Table of Contents
Chapter 16 (Computer Simulation with Crystal Ball)
A Case Study: Freddie the Newsboy’s Problem (Section 16.1)
Bidding for a Construction Project (Section 16.2)
Project Management: Reliable Construction Co. (Section 16.3)
Cash Flow Management: Everglade Golden Years Co. (Section 16.4)
Financial Risk Analysis: Think-Big Development Co. (Section 16.5)
Revenue Management in the Travel Industry (Section 16.6)
Choosing the Right Distribution (Section 16.7)
Decision Making with Decision Tables (Section 16.8)
Optimizing with OptQuest (Section 16.9)
16.2–16.24
16.25–16.31
16.32–16.43
16.44–16.49
16.50–16.55
16.56–16.61
16.62–16.83
16.84–16.99
16.100–16.118
Monte-Carlo Simulation with Crystal Ball (UW Lecture)
16.119–16.137
These slides are based upon a lecture from the MBA core course in Management Science at the
University of Washington (as taught by one of the authors).
McGraw-Hill/Irwin
16.1
© The McGraw-Hill Companies, Inc., 2003
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.
McGraw-Hill/Irwin
16.2
© The McGraw-Hill Companies, Inc., 2003
Spreadsheet Model for Applying Simulation
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
B
C
D
E
F
Uniform
Minimum
40
Maximum
70
Freddie the Newsboy
Unit Sale Price
Unit Purchase Cost
Unit Salv age Value
Order Quant ity
Simulated Dem and
Demand (rounded)
Sales Rev enue
Purchasing Cost
Salv age Value
McGraw-Hill/Irwin
Prof it
Data
$2. 50
$1. 50
$0. 50
Deci si on Var iable
60
Simulation
55
55
$137.50
$90.00
$2. 50
$50.00
16.3
© The McGraw-Hill Companies, Inc., 2003
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.
McGraw-Hill/Irwin
16.4
© The McGraw-Hill Companies, Inc., 2003
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.
2.
3.
4.
5.
6.
Select the cell by clicking on it.
If the cell does not already contain a value, enter any number into the cell.
Click on the Define Assumption button (first button in Crystal Ball toolbar).
Select a probability distribution from the Distribution Gallery.
Click OK to bring up the dialogue box for the selected distribution.
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.
McGraw-Hill/Irwin
16.5
© The McGraw-Hill Companies, Inc., 2003
F orec a
st
D ec isio
n
As s um
pt ion
McGraw-Hill/Irwin
16.6
© The McGraw-Hill Companies, Inc., 2003
C ry s tal
Ball He
lp
ata
R eport
Ex trac t
D
C rea te
Ch art
hart
Sens itiv
ity
T re nd C
Chart
t Windo
ws
Ov erla
y
F oecas
Single
S tep
R eset S
imu la tio
n
Sto p S
imulat io
n
Sta rt S
im ulatio
n
R un Pr
efe ren c
es
C le ar D
at a
Pas te D
at a
C opy D
at a
Selec t
F orec a
st s
Selec t
D ec isio
ns
Selec t
A ss um
pt ions
D efine
D efine
D efine
The Crystal Ball Toolbar
Crystal Ball Distribution Gallery
McGraw-Hill/Irwin
16.7
© The McGraw-Hill Companies, Inc., 2003
Crystal Ball Uniform Distribution Dialogue Box
McGraw-Hill/Irwin
16.8
© The McGraw-Hill Companies, Inc., 2003
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.
McGraw-Hill/Irwin
16.9
© The McGraw-Hill Companies, Inc., 2003
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.
McGraw-Hill/Irwin
16.10
© The McGraw-Hill Companies, Inc., 2003
Crystal Ball Define Forecast Dialogue Box
McGraw-Hill/Irwin
16.11
© The McGraw-Hill Companies, Inc., 2003
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.
McGraw-Hill/Irwin
16.12
© The McGraw-Hill Companies, Inc., 2003
The Crystal Ball Run Preferences Dialogue Box
McGraw-Hill/Irwin
16.13
© The McGraw-Hill Companies, Inc., 2003
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
McGraw-Hill/Irwin
16.14
© The McGraw-Hill Companies, Inc., 2003
The Frequency Chart for Freddie’s Profit
McGraw-Hill/Irwin
16.15
© The McGraw-Hill Companies, Inc., 2003
The Statistics Table for Freddie’s Profit
McGraw-Hill/Irwin
16.16
© The McGraw-Hill Companies, Inc., 2003
The Percentiles Table for Freddie’s Profit
McGraw-Hill/Irwin
16.17
© The McGraw-Hill Companies, Inc., 2003
The Cumulative Chart for Freddie’s Profit
McGraw-Hill/Irwin
16.18
© The McGraw-Hill Companies, Inc., 2003
The Reverse Cumulative Chart for Freddie’s Profit
McGraw-Hill/Irwin
16.19
© The McGraw-Hill Companies, Inc., 2003
Certainty that Profit ≥ $40
McGraw-Hill/Irwin
16.20
© The McGraw-Hill Companies, Inc., 2003
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.
