Exam 2 Bus. Spread. Modeling

Decision alternatives

the choices available

Uncertain events (states of nature)

things that may occur after the decision, along with their outcomes

Payoffs

the value of each combination of decision and outcome, usually summarized in a payoff table (rows = alternatives, columns = outcomes)

Maximax

Optimistic- Find the best payoff in each row, then choose the row with the largest of those

Maximin

Pessimistic/conservative- Find the worst payoff in each row, then choose the row with the largest of those

Minimax

Used for cost tables- Find the worst (largest) cost in each row, then choose the row with the smallest of those. It is the cost version of maximin.

Minimax regret

Avoid regret- Build a regret (opportunity loss) table, find the maximum regret in each row, then choose the row with the smallest of those

Average payoff

Treat all outcomes as equally likely- Average each row, then choose the highest

Regret (opportunity loss)

best payoff in that outcome’s column − the payoff you actually got

Expected value strategy

weight each payoff by its probability, sum across the row, and choose the alternative with the highest expected value

Expected opportunity loss

weight the regrets by probability and sum. Choose the alternative with the lowest value. It always points to the same decision as the expected value strategy

Expected opportunity loss

weight the regrets by probability and sum. Choose the alternative with the lowest value. It always points to the same decision as the expected value strategy

EVPI (Expected Value of Perfect Information)

the most you’d pay for a perfect prediction of the outcome.

= (expected payoff with perfect information) − (best expected value without it)

also equals the minimum expected opportunity loss.

EVSI (Expected Value of Sample Information)

the value of imperfect information, such as a market survey or test.

= (expected value with the sample information) − (expected value without it)

EVSI ≤ EVPI always. If the information costs more than its EVSI, don’t buy it.

Decision trees

A graphical model of sequential decisions and uncertain events.

Decision node (square)

a point where you choose

Event node (circle)

a point where chance determines the outcome

Branches

the lines leaving a node, each representing an alternative or outcome

Decision strategy

a plan specifying which decision to make at every decision node, depending on how events unfold

Solving the tree

work backward (right to left). At event nodes, calculate expected values. At decision nodes, pick the best branch

Certainty equivalent

the guaranteed amount a decision maker considers equally attractive to a risky gamble

Risk-averse

certainty equivalent < expected value

Risk-neutral

certainty equivalent = expected value

Risk-seeking

certainty equivalent > expected value

Historical analogy

forecast something new by comparing it to a similar past situation (e.g., predicting sales of a new product from the launch of a similar one)

Delphi method

a panel of experts gives forecasts anonymously. Results are summarized and shared back, and the experts revise. This repeats until the group reaches consensus. Anonymity prevents one dominant person from swaying everyone.

Indicator

a measure believed to influence or predict the variable you want to forecast (e.g., housing permits as an indicator of future construction demand).

Index

a quantitatively developed indicator, often a composite of several measures (e.g., Dow Jones Industrial Average, S&P 500, inflation/consumer price index).

Statistical forecasting models

use historical time series data

Time series

Historical data recorded in order over time (hourly, daily, weekly, monthly, yearly)

Stationary time series

Fluctuates around a constant mean with no trend or seasonality. The variation is just random.

Trend

Gradual, long-term upward or downward movement

Seasonal effect

Pattern that repeats at fixed intervals (e.g., holiday retail spikes every December)

Cyclical effect

Rises and falls over longer periods, usually several years, with no fixed length (e.g., business cycles, recessions)

Seasonal vs. cyclical

seasonal is regular and predictable in length. Cyclical is longer and irregular in length

Simple moving average

Averages the most recent k actual values to forecast the next period, which smooths out random fluctuations.

Simple moving average formula

F(t+1) = (A_t + A_(t-1) + … + A_(t-k+1)) / k

Larger k gives a smoother forecast that reacts more slowly.

Smaller k reacts faster but is noisier.

Simple exponential smoothing

A short-range forecasting technique for stationary data. It uses a smoothing constant (α), with 0 ≤ α ≤ 1.

Simple exponential smoothing formula

F(t+1) = F_t + α(A_t − F_t)