1. Prepared by Lee Revere and John Large
Chapter 15
Simulation Modeling
Prepared by Lee Revere and John Large
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-1

2. 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, 9e
by Render/Stair/Hanna
15-2

3. 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
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-3

4. 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

5. 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

6. 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

7. 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 for Management, 9e
by Render/Stair/Hanna
15-7

8. 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 for Management, 9e
by Render/Stair/Hanna
15-8

9. 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

10. Monte Carlo Simulation
The Monte Carlo simulation is
applicable to business problems
that exhibit chance, or uncertainty.
For example:
Inventory demand
Lead time for inventory
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

11. 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

12. 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.
Let’s use Monte Carlo simulation to analyze Harry’s inventory… 10
0.05 1 20
0.10 2 40
0.20 3 4 5 30
0.15
Demand Frequency Probability
for Tires
= 10/200
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-12

13. Harry’s Auto Tires: Monte Carlo Example (continued)
Step 1: Set up the probability distribution for radial tire.
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%
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-13

14. Harry’s Auto Tires: Monte Carlo Example (continued)
Step 2: Build a cumulative probability distribution.
15% of the time the demand was 0 or 1 tire: P(0) = 5% + P(1) = 10%
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-14

15. Harry’s Auto Tires: Monte Carlo Example (continued)
Step 3: Establish an interval of random numbers.
Demand
Frequency
Probability
Cumulative Probability
Random Number Interval 10
0.05 1 20
0.10
0.15 2 40
0.20
0.35 3 60
0.30
0.65 4
0.85 5 30
1.00
Must be in correct proportion
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

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

17. 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 2 3 1
Random number:
Simulated demand:
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-17

18. 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

19. Three Hills Power Generator Breakdown Times: Monte Carlo (continued)
Steps 1-3: Determine probability, cumulative probability, and random number interval - BREAKDOWNS. 5
0.05 1 6
0.06
0.11
1 ½ 16
0.16
0.27 2 33
0.33
0.60
2 ½ 21
0.21
0.81 3 19
0.19
1.00
Time Between Breakdowns (Hrs)
Number of Times Observed
Probability
Cumulative Probability
Random Number Interval
Total
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-19

20. Three Hills Power Generator Repair Times
Steps 1-3: Determine probability, cumulative probability, and random number interval - REPAIRS. 1 28
0.28 2 52
0.52
0.80 3 20
0.20
1.00
Repair Time Required (Hours)
Number of Times Observed
Probability
Cumulative Probability
Random Number Interval
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-20

21. Three Hills Power Generator Breakdown Times: Monte Carlo (continued)
Steps 4 & 5: Generate random numbers and simulate.
Machine is down
No. of hrs.
Breakdowns
Time b/t
Breakdown
Time of
Time Repair
Can Begin
Time Repair
Ends
Simulation
Trial
Random
Number
Random
Number
Repair Time 1 57 2
2:00 7
3:00 17
1.5
3:30 60
5:30 3 36 77
7:30 4 72
2.5
8:00 49
10:00 5 85
11:00 76
13:00 : 14 89
4:00
6:00 42 15 13 52
4.5
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-21

22. 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, $3,300
= $4,320
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-22

23. Operational Gaming Simulation Model
Operational gaming refers to
simulation involving competing
players.
Examples:
Military games
Business games
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-23

24. 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 for Management, 9e
by Render/Stair/Hanna
15-24

25. Econometric Simulation Models
Foreign Trade Policy
Government Spending
Corporate Tax Rates
Income Tax Levels
Interest Rates
Economic Model
GNP
Inflation Rates
Unemployment Rates
Monetary Supplies
Population Growth Rates
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-25

26. 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

27. The Role of Computers in Simulation
General-purpose languages Visual Basic, C++, Java
Special-purpose simulation languages GPSS/H, SLAM II, SIMSCRIPT II 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

28. 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

29. Harry’s Auto Tires: Excel Demonstration Results
To accompany Quantitative Analysis for Management, 9e
by Render/Stair/Hanna
15-29