The document provides an overview of simulation modeling. It discusses that simulation is used to mathematically imitate real-world situations in order to study their properties, operating characteristics, and draw conclusions. It outlines the seven steps of simulation as defining a problem, introducing important variables, constructing a simulation model, specifying variable values, conducting the simulation, examining results, and selecting the best course of action. Monte Carlo simulation is described as using random sampling to experiment on probabilistic elements. Two examples of Monte Carlo simulation are provided to analyze inventory management and power generator maintenance costs.

1. Simulation
Modeling
Prepared by Lee Revere and John Large
To accompany Quantitative Analysis 15-1 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

2. 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 15-2 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

3. 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 15-3 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

4. Advantages of Simulation
 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 15-4 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

5. Disadvantages of
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 real-
world problem.
 Each model is unique and not
typically transferable to other
problems.
To accompany Quantitative Analysis 15-5 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

6. Simulation Models
Categories
 Monte Carlo
consumer demand
inventory analysis
queuing problems
maintenance policy
 Operational Gaming
 Systems Simulation
To accompany Quantitative Analysis 15-6 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

7. Monte Carlo
Simulation
The Monte Carlo simulation is
applicable to business problems
that exhibit chance, or uncertainty.
For example:
1. Inventory demand
2. Lead time for inventory
3. Times between machine breakdowns
4. Times between arrivals
5. Service times
6. Times to complete project activities
7. Number of employees absent
To accompany Quantitative Analysis 15-7 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

8. 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 15-8 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

9. 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 Frequency Probability
for Tires
0 10 0.05 = 10/200
1 20 0.10
2 40 0.20
3 60 0.30
4 40 0.2
5 30
0 0.15
200 1.00
Let’s use Monte Carlo simulation to
analyze Harry’s inventory…
To accompany Quantitative Analysis 15-9 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

10. Harry’s Auto Tires:
Monte Carlo Example
(continued)
Step 1: Set up the probability distribution
for radial tire.
Demand Probability
1
0.9 Using historical data, Harry determined
0.8 that 5% of the time 0 tires were demanded,
0.7 10% of the time 1 tire was demand, etc…
0.6
p(X)
0.5
0.4
0.3
0.2 P(1) = 10%
0.1
0
0 1 2 3 4 5
X
To accompany Quantitative Analysis 15-10 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

11. Harry’s Auto Tires:
Monte Carlo Example
(continued)
Step 2: Build a cumulative probability
distribution.
Demand Cumulative Probability
1 15% of the time the demand was 0
0.9 or 1 tire: P(0) = 5% + P(1) = 10%
0.8
0.7
0.6
P(X)
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5
X
To accompany Quantitative Analysis 15-11 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

12. Harry’s Auto Tires: Monte
Carlo Example (continued)
Step 3: Establish an interval of random
numbers.
Probability
Random
Demand
Number
Interval
Must be in correct proportion
0 10 0.05 0.05 01 - 05
1 20 0.10 0.15 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 15-12 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

13. Harry’s Auto Tires: Monte
Carlo Example (continued)
Step 4: Generate random numbers.
52 06 50 88 53 30 10 47 99 37 66 91 35 32 00 84 57 07
37 63 28 02 74 35 24 03 29 60 74 85 90 73 59 55 17 60
82 57 68 28 05 94 03 11 27 79 90 87 92 41 09 25 36 77
69 02 36 49 71 99 32 10 75 21 95 90 94 38 97 71 72 49
98 94 90 36 06 78 23 67 89 85 29 21 25 73 69 34 85 76
96 52 62 87 49 56 59 23 78 71 72 90 57 01 98 57 31 95
33 69 27 21 11 60 95 89 68 48 17 89 34 09 93 50 44 51
50 33 50 95 13 44 34 62 64 39 55 29 30 64 49 44 30 16
88 32 18 50 62 57 34 56 62 31 15 40 90 34 51 95 26 14
90 30 36 24 69 82 51 74 30 35 36 85 01 55 92 64 09 85
50 48 61 18 85 23 08 54 17 12 80 69 24 84 92 16 49 59
27 88 21 62 69 64 48 31 12 73 02 68 00 16 16 46 13 85
45 14 46 32 13 49 66 62 74 41 86 98 92 98 84 54 33 40
81 02 01 78 82 74 97 37 45 31 94 99 42 49 27 64 89 42
66 83 14 74 27 76 03 33 11 97 59 81 72 00 64 61 13 52
74 05 82 82 93 09 96 33 52 78 13 06 28 30 94 23 37 39
30 34 87 01 74 11 46 82 59 94 25 34 32 23 17 01 58 73
To accompany Quantitative Analysis 15-13 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

14. 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 Interval of
Demanded Random Numbers
0 01 - 05
1 06 - 15
2 16 - 35
3 2 36 - 65
4 66 - 85
5 3 1 86 - 100
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 15-14 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

15. 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 15-15 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

16. Three Hills Power
Generator Breakdown Times:
Monte Carlo (continued)
Steps 1-3: Determine probability,
cumulative probability, and random
number interval - BREAKDOWNS.
Random Number
Times Observed
Number of
Interval
Cumulative
Probability
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
Total 100 1.00
To accompany Quantitative Analysis 15-16 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

17. Three Hills Power
Generator Repair
Times
Steps 1-3: Determine probability,
cumulative probability, and random
number interval - REPAIRS.
Repair Time
Cumulative
Required
Probability
(Hours)
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 15-17 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

18. Three Hills Power
Generator Breakdown Times:
Monte Carlo (continued)
Steps 4 & 5: Generate random numbers and simulate.
Machine is down
Time Repair
Time Repair
Repair Time
Breakdowns
Breakdown
Simulation
Can Begin
No. of hrs.
Random
Random
Time b/t
Number
Number
Time of
Ends
Trial
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 15-18 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

19. 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 15-19 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

20. Operational Gaming
Simulation Model
Operational gaming refers to
simulation involving competing
players.
Examples:
Military games
Business games
To accompany Quantitative Analysis 15-20 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

21. Systems Simulation
Model
Systems simulation is similar to
business gaming because it allows
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 15-21 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna

22. 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 15-22 © 2006 by Prentice Hall, Inc.
for Management, 9e Upper Saddle River, NJ 07458
by Render/Stair/Hanna