```Chapter 15
Simulation
Modeling
Prepared by Lee Revere and John Large
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-1
© 2006 by Prentice Hall, Inc.
Learning Objectives
Students will be able to:
1. Tackle a wide variety of problems
by simulation.
2. Understand the seven steps of
conducting a simulation.
4. Develop random number intervals
and use them to generate outcomes.
5. Understand the alternative
simulation packages available
commercially.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-2
© 2006 by Prentice Hall, Inc.
Chapter Outline
15.1 Introduction
of Simulation
15.3 Monte Carlo Simulation
15.4 Simulation and Inventory
Analysis
15.5 Simulation of a Queuing
Problem
15.6 Fixed Time Increment and
Next Event Increment
Simulation Models
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-3
© 2006 by Prentice Hall, Inc.
Chapter Outline
15.7 Simulation Model for
Maintenance Policy
15.8 Two Other Types of
Simulation
15.9 Verification and Validation
15.9 Role of Computers in
Simulation
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-4
© 2006 by Prentice Hall, Inc.
Introduction
Simulation is one of the most widely
used quantitative analysis tools. It is
used to:
 imitate a real-world situation
mathematically.
 study its properties and
operating characteristics.
 draw conclusions and make
action decisions.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-5
© 2006 by Prentice Hall, Inc.
Introduction: Seven
Steps of Simulation
Define a Problem
Introduce Important Variables
Construct Simulation Model
Specify Values to be Variables
Conduct the Simulation
Examine the Results
Select Best Course of Action
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-6
© 2006 by Prentice Hall, Inc.
 Straightforward and flexible
 Computer software make simulation
models easy to develop
 Enables analysis of large, complex,
real-world situations
 Allows “what-if?” questions
 Does not interfere with real-world
system
 Enables study of interactions
 Enables time compression
 Enables the inclusion of real-world
complications
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-7
© 2006 by Prentice Hall, Inc.
Simulation
 Often requires long, expensive
development process.
 Does not generate optimal solutions;
it is a trial-and-error approach.
 Requires managers to generate all
conditions and constraints of realworld problem.
 Each model is unique and not
typically transferable to other
problems.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-8
© 2006 by Prentice Hall, Inc.
Simulation Models
Categories
 Monte Carlo
consumer demand
inventory analysis
queuing problems
maintenance policy
 Operational Gaming
 Systems Simulation
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-9
© 2006 by Prentice Hall, Inc.
Monte Carlo
Simulation
The Monte Carlo simulation is
that exhibit chance, or uncertainty.
For example:
1.
2.
3.
4.
5.
6.
7.
Inventory demand
Times between machine breakdowns
Times between arrivals
Service times
Times to complete project activities
Number of employees absent
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-10
© 2006 by Prentice Hall, Inc.
Monte Carlo
Simulation (continued)
The basis of the Monte Carlo simulation
is experimentation on the probabilistic
elements through random sampling. It is
used with probabilistic variables.
Five steps:
1. Set up probability distributions
2. Build cumulative probability
distributions
3. Establish interval of random
numbers for each variable
4. Generate random numbers
5. Simulate trials
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-11
© 2006 by Prentice Hall, Inc.
Harry’s Auto Tires:
Monte Carlo Example
A popular radial tire accounts for a large
portion of the sales at Harry’s Auto Tire.
Harry wishes to determine a policy for
managing his inventory of radial tires.
Demand
for Tires
Frequency Probability
0
1
2
3
4
5
10
20
40
60
40
030
200
0.05 = 10/200
0.10
0.20
0.30
0.2
0.15
1.00
Let’s use Monte Carlo simulation to
analyze Harry’s inventory…
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-12
© 2006 by Prentice Hall, Inc.
Harry’s Auto Tires:
Monte Carlo Example
(continued)
Step 1: Set up the probability distribution
p(X)
Demand Probability
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Using historical data, Harry determined
that 5% of the time 0 tires were demanded,
10% of the time 1 tire was demand, etc…
P(1) = 10%
0
1
2
3
4
5
X
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-13
© 2006 by Prentice Hall, Inc.
