Simulation Modeling and Analysis

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Simulation Modeling and Analysis
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1.1 Introduction
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Simulation

• Definition The imitation of the operation of a
  real world process or system over time.
• Basic steps In a simulation we
• Generate of an artificial history using a model.
• Observe that history.
• Draw conclusions about the real system from the
  artificial history of the simulation.
• Another definition the practice of building
  models to represent existing real-world systems,
  or hypothetical future systems, and of
  experimenting with these models to explain system
  behavior, improve system performance, or design
  new systems with desirable performances.
  (Khoshnevis, 1994).

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Simulation

• A Simulation model
• is computer representations of real systems
• is based on the assumptions as to how system
  works and describes how entities interacts.
• generates the artificial history of events
• is used to evaluate the performance of what
  if scenarios (based on the simulation output)
  about
• Changes to an existing system
• Alternative options in designing systems
• is necessary for analyzing many real-world
  systems since mathematical models or analytical
  models (e.g. queuing models, differential
  calculus, probability theory) dont exist or too
  complex.

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When is Simulation Appropriate?

• To determine operational capacities. (A machines
  theoretical capacity vs. the operational capacity
  we put it in our system)
• To experiment with policies or designs that
  cannot be otherwise tested. (too risky or costly
  to try on the real system)
• To provide low-risk on the job training.
• To visualize system performance (animation)

• A system is too complex for analytical solutions.
• We wish to study informational, organizational,
  or environmental changes. (Changes hard to
  include in analytical models, if not impossible)
• To identify key factors affecting performance.
  (ability to isolate factors)
• To verify analytical models.

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When is Simulation Inappropriate?

• When the problem is very simple and an analytical
  solution can be found
• - Example a service station with Poisson
  arrivals and general service times (M/G/1).
  Analytical solution exist.
• When direct experimentation is feasible and
  inexpensive.
• If simulation project costs exceed expected
  returns.
• If data is not available.
• If sufficient development time resources are not
  available.
• If systems are too complex to even simulate
  (especially involving human behavior)

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Advantages of Simulation

• Many complex real-world systems are stochastic,
  making analytical methods difficult, and
  sometimes intractable simulation provides a way
  to model these systems
• Performance of proposed non-existing systems can
  be evaluated
• Many alternatives (proposed system designs or
  alternative operating policies for a single
  system) can be compared
• Control of experiments is much tighter with a
  simulation model than with the real system
  (Experiment with two policies while keeping
  everything else exactly same)
• Systems can be studied in compressed time (e.g. a
  factory), or in expanded time (e.g. CPU
  scheduling) to understand the system better.

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Disadvantages of Simulation

• Model building requires special training and
  experience.
• A simulation model can, at best, provide only
  estimates of the systems performance not exact
  true value. One must go through a statistical
  output analysis to make conclusions.
• All alternative answers must be known before the
  simulation experiments are carried out. The
  chosen best solution is restricted to the set
  of alternatives. There may be an extremely large
  number of possible answers to be evaluated this
  may make determination of the best answer
  difficult or impossible.
• Simulation analysis can be expensive and time
  consuming.
• Simulation is used sometimes when the analytical
  models and solutions are available. Particular
  case is the waiting lines for which there are
  queuing models available.
• All of these disadvantages are being offset to a
  certain degree with advanced simulation software
  and modern fast hardware.

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Systems

• Definition A system is a collection of entities
  (people, factory orders, cars, phone calls, data
  packets, ) which interact to accomplish some
  logical purpose.
• Components of a system
• Entities Object of interest in the system
• Attributes Properties of an entity
• Activity an operation carried out by entity
  during a specified period of time
• System state a collection of variables necessary
  to describe a system at any given time, relative
  to the objectives of the study.
• Event Instantaneous occurrence that changes the
  system state.

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Table 1.1. Example of systems and components
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Some of application Areas

• Designing and analyzing manufacturing systems
• Layouts, dispatching rules, a new machine or
  material handling system etc.
• Evaluating military weapons systems
• Determining hardware/software requirements and
  protocols for communications/computer system.
• Designing and operating transportation systems
  such as airport, ports etc.
• Number of staff assigned to counters and schedule
  of staff. Sequencing rule for take off and
  landing etc.

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Some of application Areas

• Evaluating designs for service organizations such
  as call centers, fast food restaurants, hospitals
  etc.
• Number of nurses and doctors and their schedule,
  number of lab test equipments, layout etc.
• Reengineering of business processes.
• Determining ordering policies for inventory
  systems
• Order size and order quantity decisions.
• Analyzing financial and economic systems.
• www.wintersim.org 1 conference on simulation.
  A very good source of simulation application
  papers.