McGraw-Hill/Irwin
16.21
© The McGraw-Hill Companies, Inc., 2003
Precision Control: Expanded Define Forecast Dialogue Box
McGraw-Hill/Irwin
16.22
© The McGraw-Hill Companies, Inc., 2003
Results with Precision Control
750 trials were required to get the 95% confidence interval around the mean within $1.
McGraw-Hill/Irwin
16.23
© The McGraw-Hill Companies, Inc., 2003
Results with Precision Control
This table shows the precision obtained for the various percentiles of profit after 750 trials.
McGraw-Hill/Irwin
16.24
© The McGraw-Hill Companies, Inc., 2003
Bidding for a Project: Reliable Construction Co.
•
Reliable Construction Co. is bidding to construct a new plant for a major
manufacturer.
•
Reliable estimates the cost of the project to be $4.55 million, There also is an
additional cost of approximately $50,000 for preparing the bid.
•
Three other construction companies also were invited to submit bids for the
project.
– Competitor 1 is known to use a 30 percent profit margin, but are unpredictable
bidders because of an inability to accurately estimate the true cost of the project.
Previous bids have ranged from 5% below the expected cost to 60% above.
– Competitor 2 uses a 25% profit margin, but is more accurate at predicting the true
cost. In the past, they have missed this profit margin by up to 15% in either
direction.
– Competitor 3 is unusually accurate in estimating project cost. It is equally likely to
set its profit margin anywhere between 20% and 30%.
Question: How much should Reliable bid for this project?
McGraw-Hill/Irwin
16.25
© The McGraw-Hill Companies, Inc., 2003
Spreadsheet Model for Applying Computer Simulation
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
B
C
D
E
Competitor 2
5.688
Competitor 3
5.688
Reliable Construction Co. Contract Bidding
Data
Our Project Cost ($million)
Our Bid Cost ($million)
Competitor Bids
Bid ($million)
Distribution
4.550
0.050
Competitor 1
5.839
Triangular
Triangular
Competitor Distribution Parameters (Proportion of Our Project Cost)
Minimum
95%
110%
Most Likely
130%
125%
Maximum
160%
140%
Competitor Distribution Parameters ($millions)
Minimum
4.323
Most Likely
5.915
Maximum
7.280
McGraw-Hill/Irwin
Minimum Competitor
Bid ($million)
5.688
Our Bid ($million)
5.400
Win Bid?
Profit ($million)
1
5.005
5.688
6.370
Uniform
120%
130%
5.460
5.915
(1=y es, 0=no)
0.800
16.26
© The McGraw-Hill Companies, Inc., 2003
Triangular Distribution for Competitor 2
McGraw-Hill/Irwin
16.27
© The McGraw-Hill Companies, Inc., 2003
Frequency Chart for Reliable’s Bidding Problem
McGraw-Hill/Irwin
16.28
© The McGraw-Hill Companies, Inc., 2003
Statistics Table for Reliable’s Bidding Problem
McGraw-Hill/Irwin
16.29
© The McGraw-Hill Companies, Inc., 2003
Percentiles Table for Reliable’s Bidding Problem
McGraw-Hill/Irwin
16.30
© The McGraw-Hill Companies, Inc., 2003
Cumulative Chart for Reliable’s Bidding Problem
McGraw-Hill/Irwin
16.31
© The McGraw-Hill Companies, Inc., 2003
Project Management: Reliable Construction Co.
•
Reliable Construction Co. has won the bid to construct a new plant for a major
manufacturer.
•
The contract includes a large penalty if construction is not completed by the
deadline 47 weeks from now.
•
There are 14 tasks that need to be completed to finish the project.
– (a) excavate, (b) foundation, (c) rough wall, (d) roof, (e) exterior plumbing,
(f) interior plumbing, (g) exterior siding, (h) exterior painting, (i) electrical work,
(j) wallboard, (k) flooring, (l) interior painting, (m) exterior fixtures, (n) interior
fixtures.
– For each task, three estimates of their completion time have been made—a mostlikely, an optimistic, and a pessimistic estimate
Question: What is the probability that the project will complete by the
deadline?
McGraw-Hill/Irwin
16.32
© The McGraw-Hill Companies, Inc., 2003
Project Network for Reliable Construction Co.