Harry’s Auto Tires:
Monte Carlo Example
(continued)
Step 2: Build a cumulative probability
distribution.
P(X)
Demand Cumulative Probability
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
15% of the time the demand was 0
or 1 tire: P(0) = 5% + P(1) = 10%
0
1
2
3
4
5
X
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-14
© 2006 by Prentice Hall, Inc.
Harry’s Auto Tires: Monte
Carlo Example (continued)
0
1
10
20
0.05
0.10
0.05
0.15
01 - 05
06 - 15
2
40
0.20
0.35
16 - 35
3
60
0.30
0.65
36 - 65
4
40
0.20
0.85
66 - 85
5
30
0.15
1.00
86 - 00
Note: 5% of the time 0 tires are demanded, so the random
number interval contains 5% of the numbers between 1 and 100
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-15
© 2006 by Prentice Hall, Inc.
Must be in correct proportion
Random
Number
Interval
Demand
Probability
Step 3: Establish an interval of random
numbers.
Harry’s Auto Tires: Monte
Carlo Example (continued)
Step 4: Generate random numbers.
52
37
82
69
98
96
33
50
88
90
50
27
45
81
66
74
30
06
63
57
02
94
52
69
33
32
30
48
88
14
02
83
05
34
50 88
28 02
68 28
36 49
90 36
62 87
27 21
50 95
18 50
36 24
61 18
21 62
46 32
01 78
14 74
82 82
87 01
53
74
05
71
06
49
11
13
62
69
85
69
13
82
27
93
74
30
35
94
99
78
56
60
44
57
82
23
64
49
74
76
09
11
10
24
03
32
23
59
95
34
34
51
08
48
66
97
03
96
46
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
47
03
11
10
67
23
89
62
56
74
54
31
62
37
33
33
82
99
29
27
75
89
78
68
64
62
30
17
12
74
45
11
52
59
37 66
60 74
79 90
21 95
85 29
71 72
48 17
39 55
31 15
35 36
12 80
73 02
41 86
31 94
97 59
78 13
94 25
15-16
91 35
85 90
87 92
90 94
21 25
90 57
89 34
29 30
40 90
85 01
69 24
68 00
98 92
99 42
81 72
06 28
34 32
32
73
41
38
73
01
09
64
34
55
84
16
98
49
00
30
23
00
59
09
97
69
98
93
49
51
92
92
16
84
27
64
94
17
84
55
25
71
34
57
50
44
95
64
16
46
54
64
61
23
01
57 07
17 60
36 77
72 49
85 76
31 95
44 51
30 16
26 14
09 85
49 59
13 85
33 40
89 42
13 52
37 39
58 73
© 2006 by Prentice Hall, Inc.
Harry’s Auto Tires: Monte
Carlo Example (continued)
Step 5: Simulate a series of trials.
Using random number table on previous slide,
simulated demand for 10 days is:
Tires
Demanded
Interval of
Random Numbers
0
1
2
3
4
5
01 - 05
06 - 15
16 - 35
36 - 65
66 - 85
86 - 100
2
3
1
Random number: 52 06 50 88 53 30 10 47 99 37
Simulated demand: 3 1 3 5 3 2 1 3 5 3
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-17
© 2006 by Prentice Hall, Inc.
Three Hills Power
Company: Monte
Carlo Example
Three Hills provides power to a large
city. The company is concerned about
generator failures because a breakdown
costs about \$75 per hour versus a \$30
per hour salary for repairpersons who
work 24 hours a day, seven days a week.
Management wants to evaluate the
service maintenance cost, simulated
breakdown cost, and total cost.
Let’s use Monte Carlo simulation to
analyze Three Hills system costs.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-18
© 2006 by Prentice Hall, Inc.