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System State
The system state is a collection of variables
necessary to describe a system at any given time,
relative to the objectives of the study. Example
In a customer/teller single queue system, the
system state is Number of customers in the bank,
tellers status, arrival times of customers
Systems may be discrete or continuous
State variables change at a finite (countable)
number of points in time e.g. bank teller number
of customers changes only when someone arrives,
completes service or leaves
State variables change continuously with respect
to time e.g. airplane in flight speed and
position change continuously in time

• Many real systems have both discrete and
  continuous characteristics, e.g. traffic flow

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What is a Model?
A model is a representation of a real
system. Physical Models Toys, flight simulators,
wind tunnels Mathematical Models Differential
equations, stochastic models, statistical models,
mathematical programs Computer Models Simulation
models, mathematical programming, stochastics,
statistics, video games, weather forecasters
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Types of models

• Static models simulate a fixed point in time or
  no time dimension exist (Monte Carlo simulation)
• Dynamic models simulate the behaviour of the
  system over time. In discrete event systems, the
  model state changes only in response to events
  rather than the simple passage of time.
• An event is defined as an instantaneous
  occurrence that may change the state of the
  system.
• i.e. The arrival of a customer to a M/M/1 system
  (the number of customers in the system
  changes). End of simulation. A decision in
  simulation (balking, switching btw queues etc.)
• Deterministic models have a unique output for
  each input (i.e. no random variables)
• Stochastic models contain random variables, e.g.
  interarrival times of orders to a factory

We will study stochastic dynamic discrete
simulation models.
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DISCRETE-EVENT SIMULATION

• Definition Modeling of a system as it evolves
  over time by a representation where the state
  variables change instantaneously at separated
  points in time
• More precisely, state can change at only a
  countable number of points in time
• These points in time are when events occur
• Can in principle be done by hand, but usually
  done on computer

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Steps in a simulation study
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Steps in a simulation study
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Formulate the problem

• In a meeting with the project manager, simulation
  expert (this is YOU), and subject-matter expert
  (SME) following issues are discussed
• Problem statement What seems to be wrong
  roughly speaking? The symptoms
• Exm There are too many backorders occurring. How
  can we reduce them without incurring extra
  operational cost?
• Exm Operational cost of the medical clinic seems
  to be too much currently. Can we reduce the
  operational cost of the clinic without
  sacrificing much from the quality of the service?

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Set the objectives and and plan the study

• Determine the Specific questions to be answered/
  scenarios to be tried
• If we reduce the lead time variability or the
  mean lead time, how much can we reduce the back
  orders?
• If we increase the reorder point how much can we
  reduce the backorders, what could be the extra
  cost due to increased inventory levels
• If we reduce the number of doctors or nurses, how
  much extra waiting can we expect for patients?
  How much will we reduce the operational cost by
  doing so.

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Set the objectives and and plan the study

• Performance measures to be used
• Number of daily backorders, average daily
  inventory, total number of reorders
  (replenishments).
• Average waiting time of the patients, average
  utilization of the doctors and nurses.
• Scope of the model Where the model starts and
  ends
• System configurations to be modeled
• Time frame, resources, software to be used

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Collect the data and Define a model

• Collect information on the system layout and
  operating procedures
• Make sure that you talk to more than one people
  who knows about the system
• Specify the level of detail for the model
• Objectives of the study
• Backorder problem in general vs. problem specific
  to a particular item.
• Expected cycle time (throughput rate) of a
  factory vs. designing buffer spaces between two
  machines.
• Availability of data and project duration also
  affect the level of detail
• Collect data to specify model parameters
• Based on the info collected, sketch out a
  conceptual model

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Conceptual model

• Problem and objective descriptions
• The specific questions to be answered using
  simulation
• Description of the system operations in a process
  flow chart format or in a bullet by bullet format
• What data to be collected?
• List and the definitions of performance measures
  that would be collected from simulation in order
  to answer the questions
• List of assumptions made for simplification or
  for any other purpose with the justifications of
  these assumptions.

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Verification and validation

• Construct a computer program and verify
• Use a system simulation software (ARENA, Awsim,
  Automod, Promodel, Extend, Witness etc)
• Verify the simulation model Is the computer
  model is correct representation of the conceptual
  model
• Is the model valid?
• Compare its results with an existing systems
  performance
• Review the results together with SMEs for the
  correctness
• Try the model with different parameter settings
  to see if the model is giving results in accord
  to intuition.

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Designing experiments

• Specify the exact settings of the operational
  parameters or scenarios to be analyzed
• If we reduce the lead time variability by half,
  or the mean lead time by half, how much can we
  reduce the back orders?
• If we increase the reorder point by 25, how much
  can we reduce the backorders, what could be the
  extra cost due to increased inventory levels
• If we reduce the number of dermatologists and
  pediatricians by one, how much extra waiting can
  we expect for patients? How much are we reducing
  the operational cost by doing so?
• Run length, warm-up period, number of runs need
  to be determined

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Production Runs and Output analysis

• For each scenario determine
• Number of runs, run length and warm-up period
• Perform the simulation runs
• Analyze the output two major objectives
• Determining the performance of a certain system
  configuration
• Comparing alternative system configurations and
  scenarios.
• More runs? Could be needed depending on the
  accuracy needed in the output
• Document and present the result (Sell it!)
• IMPLEMENTATION Depends on if the boss buys your
  results (Sound study a good seller)

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Why simulation projects may fail?

• Lack of well defined set of objective(s) at the
  beginning of study
• Inappropriate level of model detail
• Failure to communicate with the management
  throughout the course of the simulation study.
• Treating simulation study as if it is only a
  computer programming exercise.
• Lack of technical background of the analyst.
• Lack of good system data.
• Making only single run with the model to make
  decision.
• Using wrong performance measures.

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Problem statement Health Care
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Problem statement Health Care
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Hw1

• Prbs 1,4, and 6 at the end of chapter 1.