Modeling 2 Flashcards
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
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
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
Sensitivity Analysis
How much leeway to change input until output will change?
Decision Tree
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”
Decision Making Elements
- Set of decisions available to decision-maker
- Set of possible outcomes and the probabilities of these outcomes
- A value model that prescribes results - usually monetary values - for the various combinations and decisions
SciTools Example
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
Decision Tree Sensitivity Analysis - strategy graphs
If the decision lines cross, it’s where the optimal decision will change
Tornado Graph
variable which is most sensitive (in terms of % change in EMV of optimal decision)
Simulation Modeling
- describes a real-life situation
- uncertainty controlled by random number inputs to create the simulation
Basic Simulation Model Parts
- Inputs - probability distribution, random variables, etc.
- Model - logic, randomness
- Outputs - measure performance
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)
@Risk Basics
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)
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)
Walton Bookstore #Risk (triangular)
Same as regular @Risk but
Demand = int(risktriang(min, most likely, max)) - this makes it an integer
Using @Risk to Find Distro Fit
- highlight numbers, @Risk distro fit
- confirm with histrogram (using stat tools)
Using @Risk to find Order Size that will maximize profit (Ch. 15 - Problem 19)
- 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)
Forecasting
underlying basis of all business decisions (production, inventory, personnel, facilities, etc.)
Seven Steps in Forecasting
- Determine use of the forecast
- Select the items to be forecasted
- Determine the time horizon of the forecast (short-range, medium, long)
- Select the forecasting model(s) - e.g. random walk, moving average, linear regression
- Gather data
- Make the forecast
- Validate and implement results
“Runs” Test
Tests for randomness
H0: Series is Random
Ha: Series is not random
- if p-value is small (.05 or less), can reject the null
“Runs” Test Example (Stereo Sales)
- 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
Autocorrelation Test
Tests for Randomness
Testing the original data series and comparing it with itself - is a time series related to itself?
Autocorrelation Test Example (Stereo Sales)
- data set manager
- time series and forecasting, autocorrelation
- if any of the lags are bold, suggests correlation and the data is not random
Random Walk
- finding if the differences in the data are random (not the data itself)
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
Forecasting Using Random Walk Model (point estimate - Tractor Closing Prices)
- last point of data you have + mean of differences*periods out
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)
Autoregressive Models
If significant auto correlation appears, suggest regress time series
Autoregressive Models Example (Hammer Sales)
- 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)
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
Quality of Forecasts using Random Walk & Autoregressive Models
- error measurement in actual versus forecasted - the difference of the two = residuals
- the smaller the residuals, the better the forecast
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
Calculation of the Error
- 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)
Moving Average Example (Hammer Sales)
- 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)
Exponential Smoothing
- 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)
Exponential Smoothing with Trend Adjustment
- Holt’s method = when there’s a trend up or down
- Winter’s method = seasonal trend
