Operations management by stevenson 9th ch18s

18s

Simulation

McGraw-Hill/Irwin

Copyright © 2007 by The McGraw-Hill Companies, Inc. All


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


Figure 18S.1

Uniform Distribution

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