Crystal Ball Hillier Chap 16 05-04-07

8/3/2019 Crystal Ball Hillier Chap 16 05-04-07

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© The McGraw-Hill Companies, Inc., 200316.1McGraw-Hill/Irwin

Freddie the Newsboy

• Freddie runs a newsstand in a prominent downtown location of a major city.

• Freddie sells a variety of newspapers and magazines. The most expensive of

the newspapers is the Financial Journal .

• Cost data for the Financial Journal:

– Freddie pays $1.50 per copy delivered. – Freddie charges $2.50 per copy.

– Freddie’s refund is $0.50 per unsold copy.

• Sales data for the Financial Journal:

– Freddie sells anywhere between 40 and 70 copies a day.

– The frequency of the numbers between 40 and 70 are roughly equal.


Spreadsheet Model for Applying Simulation

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Freddie the Newsboy

Data

Uni t Sale Price $2.50Uni t Purchase Cost $1.50Uni t Salvage Value $0.50

Decision VariableOrder Quantity 60

Simulation Minimum MaximumSimu la ted Demand 55 Uniform 40 70Demand ( rounded ) 55

Sales Revenue $137.50Purchasing Cost $90.00

Sal vage Va lue $2.50

Profit $50.00


Application of Crystal Ball

• Four steps must be taken to use Crystal Ball on a spreadsheet model:

1. Define the random input cells.

2. Define the output cells to forecast.

3. Set the run preferences.

4. Run the simulation.


Step 1: Define the Random Input Cells

• A random input cell is an input cell that has a random value.

• An assumed probability distribution must be entered into the cell rather than a

single number.

• Crystal Ball refers to each such random input cell as an assumption cell.

• Procedure to define an assumption cell:

1. Select the cell by clicking on it.

2. If the cell does not already contain a value, enter any number into the cell.

3. Click on the Define Assumption button (first button in Crystal Ball toolbar).

4. Select a probability distribution from the Distribution Gallery.

5. Click OK to bring up the dialogue box for the selected distribution.

6. Use the dialogue box to enter parameters for the distribution (preferably referring

to cells on the spreadsheet that contain these parameters).

7. Click on OK.


The Crystal Ball Toolbar

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Crystal Ball Distribution Gallery




Crystal Ball Uniform Distribution Dialogue Box


Static versus Dynamic Option

• When cell references are used to enter parameters for a distribution, the

Distribution Dialogue Box gives a choice between the “Static” option and the

“Dynamic” option.

• The static option means that each cell reference is only evaluated once, at the

beginning of the simulation run, and then each parameter value (e.g., Min and

Max) is used for all trials of the simulation.

• The dynamic option means that each cell reference is evaluated for each

separate trial . This would be needed if the parameter value might change from

trial to trial because it depends on another assumption cell.


Step 2: Define the Output Cells to Forecast

• Crystal Ball refers to the output of a computer simulation as a forecast , since it

is forecasting the underlying probability distribution when it is in operation.

• Each output cell that is being used to forecast a measure of performance is

referred to as a forecast cell.

• Procedure for defining a forecast cell:

1. Select the cell.

2. Click on the Define Forecast button (3rd button) in the Crystal Ball toolbar, which

brings up the Define Forecast dialogue box.

3. This dialogue box can be used to define a name and (optionally) units for the

forecast cell.

4. Click on OK.


Crystal Ball Define Forecast Dialogue Box


Step 3: Set the Run Preferences

• Setting run preferences refers to such things as choosing the number of trials to

run and deciding on other options regarding how to perform the simulation.

• This step begins by clicking on the Run Preferences button on the Crystal Ball

toolbar.

• The Run Preferences dialogue box has six tabs to set various types of options.

• The Trials tab allows you to specify the maximum number of trials to run for

the computer simulation.


The Crystal Ball Run Preferences Dialogue Box




Step #4: Run the Simulation

• To begin running the simulation, click on the Start Simulation button.

• Once started, a forecast window displays the results of the computer

simulation as it runs.

• The following can be obtained by choosing the corresponding option under the

View menu in the forecast window display:

– Frequency chart

– Statistics table

– Percentiles table

– Cumulative chart

– Reverse cumulative chart


The Frequency Chart for Freddie’s Profit


The Statistics Table for Freddie’s Profit


The Percentiles Table for Freddie’s Profit


The Cumulative Chart for Freddie’s Profit


The Reverse Cumulative Chart for Freddie’s Profit




Certainty that Profit ≥ $40


How Accurate Are the Simulation Results?

• An important number provided by the simulation is the mean profit of $46.67.

• This sample average provides an estimate of the true mean of the distribution.

The true mean might be somewhat different than $46.67.

• The mean standard error (on the Statistics Chart) of $0.60 gives some

indication of how accurate the estimate might be. The true mean will typically

(approximately 68% of the time) be within the mean standard error of the

estimated value.