Activity Code
ST ART 0
A
A. Excavate
2
B. Foundation
C. Rough wall
D. Roof
B 4
E. Exterior plumbing
C
F. Interior plumbing
10
G. Exterior siding
H. Exterior painting
D
E 4
6
I
I. Electrical work
7
J. Wallboard
K. Flooring
L. Interior painting
G
F 5
7
M. Exterior fixtures
N. Interior fixtures
J
H
8
9
K 4
L
5
M 2
N
FINISH
McGraw-Hill/Irwin
6
0
16.33
© The McGraw-Hill Companies, Inc., 2003
The Triangular Distribution for an Activity Duration
T riangular dist ribution
0
o
m
p
Elapsed t ime
McGraw-Hill/Irwin
16.34
© The McGraw-Hill Companies, Inc., 2003
Spreadsheet Model for Applying Computer Simulation
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
B
C
D
E
F
G
H
I
Activ ity
Time
(triangular )
2
4.5
11
6.5
3.5
6
7.5
10
6.5
7
4
4.5
2
6.5
Finish
Time
2
6.5
17.5
24
21
27
31.5
41.5
24
34
38
38.5
43.5
45
Simulation of Reliable Construction Co. Project
Activ ity
A
B
C
D
E
F
G
H
I
J
K
L
M
N
McGraw-Hill/Irwin
Immediate
Predecessor
Ğ
A
B
C
C
E
D
E, G
C
F, I
J
J
H
K, L
Time Estimates
o
m
p
1
2
3
2
3.5
8
6
9
18
4
5.5
10
1
4.5
5
4
4
10
5
6.5
11
5
8
17
3
7.5
9
3
9
9
4
4
4
1
5.5
7
1
2
3
5
5.5
9
Start
Time
0
2
6.5
17.5
17.5
21
24
31.5
17.5
27
34
34
41.5
38.5
Project Completion
16.35
45
© The McGraw-Hill Companies, Inc., 2003
The Triangular Distribution Dialogue Box
McGraw-Hill/Irwin
16.36
© The McGraw-Hill Companies, Inc., 2003
The Frequency Chart for Reliable’s Project Duration
McGraw-Hill/Irwin
16.37
© The McGraw-Hill Companies, Inc., 2003
The Statistics Table for Reliable’s Project Duration
McGraw-Hill/Irwin
16.38
© The McGraw-Hill Companies, Inc., 2003
The Percentiles Table for Reliable’s Project Duration
McGraw-Hill/Irwin
16.39
© The McGraw-Hill Companies, Inc., 2003
Probability of Meeting the Project Deadline
McGraw-Hill/Irwin
16.40
© The McGraw-Hill Companies, Inc., 2003
Probability of Meeting the Project Deadline
McGraw-Hill/Irwin
16.41
© The McGraw-Hill Companies, Inc., 2003
Calculate Sensitivity Option
McGraw-Hill/Irwin
16.42
© The McGraw-Hill Companies, Inc., 2003
The Sensitivity Chart for Reliable’s Project
McGraw-Hill/Irwin
16.43
© The McGraw-Hill Companies, Inc., 2003
Cash Flow Management: Everglade Golden Years Co.
•
Because of a temporary decline in business and some current or future
construction costs, the company is facing some negative cash flows in the next
few years.
•
A long-term (10-year) loan can be taken now at a 7% annual interest rate.
•
A series of short-term (1-year) loans can be taken as needed at 10% interest.
•
The cash flows over the next 10 years are not certain. For each year, an
estimate of the minimum, most-likely, and maximum cash flow has been made.
Question: How large of a long-term loan should Everglade take out now?
McGraw-Hill/Irwin
16.44
© The McGraw-Hill Companies, Inc., 2003
Projected Net Cash Flows
McGraw-Hill/Irwin
Year
Projected Net Cash Flow
(millions of dollars)
2003
–8
2004
–2
2005
–4
2006
3
2007
6
2008
3
2009
–4
2010
7
2011
–2
2012
10
16.45
© The McGraw-Hill Companies, Inc., 2003
Linear Programming Spreadsheet Model
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
B
C
D
E
F
G
H
I
J
LT
Pay back
ST
Pay back
-6.649
-0.851
-3.401
-8.207
-6.493
-1.607
0.000
-3.699
0.000
0.000
0.000
Ending
Balance
0.500
0.500
0.500
0.500
0.500
1.266
0.500
2.965
0.500
10.035
2.920
K
L
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
Minimum
Balance
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
Everglade Cash Flow Management Problem
LT Rate
ST Rate
7%
10%
Start Balance
Minimum Cash
1
0.5
Y ear
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
McGraw-Hill/Irwin
Cash
Flow
-8
-2
-4
3
6
3
-4
7
-2
10
(all cash f igures in millions of dollars)
LT
Loan
6.649
ST
Loan
0.851
3.401
8.207
6.493
1.607
0.000
3.699
0.000
0.000
0.000
LT
Interest
ST
Interest
-0.465
-0.465
-0.465
-0.465
-0.465
-0.465
-0.465
-0.465
-0.465
-0.465
-0.085
-0.340
-0.821
-0.649
-0.161
0.000
-0.370
0.000
0.000
0.000
16.46
© The McGraw-Hill Companies, Inc., 2003
Spreadsheet Model for Applying Computer Simulation
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
B
C
D
E
F
G
H
I
J
K
L
M
N
Balance
Bef ore
ST Loan
-0.35
-2.57
-7.01
-4.89
0.11
2.60
-1.86
5.10
3.64
14.17
7.05
ST
Loan
0.85
3.07
7.51
5.39
0.39
0.00
2.36
0.00
0.00
0.00
Ending
Balance
0.50
0.50
0.50
0.50
0.50
2.60
0.50
5.10
3.64