Three Hills Power
Generator Breakdown Times:
Monte Carlo (continued)
Random Number
Interval
½
5
0.05
0.05
01 - 05
1
1½
6
16
0.06
0.16
0.11
0.27
06 - 11
12 - 27
2
33
0.33
0.60
28 - 60
2½
3
21
19
0.21
0.19
0.81
1.00
81 - 81
82 - 00
Total
100
1.00
Number of
Times Observed
Cumulative
Probability
Steps 1-3: Determine probability,
cumulative probability, and random
number interval - BREAKDOWNS.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-19
© 2006 by Prentice Hall, Inc.
Three Hills Power
Generator Repair
Times
Cumulative
Probability
Repair Time
Required
(Hours)
Steps 1-3: Determine probability,
cumulative probability, and random
number interval - REPAIRS.
1
28
0.28
0.28
01 - 28
2
52
0.52
0.80
29 - 80
3
20
0.20
1.00
81 - 00
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-20
© 2006 by Prentice Hall, Inc.
Three Hills Power
Generator Breakdown Times:
Monte Carlo (continued)
Random
Number
Time b/t
Breakdowns
Time of
Breakdown
Time Repair
Can Begin
Random
Number
Time Repair
Ends
No. of hrs.
Machine is down
1
57
2
2:00
2:00
7
1
3:00
1
2
17
1.5
3:30
3:30
60
2
5:30
2
3
36
2
5:30
5:30
77
2
7:30
2
4
72
2.5
8:00
8:00
49
2 10:00
2
5
85
3
11:00
11:00
76
2 13:00
2
:
:
:
:
:
:
:
:
:
14
89
3
4:00
6:00
42
2
8:00
4
15
13
1.5
5:30
8:00
52
2 10:00
4.5
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-21
Repair Time
Simulation
Trial
Steps 4 & 5: Generate random numbers and simulate.
© 2006 by Prentice Hall, Inc.
Three Hills Power
Generator Breakdown Times:
Monte Carlo (continued)
Cost Analysis:
Service maintenance: = 34 hrs of worker
service X \$30 per hr
= \$1,020
Simulate machine breakdown costs:
= 44 total hrs of breakdown
X \$75 lost per hr of downtime
= \$3,300
Total simulated maintenance cost of the
current system: = service cost + breakdown costs
= \$1,020 + \$3,300
= \$4,320
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-22
© 2006 by Prentice Hall, Inc.
Operational Gaming
Simulation Model
Operational gaming refers to
simulation involving competing
players.
Examples:
Military games
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-23
© 2006 by Prentice Hall, Inc.
Systems Simulation
Model
Systems simulation is similar to
users to test various managerial
policies and decision. It models the
dynamics of large systems.
Examples:
 Corporate operating system
 Urban government
 Economic systems
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-24
© 2006 by Prentice Hall, Inc.
Income Tax Levels
Corporate Tax Rates
Interest Rates
Government Spending
Econometric
Simulation Models
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-25
© 2006 by Prentice Hall, Inc.
Verification and
Validation
Verification of simulation models
involves determining that the
computer model is internally
consistent and follows the logic of
the conceptual model.
Validation is the process of
comparing a simulation model
to a real system to assure
accuracy.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-26
© 2006 by Prentice Hall, Inc.
The Role of Computers
in Simulation
 General-purpose languages
Visual Basic, C++, Java
 Special-purpose simulation
languages
GPSS/H, SLAM II, SIMSCRIPT II.5
1. require less programming
2. more efficient and easier to check
for errors
3. have random number generators
built in
 Pre-written simulation programs
Extend, AutoMod, ALPHA/Sim, SIMUL8,STELLA,
Arena, AweSim!, SLX, etc.
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-27
© 2006 by Prentice Hall, Inc.
Harry’s Auto Tires:
Excel Demonstration
Create lookup
table using
cumulative
probability
Generate a
random number
and look it up in
the table
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-28
© 2006 by Prentice Hall, Inc.
Harry’s Auto Tires:
Excel Demonstration
Results
To accompany Quantitative Analysis
for Management, 9e
by Render/Stair/Hanna
15-29
© 2006 by Prentice Hall, Inc.
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