Chapter 1
What is Simulation?
Dr. Jason Merrick
Operations Research
• A mathematical model is an abstraction of the
real world.
• The aim of operations research is to use
mathematical modeling to assist in a decision
making process.
• Suppose that a decision maker has to make a
decision concerning changes to an existing
system or the design of a new system.
• What options are available to predict the new
system’s performance?
What is Simulation?
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What is Simulation?
• A simulation is a computer program that imitates, or
simulates, the operations of real world systems or
processes.
Simulation
vs.
Real World
What is Simulation?
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Simulation Is ...
•
•
•
•
Very broad term, set of problems/approaches
Generally, imitation of a system via computer
Involves a model—validity?
Don’t even aspire to analytic solution
– Don’t get exact results (bad)
– Allows for complex, realistic models (good)
• Approximate answer to exact problem is better
than exact answer to approximate problem
• Consistently ranked as most useful, powerful of
mathematical-modeling approaches
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Some Application Areas
• Manufacturing—scheduling, inventory
• Staffing personal-service operations
– Banks, fast food, theme parks, Post Office, ...
•
•
•
•
•
•
Distribution and logistics
Health care—emergency, operating rooms
Computer systems
Telecommunications
Military
Public policy
– Emergency planning
– Courts, prisons, probation/parole
What is Simulation?
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Maritime Risk Analysis
•
The Prince William Sound Risk Analysis
•
Testing alternatives for reducing the risk of
oil spills in an environmentally sensitive
area.
•
The simulation was used to count the
occurrence of risky situations.
•
For each of these risky situations, the
probability of an oil spill producing
accident was estimated using accident and
incident data and expert judgment.
•
The simulation allowed non-mathematical
people, such as the oil company
presidents, to understand how alternative
operating procedures could reduce the
risk.
What is Simulation?
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Aviation
• Used to test the efficiency
of changes to the airspace.
• What changes?
– The number, length and
capacity of runways.
– Changes to baggage
handling procedures.
– Changes to flight paths.
– Effect of new plane designs.
• What does the simulation
count?
– Delay times.
– Cost of delays.
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Medical Systems
• This is a surgical training
simulation.
• A virtual human body is
simulated.
• The trainee surgeon
performs the surgery
using the type of tools
used in fine surgery.
• The program simulates the
reaction of the patient.
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Systems
• Physical facility/process, actual or planned
• Study its performance
–
–
–
–
Measure
Improve
Design (if it doesn’t exist)
Maybe control in real time
• Sometimes possible to “play” with the system
• But sometimes impossible to do so
– Doesn’t exist
– Disruptive, expensive
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Experiment with the Actual System
vs. Experiment with a Model
• In some cases it may be possible to physically
change the actual system to see how it will
operate under new conditions.
– There is no question of the validity of these results.
• However, it is rarely feasible to do this.
– In the bank example, if the new system does not operate
well then the bank could lose customers.
• By using a model, alternatives may be tested
without the real world consequences.
– However, does the model accurately reflect the system for
the purpose of the decisions to be made? Validity and
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verification.
Models
• Abstraction/simplification of the system used as
a proxy for the system itself
• Can try wide-ranging ideas in the model
– Make your mistakes on the computer where they don’t
count, rather for real where they do count
• Issue of model validity
• Two types of models
– Physical (iconic)
– Logical/Mathematical -- quantitative and logical assumptions,
approximations
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Physical Model vs. Mathematical Model
• Examples of physical models are
– clay cars used to test new car designs in wind tunnels,
– airplane simulators used to train pilots or
– a mock up of a fast food restaurant in a warehouse with
people hired to be customers (true story!!!).
• Again physical models are often found more
credible.
– They are hands on and do not have a black box of
mathematical techniques.
• However, physical models are often not possible
or not feasible, i.e. too expensive.
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What Do You Do with a Logical Model?
• If model is simple enough, use traditional
mathematics (queueing theory, differential
equations, linear programming) to get “answers”
• Nice in the sense that you get “exact” answers to
the model
– But might involve many simplifying assumptions to make the
model analytically tractable -- validity??