14.17
7.05
O
P
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
>=
Minimum
Balance
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
Everglade Cash Flow Management Problem When Applying Simulation
LT Rate
ST Rate
7%
10%
Start Balance
Minimum Cash
1
0.5
Y ear
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
Cash Flow (Triangular Distribution)
Most
Minimum
Likely
Maximum
-9
-8
-7
-4
-2
1
-7
-4
0
0
3
7
3
6
9
1
3
5
-6
-4
-2
4
7
12
-5
-2
4
5
10
18
McGraw-Hill/Irwin
(all cash f igures in millions of dollars)
Simulated
Cash
Flow
-8.00
-1.67
-3.67
3.33
6.00
3.00
-4.00
7.67
-1.00
11.00
LT
Loan
6.65
LT
Interest
ST
Interest
-0.47
-0.47
-0.47
-0.47
-0.47
-0.47
-0.47
-0.47
-0.47
-0.47
-0.09
-0.31
-0.75
-0.54
-0.04
0
-0.24
0
0
0
16.47
LT
Pay back
ST
Pay back
-6.65
-0.85
-3.07
-7.51
-5.39
-0.39
0
-2.36
0
0
0
© The McGraw-Hill Companies, Inc., 2003
Frequency Chart for Everglade’s Ending Balance
McGraw-Hill/Irwin
16.48
© The McGraw-Hill Companies, Inc., 2003
Cumulative Chart for Everglade’s Ending Balance
McGraw-Hill/Irwin
16.49
© The McGraw-Hill Companies, Inc., 2003
Financial Risk Analysis: Think-Big Development Co.
•
The Think-Big Development Co. is a major investor in commercial real estate
development projects.
•
It has been considering taking a share in three large construction projects—a
high-rise office building, a hotel, and a shopping center.
•
In each case, three years will be spent in construction, they will retain
ownership for another three years while establishing the property, and then sell
the property in the seventh year.
•
Proposal: Don’t take any share in the high-rise, take a 16.5% share of the
hotel, and take a 13.11% share of the shopping center.
•
Management wants risk analysis to be performed (with computer simulation)
to obtain a risk profile (frequency distribution) of what the total NPV might
turn out to be for this proposal.
McGraw-Hill/Irwin
16.50
© The McGraw-Hill Companies, Inc., 2003
Estimated Cash Flows for 100 Percent Share
Hotel Project
Shopping Center Project
Year
Cash Flow ($1,000,000s)
Year
Cash Flow ($1,000,000s)
0
–80
0
–90
1
Normal (–80, 5)
1
Normal (–50, 5)
2
Normal (–80, 10)
2
Normal (–20, 5)
3
Normal (–70, 15)
3
Normal (–60, 10)
4
Normal (+30, 20)
4
Normal (+15, 15)
5
Normal (+40, 20)
5
Normal (+25, 15)
6
Normal (+50, 20)
6
Normal (+40, 15)
7
Uniform (200, 844)
7
Uniform (160, 600)
McGraw-Hill/Irwin
16.51
© The McGraw-Hill Companies, Inc., 2003
Spreadsheet Model for Applying Computer Simulation
A
B
C
D
3
Proj ect Si mulated
4
Cash Fl ow
5 Hotel Pr oject:
($mi lli ons)
6
Construction Costs:
Y ear 0
-80
7
Y ear 1
-80
8
Y ear 2
-80
9
Y ear 3
-70
10
Revenue per Share
Y ear 4
30
11
Y ear 5
40
12
Y ear 6
50
13
Selling Price per Share
Y ear 7
522
14
15 Shopping Center Project
16
Construction Costs:
Y ear 0
-90
17
Y ear 1
-50
18
Y ear 2
-20
19
Y ear 3
-60
20
Revenue per Share
Y ear 4
15
21
Y ear 5
25
22
Y ear 6
40
23
Selling Price per Share
Y ear 7
387.5
24
25
Thi nk Big's
26
Simulated Cash Flow
27
($mi lli ons)
28
Y ear 0
-24.999
29
Y ear 1
-19.755
30
Y ear 2
-15.822
31
Y ear 3
-19.416
32
Y ear 4
6.917
33
Y ear 5
9.878
34
Y ear 6
13. 494
35
Y ear 7
136.931
36
37
Net Present Value ($millions)
18. 120
McGraw-Hill/Irwin
16.52
E
F
G
Normal
Normal
Normal
Normal
Normal
Normal
Uniform
-80
-80
-70
30
40
50
200
5
10
15
20
20
20
844
(mean, st. dev . )
(mean, st. dev . )
(mean, st. dev . )
(mean, st. dev . )
(mean, st. dev . )
(mean, st. dev . )
(min, max)
Normal
Normal
Normal
Normal
Normal
Normal
Uniform
-50
-20
-60
15
25
40
160
5
5
10
15
15
15
615
(mean, st. dev . )
(mean, st. dev . )
(mean, st. dev . )
(mean, st. dev . )
(mean, st. dev . )
(mean, st. dev . )
(min, max)
Hotel
Shopping Center
Cost of Capit al
H
Shar e
16. 50%
13. 11%
10%
© The McGraw-Hill Companies, Inc., 2003
The Normal Distribution Dialogue Box
McGraw-Hill/Irwin
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Risk Profile (Frequency Chart) for Think-Big
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Percentiles Chart for Think-Big
McGraw-Hill/Irwin
16.55
© The McGraw-Hill Companies, Inc., 2003
Transcontinental Airlines Overbooking Problem
•
•
•
•
•
•
•
Transcontinental has a daily flight (excluding weekends) from San Francisco
to Chicago that is mainly used by business travelers.
