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# Computer Simulation - PowerPoint PPT Presentation

Computer Simulation. The Essence of Computer Simulation. A stochastic system is a system that evolves over time according to one or more probability distributions.

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Presentation Transcript

### Computer Simulation

• A stochastic system is a system that evolves over time according to one or more probability distributions.

• Computer simulation imitates the operation of such a system by using the corresponding probability distributions to randomly generate the various events that occur in the system.

• Rather than literally operating a physical system, the computer just records the occurrences of the simulated events and the resulting performance of the system.

• Computer simulation is typically used when the stochastic system ivolved is too complex to be analyzed satisfactorily by analytical models.

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• Rules of the game:

• Each play of the game involves repeatedly flipping an unbiased coin until the difference between the number of heads and tails tossed is three.

• To play the game, you are required to pay \$1 for each flip of the coin. You are not allowed to quit during the play of a game.

• You receive \$8 at the end of each play of the game.

• Examples:

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• A computer cannot flip coins. Instead it generates a sequence of random numbers.

• A number is a random number between 0 and 1 if it has been generated in such a way that every possible number within the interval has an equal chance of occurring.

• An easy way to generate random numbers is to use the RAND() function in Excel.

• To simulate the flip of a coin, let half the possible random numbers correspond to heads and the other half to tails.

• 0.0000 to 0.4999 correspond to heads.

• 0.5000 to 0.9999 correspond to tails.

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• Freddie runs a newsstand in a prominent downtown location of a major city.

• Freddie sells a variety of newspapers and magazines. The most expensive of the newspapers is the Financial Journal.

• Cost data for the Financial Journal:

• Freddie pays \$1.50 per copy delivered.

• Freddie charges \$2.50 per copy.

• Freddie’s refund is \$0.50 per unsold copy.

• Sales data for the Financial Journal:

• Freddie sells anywhere between 40 and 70 copies a day.

• The frequency of the numbers between 40 and 70 are roughly equal.

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• Four steps must be taken to use Crystal Ball on a spreadsheet model:

• Define the random input cells.

• Define the output cells to forecast.

• Set the run preferences.

• Run the simulation.

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• A random input cell is an input cell that has a random value.

• An assumed probability distribution must be entered into the cell rather than a single number.

• Crystal Ball refers to each such random input cell as an assumption cell.

• Procedure to define an assumption cell:

• Select the cell by clicking on it.

• If the cell does not already contain a value, enter any number into the cell.

• Click on the Define Assumption button.

• Select a probability distribution from the Distribution Gallery.

• Click OK to bring up the dialogue box for the selected distribution.

• Use the dialogue box to enter parameters for the distribution (preferably referring to cells on the spreadsheet that contain these parameters).

• Click on OK.

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• Crystal Ball refers to the output of a computer simulation as a forecast, since it is forecasting the underlying probability distribution when it is in operation.

• Each output cell that is being used to forecast a measure of performance is referred to as a forecast cell.

• Procedure for defining a forecast cell:

• Select the cell.

• Click on the Define Forecast button on the Crystal Ball tab or toolbar, which brings up the Define Forecast dialogue box.

• This dialogue box can be used to define a name and (optionally) units for the forecast cell.

• Click on OK.

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• Setting run preferences refers to such things as choosing the number of trials to run and deciding on other options regarding how to perform the simulation.

• This step begins by clicking on the Run Preferences button on the Crystal Ball tab or toolbar.

• The Run Preferences dialogue box has five tabs to set various types of options.

• The Trials tab allows you to specify the maximum number of trials to run for the computer simulation.

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• To begin running the simulation, click on the Start Simulation button.

• Once started, a forecast window displays the results of the computer simulation as it runs.

• The following can be obtained by choosing the corresponding option under the View menu in the forecast window display:

• Frequency chart

• Statistics table

• Percentiles table

• Cumulative chart

• Reverse cumulative chart

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• A continuous distribution is used if any values are possible, including both integer and fractional numbers, over the entire range of possible values.

• A discrete distribution is used if only certain specific values (e.g., only some integer values) are possible.

• However, if the only possible values are integer numbers over a relatively broad range, a continuous distribution may be used as an approximation by rounding any fractional value to the nearest integer.

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• Some value most likely (the mean)

• Values close to mean more likely

• Symmetric (as likely above as below mean)

• Extreme values possible, but rare

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• Fixed minimum and maximum value

• All values equally likely

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• Fixed minimum and maximum value

• All integer values equally likely

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• Widely used to describe time between random events (e.g., time between arrivals)

• Events are independent

• Rate = average number of events per unit time (e.g., arrivals per hour)

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• Describes whether an event occurs or not

• Two possible outcomes: 1 (Yes) or 0 (No)

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• Describes number of times an event occurs in a fixed number of trials (e.g., number of heads in 10 flips of a coin)

• For each trial, only two outcomes are possible

• Trials independent

• Probability remains the same for each trial

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