1. Chapter 1 What is Simulation?
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
Chapter 1 What is Simulation?
Dr. Jason Merrick

2. 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?

3. What is Simulation? Simulation vs. Real World
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?

4. Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

5. Some Application Areas
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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?

6. 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?

7. 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.
What is Simulation?

8. 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.
What is Simulation?

9. Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

10. 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 verification.
What is Simulation?

11. Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

12. 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.
What is Simulation?

13. What Do You Do with a Logical Model?
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

14. Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

15. Simulation with Arena—Chapter 1 What is Simulation?
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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
What is Simulation?

16. Simulation with Arena—Chapter 1 What is Simulation?
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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
What is Simulation?

17. Advantages of Simulation
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

18. Advantages of Simulation (cont’d.)
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

19. Simulation with Arena—Chapter 1 What is Simulation?
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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
RIRO: Random In, Random Out
What is Simulation?

20. Different Kinds of Simulation
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

21. Different Kinds of Simulation
Static 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.
Continuous Simulation
Looks at the aggregate flow of the components over time.
Dynamic Simulation
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.
Discrete Simulation
Events happen at discrete points in time.
What is Simulation?

22. Simulation by Hand: The Buffon Needle Problem
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
P (needle crosses a line) =
Repeat; tally = proportion of times a line is crossed
Estimate p by
What is Simulation?

23. Simulation with Arena—Chapter 1 What is Simulation?
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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)
What is Simulation?

24. 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.
What is Simulation?

25. 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.
What is Simulation?

26. Using Computers to Simulate
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

27. Using Computers to Simulate (cont’d.)
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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?
What is Simulation?

28. Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
Where Arena Fits In
Arena Template
Standard Edition
Professional Edition
A single
graphical user
interface
consistent at
any level of
modeling
Higher
Level of
Modeling
Lower
SIMAN Template
Vertical Solutions
User-Created Templates
Commonly used constructs
Company-specific processes
Company-specific templates
etc.
Application Solution Templates
Call$im
BP$im
Common Panel
Many common modeling constructs
Very accessible, easy to use
Reasonable flexibility
Support, Transfer Panels
Access to more detailed modeling for greater
flexibility
Blocks, Elements Panels
All the flexibility of the SIMAN simulation
language
User-Written Visual Basic, C/C++, FORTRAN
Code
The ultimate in flexibility
C/C++/FORTRAN requires compiler
Hierarchical structure
Multiple levels of modeling
Can mix different modeling levels together in the same model
Often, start high then go lower as needed
Get ease-of-use advantage of simulators without sacrificing modeling flexibility
What is Simulation?

29. When Simulations are Used
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

30. When Simulations are Used (cont’d.)
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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
What is Simulation?

31. When Simulations are Used (cont’d.)
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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?

32. When Simulations are Used (cont’d.)
Simulation with Arena—Chapter 1 What is Simulation?
4/17/2017
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?