• Many complex systems require complex models
for validity—simulation needed
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Computer Simulation
• Methods for studying a wide variety of models of
real-world systems
– Use numerical evaluation on computer
– Use software to imitate the system’s operations and
characteristics, often over time
• In practice, is the process of designing and
creating computerized model of system and
doing numerical computer-based experiments
• Real power—application to complex systems
• Simulation can tolerate complex models
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Popularity
• M.S. grads, CWRU O.R. Department (1978)
– Asked about value after graduation; rankings:
1. Statistical analysis, 2. Forecasting, 3. Systems analysis, 4.
Information systems, 5. Simulation
• 137 large firms (1979)
1. Statistical analysis (93% used it)
2. Simulation (84%)
– Followed by LP, PERT/CPM, inventory, NLP
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Popularity (cont’d.)
• (A)IIE, O.R. division members (1980)
– First in utility and interest: Simulation
– But first in familiarity: LP (simulation was second)
• Longitudinal study of corporate practice (1983,
1989, 1993)
1. Statistical analysis
2. Simulation
• Survey of such surveys (1989)
– Consistent heavy use of simulation
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Advantages of Simulation
• Flexibility to model things as they are (even if
messy and complicated)
– Avoid “looking where the light is” (a morality play):
You’re walking along in the dark and see someone on hands and knees searching the ground under a street light.
You:
“What’s wrong? Can I help you?”
Other person:
“I dropped my car keys and can’t find them.”
You:
“Oh, so you dropped them around here, huh?”
Other person:
“No, I dropped them over there.” (Points into the darkness.)
You:
“Then why are you looking here?”
Other person:
“Because this is where the light is.”
• Allows uncertainty, non-stationarity in modeling
– The only thing that’s for sure: nothing is for sure
– Danger of ignoring system variability
– Model validity
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Advantages of Simulation (cont’d.)
• Advances in computing/cost ratios
– Estimated that 75% of computing power is used for various
kinds of simulations
– Dedicated machines (e.g., real-time shop-floor control)
• Advances in simulation software
– Far easier to use (GUIs)
– No longer as restrictive in modeling constructs (hierarchical,
down to C)
– Statistical design & analysis capabilities
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The Bad News
• Don’t get exact answers, only approximations,
estimates
– Also true of many other modern methods
– Can bound errors by machine roundoff
• Get random output (RIRO) from stochastic
simulations
– Statistical design, analysis of simulation experiments
– Exploit: noise control, replicability, sequential sampling,
variance-reduction techniques
– Catch: “standard” statistical methods seldom work
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Different Kinds of Simulation
• Static vs. Dynamic
– Does time have a role in the model?
• Continuous-change vs. Discrete-change
– Can the “state” change continuously or only at discrete
points in time?
• Deterministic vs. Stochastic
– Is everything for sure or is there uncertainty?
• Most operational models:
– Dynamic, Discrete-change, Stochastic
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Different Kinds of Simulation
• Static Simulation
• Dynamic Simulation
– Look at a system at a fixed
time or a system that does
not change over time.
– e.g. Monte Carlo methods
• Deterministic Simulation
– No random or uncertain
components.
– A representation of a
system as it changes over
time.
– e.g. production processes in
a factory.
• Stochastic Simulation
– Some components have to
be modeled probabilistically.
• Continuous Simulation
– Looks at the aggregate flow
of the components over
time.
• Discrete Simulation
What is Simulation?
– Events happen at discrete
points in time.
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Simulation by Hand:
The Buffon Needle Problem
• Estimate p (George Louis Leclerc, c. 1733)
• Toss needle of length l onto table with stripes d
(>l) apart
2l
• P (needle crosses a line) = p d
• Repeat; tally
crossed p
= proportion of times a line is
• Estimate p by
p d
2l
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Why Toss Needles?
• Buffon needle problem seems silly now, but it has
important simulation features:
– Experiment to estimate something hard to compute exactly
(in 1733)
– Randomness, so estimate will not be exact; estimate the
error in the estimate
– Replication (the more the better) to reduce error
– Sequential sampling to control error -- keep tossing until
probable error in estimate is “small enough”
– Variance reduction (Buffon Cross)
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Monte Carlo Simulation
•
Monte Carlo simulation is a sampling experiment whose purpose
is to estimate the distribution of an outcome variable that depends
upon one or more probabilistic input variables.