There are 150 seats available in a single cabin.
The average fare per seat is $300. This is a nonrefundable fare, so no-shows
forfeit the entire fare.
The fixed cost of operating the flight is $30,000.
The average number of reservation requests for this flight has been 195, with a
standard deviation of 30.
Only 80% of passengers with a reservation actually show up to take the flight,
so it makes sense to take more than 150 reservations (overbooking).
If more passengers arrive to take the flight than there are seats, some
passengers must be “bumped”. The total cost (including rebooking, travel
vouchers, and lost goodwill) is estimated to be $450.
Question: How many reservations should Transcontinental accept for this
flight?
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Spreadsheet Model for Applying Computer Simulation
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
B
C
D
E
F
Normal
Mean
195
Standard Dev .
30
Binomial
Tickets
Purchased
190
Probability
to Show up
80%
Ticket Rev enue
Bumping Cost
Fixed Cost
Prof it
$45,000
$900
$30,000
$14,100
Transcontinental Airlines Overbooking
Av ailable Seats
Fixed Cost
Av g. Fare / Seat
Cost of Bumping
Ticket Demand
Demand (rounded)
Reserv ations to Accept
Data
150
$30,000
$300
$450
195
195
190
Number that Show
152
Number of Filled Seats
Number Denied Boarding
150
2
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Binomial Distribution with Dynamic Option for
Number that Show
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Frequency Chart for Profit
McGraw-Hill/Irwin
16.59
© The McGraw-Hill Companies, Inc., 2003
Frequency Chart for Number of Filled Seats
McGraw-Hill/Irwin
16.60
© The McGraw-Hill Companies, Inc., 2003
Frequency Chart for Number Denied Boarding
McGraw-Hill/Irwin
16.61
© The McGraw-Hill Companies, Inc., 2003
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.
McGraw-Hill/Irwin
16.62
© The McGraw-Hill Companies, Inc., 2003
A Popular Central-Tendency Distribution: Normal
•
•
•
•
McGraw-Hill/Irwin
Some value most likely (the mean)
Values close to mean more likely
Symmetric (as likely above as below mean)
Extreme values possible, but rare
16.63
© The McGraw-Hill Companies, Inc., 2003
A Popular Central-Tendency Distribution: Triangular
•
•
•
•
McGraw-Hill/Irwin
Some value most likely
Values close to most likely value more common
Can be asymmetric
Fixed upper and lower bound
16.64
© The McGraw-Hill Companies, Inc., 2003
A Popular Central-Tendency Distribution: Lognormal
•
•
•
•
McGraw-Hill/Irwin
Some value most likely
Positively skewed (below mean more likely)
Values cannot fall below zero
Extreme values (high end only) possible, but rare
16.65
© The McGraw-Hill Companies, Inc., 2003
The Uniform Distribution
•
•
McGraw-Hill/Irwin
Fixed minimum and maximum value
All values equally likely
16.66
© The McGraw-Hill Companies, Inc., 2003
A Three-Parameter Distribution: Weibull
•
•
•
•
•
Random value above some number (location)
Shape > 0 (usually ≤ 10)
Shape < 3 becomes more positively-skewed (below mean more likely) until it
resembles exponential distribution (equivalent at Shape = 1)
Symmetrical at Shape = 3.25, becomes negatively skewed above that
Scale defines width
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
A Three-Parameter Distribution: Beta
•
•
•
•
McGraw-Hill/Irwin
Random value between 0 and some positive number (Scale)
Shape specified using two positive values (alpha, beta)
Alpha < beta: positively skewed (below mean more likely)
Beta < alpha: negatively skewed
16.68
© The McGraw-Hill Companies, Inc., 2003
A Distribution for Random Events: Exponential
•
•
•
Widely used to describe time between random events (e.g., time between arrivals)
Events are independent
Rate = average number of events per unit time (e.g., arrivals per hour)
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
A Distribution for Random Events: Poisson
•
•
•
•
Describes the number of times an event occurs during a given period of time or space
Occurrences are independent
Any number of events is possible
Rate = average number of events per unit of time, assumed constant over time
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Distribution for Number of Times an Event Occurs: Binomial
•
•
•
•
Describes number of times an event occurs in a fixed number of trials (e.g., number of
heads in 10 flips of a coin)
For each trial, only two outcomes are possible
Trials independent
Probability remains the same for each trial
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Distribution for Number of Trials Until Event Occurs: Geometric
•
•
•
•
Describes number of trials until an event occurs (e.g., number of times to spin roulette
wheel until you win)
Probability same for each trial
Continue until succeed
Number of trials unlimited
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Distribution for Number of Trials Until n Events Occur: Negative Binomial
•
•
•
•
•
Describes number of trials until an event occurs n times
Same as geometric when Shape = n = 1
Probability same for each trial
Continue until nth success
Number of trials unlimited
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
