Transcript Supplementary notes

1
Simulation
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
 Explain what is meant by the term simulation
 List some of the reasons for simulation’s popularity
as a tool for decision making
 Explain how and why random numbers are used
are used in simulation
 Outline the advantages and limitations of simulation
 Describe the alternatives that a manager would
reject before choosing simulation as a decision
making tool
 Solve typical problems that require simulation
18S-2
Simulation
Simulation: a descriptive technique that
enables a decision maker to evaluate the
behavior of a model under various
conditions.
Simulation models complex situations
Models are simple to use and understand
Models can play “what if” experiments
Extensive software packages available
18S-3
Simulation Process
1. Identify the problem
2. Develop the simulation model
3. Test the model
4. Develop the experiments
5. Run the simulation and evaluate results
6. Repeat 4 and 5 until results are
satisfactory
18S-4
Monte Carlo Simulation
Monte Carlo method: Probabilistic simulation
technique used when a process has a
random component
 Identify a probability
distribution
 Setup intervals of
random numbers to
match probability distribution
 Obtain the random numbers
 Interpret the results
18S-5
Example S-1
18S-6
Example S-1
18S-7
Simulating Distributions
 Poisson

Mean of distribution is required
 Normal

Need to know the mean and standard
deviation
Simulated =
Mean
value
+
Random X Standard
number
deviation
18S-8
Uniform Distribution
Figure 18S.1
F(x)
0
a
b
x
Simulated
a + (b - a)(Random number as a percentage)
=
value
18S-9
Negative Exponential Distribution
Figure 18S.2
F(t)
P ( t  T ) . RN
0
T
t
18S-10
Computer Simulation
 Simulation languages
 SIMSCRIPT II.5
 GPSS/H
 GPSS/PC
 RESQ
18S-11
Advantages of Simulation
 Solves problems that are difficult or
impossible to solve mathematically
 Allows experimentation without risk to actual
system
 Compresses time to
show long-term effects
 Serves as training tool
for decision makers
18S-12
Limitations of Simulation
 Does not produce optimum solution
 Model development may be difficult
 Computer run time may be substantial
 Monte Carlo simulation only applicable to
random systems
18S-13