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Pace > Modeling 2 > Flashcards

Modeling 2 Flashcards

1
Q

Decision Analysis - Payoff Table

A

Matrix made up of:

  • rows (decisions)
  • columns (payoffs)
  • outcomes (states of nature - beyond control)
  • probabilities (what’s the chance - a reasonable estimate - that outcome will occur) - payoff tables can be with or without probabilities
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2
Q

Simple Decision Model - without probability

A
  • Maximin - Determine Min of all the possible payoffs and find the max of those - conservative
  • Maximax - determine max of all the possible payoffs and find the max of those - aggressive
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3
Q

Simple Decision Model - with probability

A
  • EMV (expected monetary value) - sumproduct(outcomes, $probabilities$) - highest of those is optimal decision - NOT the profit, it’s the average…doesn’t guarantee the best outcome, it’s the most rational outcome
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4
Q

Sensitivity Analysis

A

How much leeway to change input until output will change?

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5
Q

Decision Tree

A

Link cells from input to create tree

  • don’t overwrite number is blue (macros)
  • lock cells for probability (if you’re going to be copying branches)
  • optimal decision is labeled “true”
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6
Q

Decision Making Elements

A
  1. Set of decisions available to decision-maker
  2. Set of possible outcomes and the probabilities of these outcomes
  3. A value model that prescribes results - usually monetary values - for the various combinations and decisions
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7
Q

SciTools Example

A 
Decisions available:
1. submit/don't submit
2. if submit, how much bid?
Possible outcomes:
1. don't submit
2. submit $115K - win
3. submit $115K - lose
4. submit $120K - win
5. submit $120K - lose
etc.
Monetary Value:
1. don't submit - $0
2. submit $115K - win = 115K - money used to prepare bid - money for supplies
3.  submit $115K - lose = loss of money used to prepare bid
etc.
--- Can use payoff table and EMV or decision tree
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8
Q

Decision Tree Sensitivity Analysis - strategy graphs

A

If the decision lines cross, it’s where the optimal decision will change

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9
Q

Tornado Graph

A

variable which is most sensitive (in terms of % change in EMV of optimal decision)

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10
Q

Simulation Modeling

A
  • describes a real-life situation

- uncertainty controlled by random number inputs to create the simulation

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11
Q

Basic Simulation Model Parts

A
  1. Inputs - probability distribution, random variables, etc.
  2. Model - logic, randomness
  3. Outputs - measure performance
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12
Q

Simulation Modeling (Walton Bookstore)

A
  • want to optimize profit in terms of the order quantity
  • complete v-lookup table with cum(P)
  • complete inputs (revenue, profit, etc.)
  • create replications with random numbers
  • find stats based on generated outcomes given random numbers
  • find optimum using:
    1. point estimate - placing the options in the correct cell to see optimal outcome
    2. use statistical inference by freezing the numbers and setting up confidence intervals (note: overlap means there is no difference between the variables! they are both optimal or not)
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13
Q

@Risk Basics

A

Define Distribution - used for special analysis and not creating simulations
Distribution Fitting - takes chi-squared tests and compares it with distributions to find out what type it is
Simulation - perform simulation once you’ve defined the output
Simulation detail statistics - your outputs and what you asked @risk to do - summarized
Simulation Data - actual values (you can copy and paste into spreadsheet to analyze using Stat tools)

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14
Q

Walton Bookstore @Risk

A

Same as simulation modeling but:

  • Demand = riskdiscrete(demand range, probability range)
  • Create output on Profit cell
  • To run for all possible order quantities, order cell = =risksimtable(range of 5 numbers)
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15
Q

Walton Bookstore #Risk (triangular)

A

Same as regular @Risk but

Demand = int(risktriang(min, most likely, max)) - this makes it an integer

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16
Q

Using @Risk to Find Distro Fit

A
  • highlight numbers, @Risk distro fit

- confirm with histrogram (using stat tools)

17
Q

Using @Risk to find Order Size that will maximize profit (Ch. 15 - Problem 19)

A
  • Order Size = risksimtable(range of possible orders)
  • Demand = round(risknormal(mean, SD),0)…round will make it an integer each time
  • Standard Revenue = demand*selling price
  • Standard Cost = order size*order cost
  • Disposal Revenue (when demand is less than the order size - have to dispose of them) = max(diff btw order size and demand,0)*disposal price
  • Reorder Cost (when you don’t have enough cars) = max(diff between demand and order size,0)*reorder cost
  • Profit = standard revenue - standard cost + disposal revenue - reorder cost
  • Create Output for profit cell
  • run all 5 simulations - copy and paste outcome into spreadsheet and run stat tools statistical inference to find the highest confidence interval (that doesn’t overlap)
18
Q

Forecasting

A

underlying basis of all business decisions (production, inventory, personnel, facilities, etc.)

