Introduction to Simulation

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Introduction to Simulation
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What is simulation?

• A simulation is the imitation of the operation of
  a real-world system over time.
• It involves the generation of an artificial
  history of a system.
• The observations of the artificial history are
  used to draw inferences about the operating
  characteristics of the system.

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Simulation Models

• A simulation model consists of a set of
  assumptions that describe the operation of a
  system.
• These assumptions are expressed in mathematical,
  logical, and symbolic relationships between the
  entities of the system.

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Simulation Models

• The simulation model, once developed and
  validated, can be used to investigate a wide
  variety of what-if questions about the
  real-world system.

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Monte Carlo Simulation
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A Manual Algorithm

• 1. Calculate the relative frequency of occurrence
  of each possible outcome
• relative frequency number of times x occurs /
  total number of observations Pr(outcome x)

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Spare Parts Example
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A Manual Algorithm

• 2. Calculate the cumulative distribution of the
  possible outcomes - Pr(outcome lt x)

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Spare Parts Example
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A Manual Algorithm

• 3. Use random numbers to simulate the possible
  outcomes by associating these numbers with the
  intervals of the cumulative distribution.
• random numbers a set of numbers, each of which
  has the same probability of occurring

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Spare Parts Example
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A Manual Algorithm

• 4. Repeat step 3 a suitable number of times to
  generate the desired statistics.

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Spare Parts Example
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Simulation with Spreadsheets
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Random Variable Generation

• RAND() - this function returns a uniformly
  distributed random number between 0.0 and 1.0.
• NORMINV(RAND,???) - this function returns a
  normally distributed random variable with mean?
  and standard deviation ??
• Some other distributions can be generated by
  formula.

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Empirical Distributions

• Empirical distributions are distributions based
  on observed historical data that are not fit to
  any specific probability distribution.
• Embedded ifs
• IF(logical_test,value_if_true,value_if_false)
• Table lookups
• VLOOKUP

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Replicating the Model

• Data Tables
• To set up a two-input data table
• In a cell, enter the formula that will use the
  substituted values.
• Starting in the cell below the formula, enter the
  values that you want substituted into one input
  cell. Enter these values in the same column as
  the formula.

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Replicating the Model

• Starting in the cell to the right of the formula,
  enter the values that you want substituted into
  the other input cell. Enter these values in the
  same row as the formula.

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Data Analysis

• Descriptive Statistics
• Histogram
• Anova
• Etc.