MS&E 107/207, Midterm Review

The Flaw of the Averages

Mindle 1 / Uncertainty vs. Risk

* Risk is in the eye of the beholder

* Risk reflects how uncertain outcomes cause loss or injury to a particular individual or group * Risk attitude measures the willigness to incur risk in the quest of reward * Different risks to the same uncertainty

Mindle 2 / An uncertain number is a shape

* A distribution

* “Uncertain numbers”

* Risk is subjective

* Give-me-a-number mentality

* Management of uncertainty: “Commitment to trade short-term rewards for long-term gains” * Flat Shape

* To display a distribution: a histogram

* Other important shape: cumulative distribution; shows the probability that the number is less than a given value * The average, mean or expected value; of the uncertain number is the balance point of the distribution * The median; quantify that the uncertain number has a 50/50 change of being greater or less than * The mode is the place at which the histogram has its highest peak, the most likely Mindle 3 / Combinations of uncertain numbers

* A combination of uncertain numbers is a SHAPE that goes up in the middle * This effect arises from diversification (central limit theorem) * What enough independent uncertain numbers are added together, the resulting distribution becomes bell shaped * Normal Distribution -> Highest in the middle, slow in the extremes * Resampling

Standard Deviation = Sigma^2 = Variance

“The balance point of the graph is the average”

Mindle 4 / Jensen’s Inequality

* “Average inputs don’t always yield outputs” *Unless the model is linear * Some times when you plug averages of uncertain values into your plans, its overestimates the average outcome, and sometimes it underestimates the average outcome. Mindle 5 / Interrelated Uncertains

* Diversification -> Reduce risk

Weak form of the Flaw of Averages:

You get the average, but not the risks

Strong form of the Flaw of Averages:

You don’t get anything wrong

Decision Making with Insight

Chapter 1

Profit = Revenue – Expense

Models

* It is much less costly to make mistakes in a model than in real world * A model can yield unexpected insights into real world problems * A model allows you to apply analytical tools not available in the real world * The discipline of building a model forces you to better understand the relationships being modeled and the data required for analysis * A model serves as a mean of communication

Sum product

Data Table:

A data table allows you to repeatedly evaluate a particular formula within the model while systematically varying one or to two input cells on which the formula depends Chapter 2

Uncertain Profit:

The items on which profit depends are:

* Sales in units

* Price per unit

* Unit cost: The marginal cost per unit of production, marketing and sales * Fixed costs: Fixed overhead, advertising, and so on

MonteCarlo Simulation: The Basic Steps

1. Build a model of the uncertain situation

2. Specify the simulation setting

3. Run the simulation and examine the results

* Averages of Uncertain Numbers: Diversification: As uncertain numbers are averaged, uncertainty is reduced. This is known as diversification ad is an important manifestation of the Central Limit Theorem. * Some Important Classes of Uncertain Numbers: Idealized Distributions: There are several important classes of idealized uncertain numbers. The most important of these are normal random variables. * Uncertain Numbers and Bad Outcomes: Risk Management: Uncertainty is and objective feature of the universe. Risk is in the eye of the beholder; it depends on what you are afraid of. Risk management is the attempt to minimize the undesired outcomes of uncertainty.

Random Variables

A random variable is a precise mathematical description of a number that you are uncertain...