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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.

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### Chapter 1What is Simulation?

Dr. Jason Merrick

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

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?

• 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?

• 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?

• 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?

• 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?

• M.S. grads, CWRU O.R. Department (1978)

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?

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?

• 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.

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?

• Estimated that 75% of computing power is used for various kinds of simulations

• Dedicated machines (e.g., real-time shop-floor control)

• Far easier to use (GUIs)

• No longer as restrictive in modeling constructs (hierarchical, down to C)

• Statistical design & analysis capabilities

What is Simulation?

• 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

What is 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?

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.

Different Kinds of Simulation

What is Simulation?

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?

• 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?

• 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?

• 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?

• 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

• Usually static models

• Financial scenarios, distribution sampling, SQC

What is Simulation?

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?

User-Created Templates

Commonly used constructs

Company-specific processes

Company-specific templates

A single

etc.

graphical user

interface

consistent at

any level of

Application Solution Templates

modeling

Call\$im

Vertical Solutions

BP\$im

etc.

Common Panel

Many common modeling constructs

Very accessible, easy to use

Reasonable flexibility

Level of

Professional Edition

Modeling

Arena Template

Support, Transfer Panels

flexibility

Standard Edition

Blocks, Elements Panels

All the flexibility of the SIMAN simulation

SIMAN Template

language

User-Written Visual Basic, C/C++, FORTRAN

Code

The ultimate in flexibility

C/C++/FORTRAN requires compiler

Lower

Where Arena Fits In

• 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?

• 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?

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?

When Simulations are Used (cont’d.)

• The recent past (late 1980s)

• Microcomputer power

• Software expanded into GUIs, animation

• Wider acceptance across more areas

• Services

• Health care

• Still mostly in large firms

• Often a simulation is part of the “specs”

What is Simulation?

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?