19
Q

Seven Steps in Forecasting

A
  1. Determine use of the forecast
  2. Select the items to be forecasted
  3. Determine the time horizon of the forecast (short-range, medium, long)
  4. Select the forecasting model(s) - e.g. random walk, moving average, linear regression
  5. Gather data
  6. Make the forecast
  7. Validate and implement results
20
Q

“Runs” Test

A

Tests for randomness
H0: Series is Random
Ha: Series is not random
- if p-value is small (.05 or less), can reject the null

21
Q

“Runs” Test Example (Stereo Sales)

A
  • data set manager
  • time series and forecasting, runs test for randomness
  • look at the p-value, if it’s small (.05 or less), can reject the null and the data isn’t random
22
Q

Autocorrelation Test

A

Tests for Randomness

Testing the original data series and comparing it with itself - is a time series related to itself?

23
Q

Autocorrelation Test Example (Stereo Sales)

A
  • data set manager
  • time series and forecasting, autocorrelation
  • if any of the lags are bold, suggests correlation and the data is not random
24
Q

Random Walk

A
  • finding if the differences in the data are random (not the data itself)
25
Q

Random Walk Example (Tractor Closing Prices)

A
  • Does this time series form a Random Walk model?
    data set manager
  • data set manager
  • create the differences - data utilities, difference, closing price, always use the first difference….ok
  • Is this walk random? test with “runs” - ON THE DIFFERENCES
  • P-value is large (>.05), can’t reject the null so the data is random - that implies that this time series forms a random walk model
26
Q

Forecasting Using Random Walk Model (point estimate - Tractor Closing Prices)

A
  • last point of data you have + mean of differences*periods out
27
Q

Forecasting Using Random Walk Model (confidence interval - Tractor Closing Prices)

A

95% LCL = point estimate of the first period out-(z-score 2)Standard error of 1 period out (SD of differences)
95% UCL = point estimate of the first period out+(z-score 2)Standard error of 1 period out (SD of differences)
More than one period:
95% LCL = point estimate of the X period out-(z-score 2)Standard error of X period out (sqrt(X)SD of differences)
95% UCL = point estimate of the X period out+(z-score 2)Standard error of X period out (sqrt(X)SD of differences)

28
Q

Autoregressive Models

A

If significant auto correlation appears, suggest regress time series

29
Q

Autoregressive Models Example (Hammer Sales)

A
  • data set manager
  • run autocorrelation - says data is not random and the data set is related to itself in lag 1, 2 and 3 in a statistically significant sense (they are bolded)
  • original data set, data utilities, lags, want 3 lags
  • create a multiple regression model (regression & classification) where sales is the dependent model and the three lags are the independent variables, check residuals vs. fitted values, ok
  • p-values indicate whether you should adjust the model by discarding any independent variables (if the p-value is above .05, discard)
  • re-do the regression with only the significant models
  • sales = 13.763 + .793(lag1)
30
Q

Forecasting using Autoregressive Model (Hammer Sales)

A
  • plug lag1 (last data point you have) into formula

- OR use excel by creating second “predictive data set” and using regression advanced options

31
Q

Quality of Forecasts using Random Walk & Autoregressive Models

A
  • error measurement in actual versus forecasted - the difference of the two = residuals
  • the smaller the residuals, the better the forecast
32
Q

Mean Absolute Error

A
  • mean of the absolute values of the residuals - the smaller this number, the better the fit of the data to the regression
33
Q

Calculation of the Error

A
  • moving average - used if there’s little or no trend

- weighted moving average - used when there is a trend (treats older data less important than newer data)

34
Q

Moving Average Example (Hammer Sales)

A
  • original data, time series and forecasting, forecast, check sales and fill in settings
  • try different “spans” to get the optimal (where the MAE is at it’s smallest)
35
Q

Exponential Smoothing

A
  • form of weighted moving average (when a trend is present)
  • smoothing constant = alpha - the smaller the alpha, the smoother the forecast (not necessarily the lowest errors and therefore, better fit)
36
Q

Exponential Smoothing with Trend Adjustment

A
  • Holt’s method = when there’s a trend up or down

- Winter’s method = seasonal trend

Pace (13 decks)

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