The Custom Distribution (Set of Discrete Values)
•
•
•
Enter set of values with varying probabilities
For each discrete value, enter “Value” and “Prob.” (leave other boxes blank)
Clicking Enter clears boxes for entering next discrete value
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
The Custom Distribution (Range of Discrete Values)
•
•
•
•
Enter range of discrete values, each equally likely
Enter lower and upper end of range in “Value” and “Value2”
Enter the total probability for the whole set in “Prob.”
Enter the distance between discrete values in “Step”
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
The Custom Distribution (Continuous Distribution)
•
•
•
•
•
Enter the lower and upper end of range in “Value” and “Value2”
Enter the total probability for the range in “Prob.”
Leave “Step” blank for a continuous distribution
Drag the corners of the distribution graph up or down to change relative probabilities
Dragging corners may affect total probability. Click on “Rescale” to reset total probability.
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
The Custom Distribution (Combination)
•
•
•
Any combination of discrete values, ranges of discrete values, or
continuous distributions can be entered
Input each element, click on Enter, input next element, etc.
If cumulative probabilities do not add to 1, click on “Rescale”
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Historical Demand Data for the Financial Times
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
58
59
60
61
62
63
B
C
D
E
F
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
55
56
57
58
59
60
Historical
Demand
Data
62
45
59
65
50
64
56
51
55
61
40
47
63
68
67
67
68
41
42
64
45
59
70
Freddie the Newsboy
McGraw-Hill/Irwin
Unit Sale Price
Unit Purchase Cost
Unit Salv age Value
Order Quant ity
Simulated Dem and
Demand (rounded)
Data
$2. 50
$1. 50
$0. 50
Deci si on Var iable
60
Simulation
55
55
Sales Rev enue
Purchasing Cost
Salv age Value
$137.50
$90.00
$2. 50
Prof it
$50.00
16.78
© The McGraw-Hill Companies, Inc., 2003
Procedure for Fitting the Best Distribution to Data
1. Gather the data needed to identify the best distribution to enter into an assumption
cell.
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 the
distribution that best fits the data.
4. Choose Define Assumption from the Crystal Ball toolbar, which brings up the
Distribution Gallery dialogue box.
5. Click the Fit button on the dialogue box, which brings up the Fit Distribution
dialogue box.
6. Use the Range box in this dialogue box to enter the range of the historical data in
your worksheet.
7. Click the Next button in the dialogue box, which brings up the Second Fit
Distribution Dialogue box.
McGraw-Hill/Irwin
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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 should be 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.
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
The First Fit Distribution Dialogue Box
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
The Second Fit Distribution Dialogue Box
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Comparison Chart Showing Best Fit
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
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.
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
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 just those to be simulated).
7. Click on OK.
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Define Decision Variable Dialogue Box
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© The McGraw-Hill Companies, Inc., 2003
Decision Table: Specify Target Cell
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Decision Table: Specify Decision Variable(s) to Vary
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Decision Table: Specify Options
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
The Decision Table for Freddie’s Order Quantity
McGraw-Hill/Irwin
16.90
© The McGraw-Hill Companies, Inc., 2003
Overlay Chart Comparing Order Quantities of 55 and 60
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Trend Chart for Freddie’s Order Quantity
McGraw-Hill/Irwin
16.92
© The McGraw-Hill Companies, Inc., 2003
Decision Variable for Reliable’s Bidding Problem
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Decision Table: Specify Target Cell
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Decision Table: Specify Decision Variable
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Decision Table: Specify Options
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Decision Table for Reliable’s Bid
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Decision Table for Transcontinental’s
Reservations to Accept
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Trend Chart for Transcontinental’s
Reservations to Accept
McGraw-Hill/Irwin
16.99
© The McGraw-Hill Companies, Inc., 2003
Optimizing with OptQuest
•
Crystal Ball includes a module called OptQuest that automatically searches
for an optimal solution for a simulation model with any number of decision
variables.
