Flashcards in Modeling 2 Deck (36):

1

## Decision Analysis - Payoff Table

###
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

2

## Simple Decision Model - without probability

###
- 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

3

## Simple Decision Model - with probability

### - 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

4

## Sensitivity Analysis

### How much leeway to change input until output will change?

5

## Decision Tree

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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"

6

## Decision Making Elements

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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

7

## SciTools Example

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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

8

## Decision Tree Sensitivity Analysis - strategy graphs

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

9

## Tornado Graph

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

10

## Simulation Modeling

###
- describes a real-life situation

- uncertainty controlled by random number inputs to create the simulation

11

## Basic Simulation Model Parts

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1. Inputs - probability distribution, random variables, etc.

2. Model - logic, randomness

3. Outputs - measure performance

12

## Simulation Modeling (Walton Bookstore)

###
- 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)

13

## @Risk Basics

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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)

14

## Walton Bookstore @Risk

###
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)

15

## Walton Bookstore #Risk (triangular)

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Same as regular @Risk but

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

16

## Using @Risk to Find Distro Fit

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- highlight numbers, @Risk distro fit

- confirm with histrogram (using stat tools)

17

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

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- 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

## Forecasting

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

19

## Seven Steps in Forecasting

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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

## "Runs" Test

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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

## "Runs" Test Example (Stereo Sales)

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- 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

## Autocorrelation Test

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Tests for Randomness

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

23

## Autocorrelation Test Example (Stereo Sales)

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- data set manager

- time series and forecasting, autocorrelation

- if any of the lags are bold, suggests correlation and the data is not random

24

## Random Walk

### - finding if the differences in the data are random (not the data itself)

25

##
Random Walk Example (Tractor Closing Prices)

###
- 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

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

### - last point of data you have + mean of differences*periods out

27

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

###
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

## Autoregressive Models

### If significant auto correlation appears, suggest regress time series

29

## Autoregressive Models Example (Hammer Sales)

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- 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

## Forecasting using Autoregressive Model (Hammer Sales)

###
- plug lag1 (last data point you have) into formula

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

31

## Quality of Forecasts using Random Walk & Autoregressive Models

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- error measurement in actual versus forecasted - the difference of the two = residuals

- the smaller the residuals, the better the forecast

32

## Mean Absolute Error

### - mean of the absolute values of the residuals - the smaller this number, the better the fit of the data to the regression

33

## Calculation of the Error

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- 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

## Moving Average Example (Hammer Sales)

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- 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

## Exponential Smoothing

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- 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