Module C9

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Module C9

• Simulation Concepts

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NEED FOR SIMULATION

• Mathematical models we have studied thus far have
  closed form solutions
• Obtained from formulas -- forecasting, inventory,
  queuing
• Obtained by algorithms -- linear programming,
  PERT/CPM
• However, each of these models had to satisfy a
  restrictive set of assumptions
• Many real-life situations do not meet these
  conditions
• SIMULATION can be used to get good results

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BACKGROUND

• Simulation is, in fact, the most used management
  science technique
• Simulation is not an optimization procedure like
  the one used to solve linear programs
• However, if you are considering one of a set of
  options, simulation can indicate which of these
  options appears to be the best in the set.

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BASIC IDEA

• Recognize the components of the system under
  study
• Develop a random number mapping that will map
  random numbers from a (computer generated) random
  number table into events

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PSEUDO RANDOM NUMBERS

• Random numbers should be uniformly distributed
• each digit in a random number should have a
  probability of 1/10 of occurring after any other
  digit
• no pattern should exist in the random numbers
• Random numbers generated by a computer program
  are done so by an algorithm and the above
  conditions may be slightly violated
• The result is that the random numbers are not
  truly random - they are PSEUDO RANDOM NUMBERS

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BENEFIT OF USING PSEUDO RANDOM NUMBERS

• The string of random numbers can be regenerated
• This allows us to compare policies under exactly
  the same conditions

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PROBABILITIES AND RANDOM NUMBERS

• Typically computer generated random numbers are
  numbers between 0 and 1
• We can lop off the decimal for convenience
• The probabilities of possible events will be
  expressed as 1-digit, 2-digit, 3-digit, or .
  probabilities -- the random numbers we use/assign
  should be of the same length

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RANDOM NUMBER MAPPINGS

• Suppose that the number of students that miss a
  MSIS 361B class have been observed to be 0, 1, 2,
  3, or 4 with the following probabilities
• NUMBER 0 1 2 3
  4
• PROB. .21 .35 .19 .15
  .10
• RN Map 00-20 21-55 56-74 75-89 90-99

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APPROACH

• Generate a set of random numbers and map them
  into events
• We will choose the first two digits from column 1
  of the random number table in the book

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Simulation of 5 Classes
Class Random Absences

• 1 65 2
• 2 77 3
• 3 61 2
• 4 88 3
• 5 42 1

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ANALYSISBETTER RESULTS

• We can now analyze simulated results
• Average absences (23231)/5 2.2
• For better results we can
• Repeat this 5-class simulation many times
• Run the simulation for many more than 5 classes

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Module C9 Review

• Simulation can be used to approximate complex
  systems
• Use of pseudorandom numbers
• Random Number Mapping into Events
• Calculations
• How to Gain More Confidence