Crystal Ball
Simulation of Profit Analysis Model (11 of 15)
Exhibit 14.19
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Crystal Ball
Simulation of Profit Analysis Model (12 of 15)
Exhibit 14.20
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 14-52
Crystal Ball
Simulation of Profit Analysis Model (13 of 15)
Exhibit 14.21
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Crystal Ball
Simulation of Profit Analysis Model (14 of 15)
Exhibit 14.22
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Crystal Ball
Simulation of Profit Analysis Model (15 of 15)
Exhibit 14.23
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Verification of the Simulation Model (1 of 2)
■ Analyst wants to be certain that model is internally correct and
that all operations are logical and mathematically correct.
■ Testing procedures for validity:
Run a small number of trials of the model and compare
with manually derived solutions.
Divide the model into parts and run parts separately to
reduce complexity of checking.
Simplify mathematical relationships (if possible) for
easier testing.
Compare results with actual real-world data.
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 14-56
Verification of the Simulation Model (2 of 2)
■ Analyst must determine if model starting conditions are correct
(system empty, etc).
■ Must determine how long model should run to insure steady-state
conditions.
■ A standard, fool-proof procedure for validation is not available.
■ Validity of the model rests ultimately on the expertise and
experience of the model developer.
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 14-57
Some Areas of Simulation Application 14-58
■ Queuing
■ Inventory Control
■ Production and Manufacturing
■ Finance
■ Marketing
■ Public Service Operations
■ Environmental and Resource Analysis
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Example Problem Solution (1 of 6)
Willow Creek Emergency Rescue Squad
Minor emergency requires two-person crew
Regular emergency requires a three-person crew
Major emergency requires a five-person crew
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Example Problem Solution (2 of 6)
Distribution of number of calls per night and emergency type:
Calls Probability Emergency Type Probability
0 .05 Minor .30
1 .12 Regular .56
2 .15 Major .14
3 .25 1.00
4 .22
5 .15 1. Manually simulate 10 nights of calls
6 .06 2. Determine average number of calls
1.00
each night
3. Determine maximum number of
crew members that might be needed
on any given night.
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Example Problem Solution (3 of 6)
Step 1: Develop random number ranges for the probability distributions.
Calls Probability Cumulative Random Number
Probability Range, r1
0 .05
1 .12 .05 1–5
2 .15 .17 6 – 17
3 .25 .32 18 – 32
4 .22 .57 33 – 57
5 .15 .79 58 – 79
6 .06 .94 80 – 94
1.00 1.00 95 – 99, 00
Emergency Probability Cumulative Random Number
Type Probability Range, r1
.30 1 – 30
Minor .56 .30 31 – 86
Regular .14 .86 87 – 99, 00
Major 1.00 1.00
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Example Problem Solution (4 of 6)
Step 2: Set Up a Tabular Simulation (use second column of random
numbers in Table 14.3).
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Example Problem Solution (5 of 6)
Step 2 continued:
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Example Problem Solution (6 of 6)
Step 3: Compute Results:
average number of minor emergency calls per night = 10/10 =1.0
average number of regular emergency calls per night =14/10 = 1.4
average number of major emergency calls per night = 3/10 = 0.30
If calls of all types occurred on same night, maximum number of
squad members required would be 14.
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 14-64
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 14-65