Simulation

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

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.


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

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


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.


Simulation Models
Categories
 Monte Carlo
consumer demand
inventory analysis
queuing problems
maintenance policy
 Operational Gaming
 Systems Simulation


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


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


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…


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


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


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

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


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


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.


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

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

Three Hills Power
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


Three Hills Power
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


Operational Gaming
Simulation Model
Operational gaming refers to
simulation involving competing
players.

Examples:
Military games
Business games


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


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.


Simulation

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