– It is about 68% likely that the true mean profit is between $46.07 and $47.27.

• The mean standard error can be reduced by increasing the number of trials.

However, cutting the mean standard error in half typically requires

approximately ƒour times as many trials.


Precision Control: Expanded Define Forecast Dialogue Box


Results with Precision Control

750 trials were required to get the 95% confidence interval around the mean within $1.


Results with Precision Control

This table shows the precision obtained for the various percentiles of profit after 750 trials.


Choosing the Right Distribution

• A continuous distribution is used if any values are possible, including both

integer and fractional numbers, over the entire range of possible values.

• A discrete distribution is used if only certain specific values (e.g., only some

integer values) are possible.

• However, if the only possible values are integer numbers over a relatively

broad range, a continuous distribution may be used as an approximation by

rounding any fractional value to the nearest integer.




A Popular Central-Tendency Distribution: Normal

• Some value most likely (the mean)• Values close to mean more likely• Symmetric (as likely above as below mean)• Extreme values possible, but rare


A Popular Central-Tendency Distribution: Triangular

• Some value most likely• Values close to most likely value more common• Can be asymmetric• Fixed upper and lower bound


The Uniform Distribution

• Fixed minimum and maximum value• All values equally likely


Historical Demand Data for the Financial Times

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Freddie the Newsboy Historical

DemandData Day Data

Unit Sale Price $2.50 1 62Unit Purchase Cost $1.50 2 45Unit Salvage Value $0.50 3 59

4 65Decision Variable 5 50

Order Quantity 60 6 647 56

Simulation 8 51Simulated Demand 55 9 55Demand (rounded) 55 10 61

11 40Sales Revenue $137.50 12 47

Purchasing Cost $90.00 13 63Salvage Value $2.50 14 68

15 67

Profit $50.00 16 67

17 68

55 4156 4257 6458 4559 5960 70


Procedure for Fitting the Best Distribution to Data

1. Gather the data needed to identify the best distribution to enter into an assumptioncell.

2. Enter the data into the spreadsheet containing your simulation model.

3. Select the cell that you want to define as an assumption cell that contains thedistribution that best fits the data.

4. Choose Define Assumption from the Crystal Ball toolbar, which brings up theDistribution Gallery dialogue box.

5. Click the Fit button on the dialogue box, which brings up the Fit Distributiondialogue box.

6. Use the Range box in this dialogue box to enter the range of the historical data inyour worksheet.

7. Click the Next button in the dialogue box, which brings up the Second FitDistribution Dialogue box.


Procedure for Fitting the Best Distribution to Data

8. Use this dialogue box to specify which continuous distributions are being considered

for fitting. (Discrete distributions are not considered by this procedure.)

9. Also use this dialogue box to select which ranking method shouldbe used to

evaluate how well a distribution fits the data. (The default is the chi-square test.)

10. Click OK, which brings up the comparison chart that identifies the distribution

(including its parameter values) that best fits the data.

11. If desired, the Next Distribution button can be clicked repeatedly for identifying the

other types of distributions that are next in line for fitting the data well.

12. After choosing the distribution that you want to use, click the Accept button while

that distribution is showing. This will enter the appropriate parameters into the

dialogue box for this distribution. Clicking OK then enters this distribution into the

assumption cell.




The First Fit Distribution Dialogue Box


The Second Fit Distribution Dialogue Box


Comparison Chart Showing Best Fit


Decision Making with Decision Tables

• Many simulation models include at least one decision variable

– Examples: Order quantity, Bid, Number of reservations to accept

• Crystal Ball can be used to evaluate a particular value of the decision variable

by providing a wealth of output for the forecast cells.

• However, this approach does not identify an optimal solution for the decision

variable(s).

• Trial and error can be used to try different values of the decision variable(s).

– Run a simulation for each, and see which one provides the best estimate of the

chosen measure of performance.

• The Decision Table tool in Crystal Ball does this approach in a systematic

way.


Procedure for Defining a Decision Variable

1. Select the cell containing the decision variable.

2. If the cell does not already contain a value, enter any number into the cell.

3. Click on the Define Decision button in the Crystal Ball toolbar, which brings

up the Define Decision Variable dialogue box.

4. Enter the lower and upper limit of the range of values to be simulated for the

decision variable.

5. Click on either Continuous or Discrete to define the type of variable.

6. If Discrete is selected in Step 5, use the Step box to specify the difference

between the successive possible values (not j ust those to be simulated).

7. Click on OK.


Define Decision Variable Dialogue Box




Decision Table: Specify Target Cell


Decision Table: Specify Decision Variable(s) to Vary


Decision Table: Specify Options


The Decision Table for Freddie’s Order Quantity


Overlay Chart Comparing Order Quantities of 55 and 60


Trend Chart for Freddie’s Order Quantity

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Crystal Ball Hillier Chap 16 05-04-07