•
The search is conducted by executing a series of simulation runs of leading
candidates to be the actual optimal solution.
•
The results of each run are used to determine the most promising remaining
candidate to try next.
•
A powerful search engine (based on genetic algorithms) conducts an
intelligent and efficient search.
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Recommended Crystal Ball Run Preferences
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Recommended Crystal Ball Run Preferences
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Recommended Crystal Ball Run Preferences
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Procedure for Applying OptQuest
1. Formulate your simulation model on a spreadsheet.
2. Use Crystal Ball to complete your formulation by defining your assumption
cells, forecast cells, and decision variables, as well as setting your run
preferences.
3. Choose OptQuest from the Crystal Ball Tools menu and select New under the
File menu.
4. Use the Decision Variable Selection dialogue box to select your decision
variables.
5.
6.
7.
8.
9.
Use the Constraints dialogue box to specify your constraints (if any).
Use the Forecast Selection dialogue box to specify the running time.
Use the Options dialogue box to specify the running time.
Select Start from the Run menu to run the optimization.
Choose Copy to Excel from the Edit menu to copy your results to your
spreadsheet model.
McGraw-Hill/Irwin
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OptQuest for Freddie’s Problem:
Selecting Variables and Specifying Constraints
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
OptQuest for Freddie’s Problem:
Specifying Objective and Running Time
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
OptQuest Results for Freddie’s Problem
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Project Selection: Tazer Corp.
•
Tazer Corp., a pharmaceutical manufacturing company, is beginning the
search for a breakthrough drug.
•
The following five potential R&D projects have been identified:
– Project Up: Develop a more effective antidepressant that does not cause serious
mood swings.
– Project Stable: Develop a drug that addresses manic depression.
– Project Choice: Develop a less intrusive birth control method for women.
– Project Hope: Develop a vaccine to prevent HIV infection.
– Project Release: Develop a more effective drug to lower blood pressure.
•
$1.2 billion is available (enough for only two or three projects).
Question: Which projects should Tazer Corp. undertake?
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Data for Tazer Corp. Project Selection
Revenue ($millions) if Successful
Project
R&D Investment
($millions)
Success
Rate
Mean
Standard
Deviation
Up
$400
50%
$1,400
$400
Stable
300
35
1,200
400
Choice
600
35
2,200
600
Hope
500
20
3,000
900
Release
200
45
600
200
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Spreadsheet Model for Applying Computer Simulation
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
B
C
D
E
F
G
H
I
J
Success?
0.5
0.35
0.35
0.2
0.45
Rev enue ($millions)
(if Successf ul)
1,400
1,200
2,200
3,000
600
Prof it
0.00
0.00
0.00
0.00
0.00
Decisions
0
0
0
0
0
Budget-Constrained Project Selection
Project
Up
Stable
Choice
Hope
Release
Inv ested
Budget
R&D
Inv estment
($millions)
400
300
600
500
200
Success
Rate
50%
35%
35%
20%
45%
Estimated Rev enue
$millions if Successf ul
(Normal Distribution)
Mean
St. Dev .
1,400
400
1,200
400
2,200
600
3,000
900
600
200
0
<=
1,200
McGraw-Hill/Irwin
Total prof it ($millions)
16.110
0.00
© The McGraw-Hill Companies, Inc., 2003
Binary Decision Variables
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
OptQuest for Tazer’s Project Selection:
Selecting Variables and Specifying Constraints
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
OptQuest for Freddie’s Problem:
Specifying Objective and Running Time
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
OptQuest Results for Tazer’s Project Selection
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Frequency Chart for Tazer’s Total Profit
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Maximizing Probability (Profit ≥ $100 million)
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Maximizing Probability (Profit ≥ $100 million)
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Frequency Chart for Tazer’s Project Selection
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Monte-Carlo Simulation with Crystal Ball
1. Setup Spreadsheet
Build a spreadsheet that will calculate the performance measure (e.g., profit) in
terms of the inputs (random or not). For random inputs, just enter any number.
2. Define Assumptions (Random Variables)
Define which cells are random and what distributions they should follow.
3. Define Forecast (Output or Performance Measure)
Define which cell(s) you are interested in forecasting (typically the performance
measure, e.g., profit).
4. Choose Number of Trials
Select the number of trials. If you would later like to generate the Sensitivity
Analysis chart, choose “Sensitivity Analysis” under Options in Run Preferences.