– For instance, suppose we wished to estimate the profit of a company when
demand for the product and production costs were not known with certainty.
The name comes from the similarity to random sampling in games
of chance such as roulette played in the casinos in Monte Carlo.
D is trib u tio n fo r X + Y
X is Gamma( 3 ,5 )
Y is Gamma( 5 ,3 )

P R O B A B IL IT Y
•
4 .4
1 0 .8
1 9 .3
2 7 .8
3 6 .3
4 4 .8
5 3 .3
6 1 .9
7 0 .4
7 8 .9
8 9 .5
X +Y
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Discrete Event Simulation
• Also called System Simulation.
• Explicitly models sequences of events that occur
at discrete points in time.
• A discrete event simulation run consists of
– sampling from the time of occurrence of events from
probabilistic input variables,
– continually updating the system state by following a set of
rules and
– observing the flow of the model over time by counting certain
quantities of interest.
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Using Computers to Simulate
• General-purpose languages (FORTRAN)
– Tedious, low-level, error-prone
– But, almost complete flexibility
• Support packages
– Subroutines for list processing, bookkeeping, time advance
– Widely distributed, widely modified
• Spreadsheets
– Usually static models
– Financial scenarios, distribution sampling, SQC
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Using Computers to Simulate (cont’d.)
• Simulation languages
– GPSS, SIMSCRIPT, SLAM, SIMAN
– Popular, in wide use today
– Learning curve for features, effective use, syntax
• High-level simulators
– Very easy, graphical interface
– Domain-restricted (manufacturing, communications)
– Limited flexibility—model validity?
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Where Arena Fits In
• Get ease-of-use
advantage of
simulators without
sacrificing modeling
flexibility
Blocks, Elements Panels
All the flexibility of the SIMAN simulation
language
Lower
Professional Edition
Support, Transfer Panels
Access to more detailed modeling for greater
flexibility
Standard Edition
Level of
Modeling
Common Panel
Many common modeling constructs
Very accessible, easy to use
Reasonable flexibility
A single
graphical user
interface
consistent at
any level of
modeling
Vertical Solutions
Application Solution Templates
Call$im
BP$im
etc.
Arena Template
– Multiple levels of
modeling
– Can mix different
modeling levels
together in the same
model
– Often, start high then
go lower as needed
User-Created Templates
Commonly used constructs
Company-specific processes
Company-specific templates
etc.
SIMAN Template
• Hierarchical structure
Higher
User-Written Visual Basic, C/C++, FORTRAN
Code
The ultimate in flexibility
C/C++/FORTRAN requires compiler
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When Simulations are Used
• Uses of simulation have evolved with hardware,
software
• The early years (1950s-1960s)
–
–
–
–
Very expensive, specialized tool to use
Required big computers, special training
Mostly in FORTRAN (or even Assembler)
Processing cost as high as $1000/hour for a sub-286 level
machine
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When Simulations are Used (cont’d.)
• The formative years (1970s-early 1980s)
– Computers got faster, cheaper
– Value of simulation more widely recognized
– Simulation software improved, but they were still languages
to be learned, typed, batch processed
– Often used to clean up “disasters” in auto, aerospace
industries
• Car plant; heavy demand for certain model
• Line underperforming
• Simulated, problem identified
• But demand had dried up—simulation was too late
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When Simulations are Used (cont’d.)
• The recent past (late 1980s)
– Microcomputer power
– Software expanded into GUIs, animation
– Wider acceptance across more areas
•
•
•
•
Traditional manufacturing applications
Services
Health care
“Business processes”
– Still mostly in large firms
– Often a simulation is part of the “specs”
What is Simulation?
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When Simulations are Used (cont’d.)
• The present
–
–
–
–
Proliferating into smaller firms
Becoming a standard tool
Being used earlier in design phase
Real-time control
• The future
– Exploiting interoperability of operating systems
– Specialized “templates” for industries, firms
– Automated statistical design, analysis
What is Simulation?
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Simulation with Arena - Virginia Commonwealth University