Simulation

1
Chapter 13

• Simulation

2
Background

• Simulation is one of the most frequently employed
  management science techniques.
• It is typically used to model random processes
  that are too complex to be solved by analytical
  methods.

3
Advantages

• Simulation is relatively straightforward and
  flexible.
• Simulation can be used to analyze large and
  complex real-world situations that cannot be
  solved by conventional operations management
  models.

4
Advantages

• Simulation allows for the inclusion of real-world
  complications that most models cannot permit.
• Simulation can use any probability distribution
  that the user defines it does not require
  standard distributions.

5
Advantages

• Simulations do not interfere with the real-world
  system.
• It may be too disruptive, for example, actually
  to experiment with new policies or ideas in a
  hospital, school, or manufacturing plant.
• Simulation allows us to study the interactive
  effect of individual components or variables in
  order to determine which ones are important.

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Advantages

• Time Compression is possible with simulation.
• The effects of policies over many months or years
  can be obtained by computer simulation in a short
  time.
• Simulation allows what-if types of questions.
• Managers like to know in advance what options
  will be most attractive. With a computerized
  model, a manager can try out several policy
  decisions within a matter of minutes.

7
Disadvantages

• Good simulation models can be very expensive
  they may take years to develop.
• Simulation does not generate optimal solutions to
  problems as does linear programming. It is a
  trial-and-error approach that may produce
  different solutions in repeated runs.

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Disadvantages

• Managers must generate all of the conditions and
  constraints for solutions that they want to
  examine. The simulation model does not produce
  answers by itself.
• Each simulation model is unique. Its solutions
  and inferences are not usually transferable to
  other problems.

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Uses of Simulation

• System Design - Determine (improved) operating
  conditions.
• System Analysis - Demonstrate how proposed change
  in policy will work compare new policy to
  existing one.
• Simulation Games - Train operating personnel to
  make better decisions regarding utilization of
  new info.

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Simulation Steps

• One begins a simulation by developing a
  mathematical statement of the problem.
• The model should be realistic yet solvable within
  the speed and storage constraints of the computer
  system being used.
• Input values for the model as well as probability
  estimates for the random variables must then be
  determined.

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Random Variables

• Random variable values are utilized in the model
  through a technique known as Monte Carlo
  simulation.
• Each random variable is mapped to a set of
  numbers so that each time one number in that set
  is generated, the corresponding value of the
  random variable is given as an input to the
  model.
• The mapping is done in such a way that the
  likelihood that a particular number is chosen is
  the same as the probability that the
  corresponding value of the random variable occurs.

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Pseudo Random Variables

• Because a computer program generates random
  numbers for the mapping according to some
  formula, the numbers are not truly generated in a
  random fashion.
• However, using standard statistical tests, the
  numbers can be shown to appear to be drawn from a
  random process.
• These numbers are called pseudo-random numbers.

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Simulation Models

• Fixed-time simulation model
• Time periods are incremented by a fixed amount.
  For each time period a different set of data from
  the input sequence is used to calculate the
  effects on the model.
• Next-event simulation model
• Time periods are not fixed but are determined by
  the data values from the input sequence.

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Model Validation

• Verification/validation of both the model and the
  method used by the computer to carry out the
  calculations is extremely important.
• Models which do not reflect real world behavior
  cannot be expected to generate meaningful
  results.
• Likewise, errors in programming can result in
  nonsensical results.

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Model Validation

• Validation is generally done by having an expert
  review the model and the computer code for
  errors.
• Ideally, the simulation should be run using
  actual past data. Predictions from the
  simulation model should be compared with
  historical results.

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Simulation Exercise

• Swapcraft Door-to-Door Simulation
• Salesperson visits 20 homes per night
• 50/50 chance that someone answers the door
• 50/50 chance that its a woman vs. man
• If a man answers, 20 chance of buying 2 parts,
  25 chance of buying 1 part
• If a woman answers, 25 chance of buying 1 part
• Swapcraft pays 5 commission per part sold

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Simulation Exercise
Dime
Nickel
Penny
Outcome
Quarter
No one home
Heads
Tails
Heads
Woman answers
Heads
Heads
1 part sold
Others
0 parts sold
Tails
Man answers
Heads
Heads
2 parts sold
Tails
Tails
1 part sold
Others
0 parts sold