Chapter 15
Simulation Modeling
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-1
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Learning Objectives
Students will be able to
• Tackle a wide variety of problems
by simulation
• Understand the seven steps of
conducting a simulation
• Explain the advantages and
disadvantages of simulation
• Develop Random number
intervals and use them to generate
outcomes
• Understand the alternative
simulation packages available
commercially
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-2
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Chapter Outline
15.1 Introduction
15.2 Advantages and Disadvantages 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
15.7 Simulation Model for Maintenance
Policy
15.8 Two Other Types of Simulation
15.9 Role of Computers in Simulation
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-3
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Philosophy of
Simulation
• Imitate a real-world situation
mathematically
• Study its properties and
operating characteristics
• Draw conclusions and make
action decisions
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-4
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Advantages of
Simulation
• Relatively straightforward and
flexible
• Recent advances in software make
some simulation models very 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, 8e
by Render/Stair/Hanna
15-5
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Disadvantages of
Simulation
• Often requires long, expensive
development process
• Does not generate optimal
solutions
• Requires managers to generate
all conditions and constraints of
real-world problem
• Each model is unique
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-6
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Simulation Models
Categories
• Monte Carlo
• Operational Gaming
• Systems Simulation
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-7
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Monte Carlo
Simulation
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, 8e
by Render/Stair/Hanna
15-8
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Variables We May
Wish to Simulate
• Inventory demand on daily or
weekly basis
• Lead time for inventory orders to
arrive
• Times between machine breakdowns
• Times between arrivals at service
facility
• Service times
• Times to complete project activities
• Number of employees absent from
work each day
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-9
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Harry’s Auto Tire
p(X)
Demand Probability
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
X
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-10
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Harry’s Auto Tire
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
0
1
2
3
4
5
X
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-11
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Random
Number
Interval
Demand
Probability
Harry’s Auto Tire
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
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-12
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Random Number Table
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
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
10 47
24 03
03 11
32 10
23 67
59 23
95 89
34 62
34 56
51 74
08 54
48 31
66 62
97 37
03 33
96 33
46 82
99
29
27
75
89
78
68
64
62
30
17
12
74
45
11
52
59
37
60
79
21
85
71
48
39
31
35
12
73
41
31
97
78
94
15-13
66
74
90
95
29
72
17
55
15
36
80
02
86
94
59
13
25
91
85
87
90
21
90
89
29
40
85
69
68
98
99
81
06
34
35
90
92
94
25
57
34
30
90
01
24
00
92
42
72
28
32
32 00
73 59
41 09
38 97
73 69
01 98
09 93
64 49
34 51
55 92
84 92
16 16
98 84
49 27
00 64
30 94
23 17
84
55
25
71
34
57
50
44
95
64
16
46
54
64
61
23
01
57
17
36
72
85
31
44
30
26
09
49
13
33
89
13
37
58
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
07
60
77
49
76
95
51
16
14
85
59
85
40
42
52
39
73
Random Number
Interval
½
5
0.05
0.05
01 - 05
1
6
0.06
0.11
06 - 11
1½
16
0.16
0.27
12 - 27
2
33
0.33
0.60
28 - 60
2½
21
0.21
0.81
81 - 81
3
19
0.19
1.00
82 - 00
Number of Times
Observed
Cumulative
Probability
Three Hills Power
Generator Breakdown
Times
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-14
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Cumulative
Probability
Repair Time
Required (Hours)
Three Hills Power
Generator Repair
Times
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, 8e
by Render/Stair/Hanna
15-15
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Operational Gaming
Simulation involving competing
players
Examples:
Military games
Business games
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-16
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Systems Simulation
Large, dynamic systems
Examples:
Corporate operating system
Urban government
Economic systems
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-17
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458
Income Tax Levels
Corporate Tax Rates
Interest Rates
Government Spending
Foreign Trade Policy
Inputs/Outputs of an
Economic Model
To accompany Quantitative Analysis
for Management, 8e
by Render/Stair/Hanna
15-18
© 2003 by Prentice Hall, Inc.
Upper Saddle River, NJ 07458