5. Run Simulation
Run the simulation. If you would like to change parameters and re-run the
simulation, you should “reset” the simulation (click on the “Reset Simulation button
on the toolbar or in the Run menu) first.
6. View Results
The forecast window showing the results of the simulation appears automatically
after (or during) the simulation. Many different results are available (frequency
chart, cumulative chart, statistics, percentiles, sensitivity analysis, and trend chart).
The results can be copied into the worksheet.
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
F orec a
st
D ec isio
n
As s um
pt ion
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© The McGraw-Hill Companies, Inc., 2003
C ry s tal
Ball He
lp
ata
R eport
Ex trac t
D
C rea te
Ch art
hart
Sens itiv
ity
T re nd C
Chart
t Windo
ws
Ov erla
y
F oecas
Single
S tep
R eset S
imu la tio
n
Sto p S
imulat io
n
Sta rt S
im ulatio
n
R un Pr
efe ren c
es
C le ar D
at a
Pas te D
at a
C opy D
at a
Selec t
F orec a
st s
Selec t
D ec isio
ns
Selec t
A ss um
pt ions
D efine
D efine
D efine
The Crystal Ball Toolbar
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.
McGraw-Hill/Irwin
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Step #1 (Setup Spreadsheet)
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
B
C
D
E
F
Uniform
Minimum
40
Maximum
70
Freddie the Newsboy
Unit Sale Price
Unit Purchase Cost
Unit Salv age Value
Order Quant ity
Simulated Dem and
Demand (rounded)
Sales Rev enue
Purchasing Cost
Salv age Value
McGraw-Hill/Irwin
Prof it
Data
$2. 50
$1. 50
$0. 50
Deci si on Var iable
60
Simulation
55
55
$137.50
$90.00
$2. 50
$50.00
16.122
© The McGraw-Hill Companies, Inc., 2003
Step #2 (Define Assumptions)
•
Select a cell that contains a random variable.
•
Click on the “Define Assumptions” button in the toolbar (or in Cell menu):
•
Select the type of distribution.
•
Provide the parameters of the distribution.
McGraw-Hill/Irwin
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Step #2 (Define Assumptions)
McGraw-Hill/Irwin
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Step #2 (Define Assumptions)
McGraw-Hill/Irwin
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Step #3 (Define Forecast)
•
Select the cell that contains the output variable to forecast.
•
Click on the “Define Forecast” button in the toolbar (or in the Cell menu):
Fill in the Define Forecast dialogue box:
McGraw-Hill/Irwin
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Step #4 (Choose Number of Trials)
•
Click on the “Run Preferences” button in the toolbar (or in the Run menu):
•
Select the number of trials to run:
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Step #5 (Run Simulation)
Click on the “Start Simulation” button in the toolbar (or Run in the Run menu):
McGraw-Hill/Irwin
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Step #6 (View Results)
The results of the simulation can be viewed in a variety of different ways
(frequency chart, cumulative chart, statistics, and percentiles). Choose different
options under the View menu in the forecast window.
McGraw-Hill/Irwin
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Step #6 (View Results)
The results can be copied into a worksheet or Word document (choose Copy under
the Edit menu in the simulation output window).
McGraw-Hill/Irwin
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© The McGraw-Hill Companies, Inc., 2003
Step #6 (View Results)
McGraw-Hill/Irwin
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Step #6 (View Results)
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Certainty that Profit ≥ $40
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Fitting a Distribution
•
Crystal Ball can be used to “fit” a distribution to data.
•
The following data has been collected for the previous 100 phone calls to a
mail-order house:
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
99
100
101
102
103
104
B
C
D
E
Arriv al
(minutes)
8.22
12.25
12.27
16.26
18.06
18.87
23.46
23.53
28.73
30.56
194.02
195.48
195.87
196.84
197.81
200.43
Interarriv al
Time
8.22
4.03
0.02
3.98
1.81
0.81
4.58
0.08
5.20
1.83
0.28
1.46
0.38
0.98
0.97
2.61
Length of Call
(minutes)
3.77
4.53
4.04
3.70
5.38
4.36
4.41
5.14
4.76
4.68
4.26
3.37
4.45
5.06
5.20
4.25
F
G
H
I
Phone Data
Customer #
1
2
3
4
5
6
7
8
9
10
95
96
97
98
99
100
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Av erages
Simulation
Interarriv al Length of Call
(minutes)
Time
4.51
2.004
2
4
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Using Crystal Ball to Fit Data to a Distribution
1. Select a spreadsheet cell for which you want to fit a distribution.
2. Choose Define Assumption.
3. Click the Fit button, then select the source of the fitted data.
4. Click the Next button, then select the distributions to try to fit.
5. Click OK.
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Best Fit for the Interarrival Time
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Best Fit for the Service Time
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16.137
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