcomes (states of nature).
- Establish the payoff for each combination of alternatives and outcomes.
- Choose a mathematical decision theory model.
- Apply the chosen model and make the decision.
Example: Selecting a Mortgage Instrument
- A family wants to finance a $150,000 home.
- Example options include a 1-year ARM, a 3-year ARM, and a 30-year fixed-rate mortgage.
- The payoff table displays the total interest paid under different future interest rate scenarios.
Example: Mortgage Decision Strategies
- Aggressive Strategy: Select the lowest interest cost for each mortgage type.
- Conservative Strategy: Select the mortgage with the lowest maximum interest cost.
Understanding Opportunity Loss
- Opportunity loss is essentially the "regret" felt after making a poor decision.
- It is calculated as the difference between:
- The best possible payoff for a given outcome
- The payoff associated with the chosen decision.
Example: Mortgage Decision with the Opportunity-Loss Strategy
- To use the opportunity loss strategy, compute the "opportunity loss matrix."
- Then determine the maximum opportunity loss for each mortgage and select the mortgage with the lowest value.
Decision Strategies With Outcome Probabilities
- If probabilities for each outcome are known then the expected value calculation can be used.
- The simplest case assumes each outcome is equally likely. This strategy is known as the average payoff strategy.
Example: Mortgage Decision with Average Payoff Strategy
- Calculate the expected value for the interest cost of each mortgage.
Expected Value Strategy
- The calculation is applicable when probabilities for different outcomes differ.
- The expected value calculation is the sum over all possible outcomes of their values multiplied by corresponding probability.
Decision Trees
- A graphical model to organize decision problems that involve uncertainty.
- Consists of nodes symbolizing points in time at which events unfold.
- Decision nodes represent decision points, typically depicted as squares.
- Event nodes represent events that happen over time that are outside of the decision maker's control, often illustrated as circles.
- Branches connect nodes and indicate decisions or possible outcomes.
- Represent decision sequences over time.
Five steps of Decision Tree analysis
- Define the problem
- Create the decision tree
- Assign probabilities to the states of nature
- Estimate payoffs for each possible combination of alternatives and states
- Solve the problem by calculating the expected monetary value(EMV)for each state of nature node.
Summary of Decision Strategies Under Uncertainty
- Summarize aggressive, conservative and opportunity-loss strategies to solve decisions under conditions of uncertainty.
Summary of Decision Strategies Under Uncertainty, Maximize Objective
- Summarize aggressive, conservative and opportunity-loss strategies to solve maxmize-objective decisions under conditions of uncertainty.
Probability
- Probability is the measurement of the likelihood of an event occurring, expressed as a value between 0 and 1.
- Probability Rules:
- 0 ≤ P(O₁) ≤ 1 for each outcome O.
- P(O₁)+P(O2)+...+P(On)=1.
- If events A and B are mutually exclusive, P(A or B) = P(A) + P(B).
- If events A and B are not mutually exclusive, P(A or B) = P(A) + P(B) − P(A and B).
Probability Mass Function For Rolling Two Dice
- X₁ = values of a random variable X that represents the possible sums of two dice rolls
- f(x₁) = the conditional probability for each outcome
Cumulative Distribution Function For Rolling Two Dice
- Cumulative probability of a given random variable value.
Simple Linear Regression Drawing a Scatterplot
- Scatterplot showing the relationship between two variables.
Correlation Coefficient
- Measure of the strength and direction of the linear relationship between two variables.
- Always between -1 and +1. 0 means no correlation
Regression Statistics
- Multiple R: the correlation coefficient.
- R Square: coefficient of determination. Ranges from 0 (no fit) to 1 (perfect fit).
- Adjusted R Square: adjusts R-square to account for sample size and number of variables.
- Standard Error: the variability between the observed and predicted values.
Simple Linear Regression
- Mathematical equation to model a linear relationship between two variables.
Linearity
- Linear trend in a scatter plot.
- The residuals should appear to be randomly scattered about zero, with no apparent pattern.
