Introduction to simulation model

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Introduction to simulation model
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What is model?

• Model are simulation that try to include the
  essentials while omitting unimportant details.

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Relationship between input and output parameters
and model
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Classification of problem solving
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What is simulation?

• Simulation is the process of designing a
  mathematical or logical model of a real system
  and then conducting computer-based experiments
  with the model to describe, explain, and predict
  the behavior of the real system (Stewart
  Ronald, 1990).

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When should we simulate?

• The system is complex
• Uncertainty exists in the variables
• Real experiments are impossible or costly
• The processes are repetitive
• Stakeholders cant agree on policy

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When should not we simulate?

• 1. The problem can be solved using common sense
• 2. Simulation should not be used if the problem
  can be solved analytically
• 3. Simulation should not be used if it is easier
  to perform direct experiments
• 4. If the costs exceed the savings
• 5. Simulation should not be performed if the
  resources (data, personnel )or time are not
  available.

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Types of simulation

• In dynamic simulation models, events occur
  sequentially over time. Specialized software is
  required.
• In static simulation models time is not explicit
  and the analysis can be done in Excel
  spreadsheets.

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Monte carlo simulation

• The Monte Carlo method is used for static
  simulation.
• The computer creates the values of the stochastic
  random variables.
• The distribution and its parameters are
  specified.
• Samples are repeatedly drawn from each
  distribution.
• Each sample yields one possible outcome for each
  stochastic variable.
• For each output variable, look at percentiles as
  well as the mean.
• For each input variable, look at a histogram to
  verify that we are sampling from the desired
  distribution.

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Phases of simulation project

• Phase I (design) identify the problem, set
  objectives, design the model, collect data.
• Phase II (execution) empirical modeling,
  specify the variables, validate the model,
  execute the simulation, prepare reports.
• Phase III (communication) explain the
  findings to decision-makers.

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Risk assessment

• Risk assessment means thinking about a range of
  outcomes and their probabilities.
• Variation is inevitable.
• Knowing the 95 range of possible values for the
  decision variable as well as the most likely
  value m, is the point of risk assessment.
• Risk assessment is useful when the model is
  complex

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Distribution

• Four probability distributions are used more with
  static simulation because they correspond to real
  life and can be easily simulated in Excel.

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Distribution
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Distribution
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Distribution
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Distribution
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Other Ways to Get Random Data
Tools gt Data Analysis gt Random Number Generation
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• Example 1 (machine reliability and maintenance)
• A large milling machine has three different
  bearings that fail in service. The probability
  distribution of the life of each bearing is
  identical. When a bearing fails, the mill stops,
  a repairperson is called, and a new bearing is
  installed. The delay time of the repairperson's
  arriving at the milling machine is also a random
  variable. Downtime for the mill is estimated at
  10 per minute, and the direct on-site cost of
  the repairperson is 24 per hour. It takes 20
  minutes to change one bearing, 30 minutes to
  change two bearings, and 40 minutes to change all
  three. Each bearing costs 30. A proposal has
  been made to replace all three bearings whenever
  a bearing fails instead of replacing them
  individually. Is this proposal worthwhile?
• Assuming historical data on bearing life has
  been collected and rounded to the nearest 100
  hours, but that the detailed data have been
  discarded. In addition, the delay time has been
  estimated judgmentally as either 5, 10, or 15
  minutes based on conversations with workers
  (distribution shown in Table 3.1). The form of
  the data forces us to make some assumptions about
  the simulation model. For example, because
  bearing lives are rounded to increments of 100
  hours, there will be instances when the model
  will generate multiple bearing failures at the
  same time. This is unlikely to occur in
  practice, so we can reasonably assume that no
  more than one bearing will be replaced at any
  breakdown time. The baring life distribution
  shows in Table 3.2.

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Dynamic simulation

• In a dynamic simulation, stochastic variables may
  be discrete (measured only at regular time
  intervals) or continuous (changing smoothly over
  time).
• Discrete event simulation assesses the system
  state by a clock at distinct points in time.
• A snapshot of the system state at any given
  moment is observed.

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Dynamic simulation

• The emphasis in discrete event simulation is on
  measurements such as
• - Arrival rates
• - Service rates
• - Length of queues
• - Waiting time
• - Capacity utilization
• - System throughput

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• Examples for discrete event simulation with Arena
  see extra sheet.