Example of Interpreting Regression Results
- Use of R-squared values for determining the amount of variation explained by the independent variables.
- Evaluating and determining of the significance of the model itself.
- Evaluating the statistical significance of the individual coefficients.
Systematic Model Building Approach
- Construct a model using all available independent variables.
- Check p-values to evaluate the significance of independent variables.
- Identify the independent variable with the highest p-value that is above the chosen significance level.
- Remove the variable identified in step two, re-evaluate adjusted R-squared.
- Repeat until all variables included in the model are significant.
Multicollinearity
- A statistical phenomenon where independent variables in a regression model are highly correlated with each other.
- High correlation coefficients and high Variance Inflation Factors are indicators.
- Addressing multicollinearity: removing variables or collecting more data.
Forecast Models
- Categorize methods into qualitative and quantitative models:
- Qualitative methods are used when there is not much historical data or if the model must predict far into the future. These depend on expert opinion.
- Delphi method
- Jury of executive opinion
- Sales force composite
- Consumer survey
- Market survey
- Quantitative methods are generally used when there is extensive historical data about the variable you want to predict.
- Time-series methods
- Moving average
- Exponential smoothing
- Trend projections
- Decomposition
- Causal Methods
- Simple regression
- Multiple regression
Components of a Time Series
- Four components of time series data:
- Random variation
- Seasonal variation
- Trend variation
- Cyclical variation.
Example Moving Average Forecasting
- Three-period moving average forecast is calculated as the average of the current and two preceding periods' sales values.
Error Metrics and Forecast Accuracy
- Error in a forecast: the difference between the forecast and the actual value of the time series.
Example: Using Error Metrics to Compare Moving Average Forecasts
- Evaluate the accuracy of different moving average forecasts using metrics like Mean Absolute Deviation (MAD), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE).
Exponential Smoothing Model
- Simple exponential smoothing model uses a weighted average of past observations and the previous forecast to predict future values
Example: Using Exponential Smoothing to Forecast Tablet Computes Sales
- Calculate forecasts for tablet sales using different smoothing constants.
Regression-Based Forecasting for Time Series with a Linear Trend
- Simple linear regression can be used to forecast time series data with a linear trend, with time as the independent variable.
Example: Forecasting Using Trendlines
- Example showing how a trendline can be used to forecast future values of a time series variable.
Example: Regression-Based Forecasting for Natural Gas Usage
- Calculate forecasts for gas usage using regression analysis techniques with time and seasonal components.
- Create dummy variables to represent the categorical variable for month.
Decomposition
- Method to extract trend, seasonal, and random components from a time series.
Linear Programming
- A mathematical technique used to maximize or minimize a linear objective subject to a set of linear constraints.
- Steps in developing a linear optimization model:
- Identify decision variables
- Define objective function
- Identify all constraints
- Write objective function and constraints using mathematical expressions
- Implement the model on a spreadsheet
Example: Identifying the Feasible Region and Optimal Solution
- Visual representation of the feasible region in a linear programming problem.
Corner Points
- Optimal solutions to linear programming problems occur at corner points of the feasible region.
Example: A Spreadsheet Model for Sklenka Skis
- Illustration of a linear programming model for a ski manufacturing company.
Example: Interpreting the SSC Answer Report
- Description and interpretation of spreadsheet output for a linear programming problem (including understanding slack values and other important information).
Example: Sensitivity Analysis for Decision Variables
- Illustrative data interpretation of sensitivity report with an example of what happens when the profit for a given variable is altered.
Example: Sensitivity Analysis for Constraints
- Interpretation of sensitivity report output, including examples of shadow prices for constraints.
Using Sensitivity Information to Evaluate Scenarios
- How changing inputs impacts on a linear programming model outcome.
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Description
Test your understanding of various decision-making strategies, including the minimin and opportunity loss strategies. This quiz includes matching terms and definitions, as well as questions about the decision-making process. Perfect for students and professionals looking to enhance their decision analysis skills.
