These slides summarize the most important elements of the simulation output in Risk, based on the ex

1

• These slides summarize the most important
  elements of the simulation output in _at_Risk,based
  on the example of the Dynatron Case
• For a more detailed introduction to _at_Risk see
  also Winston Albright, Section 11.6 and the
  _at_Risk-Tutorial on the companion CD-ROM
• For a general discussion of the use of
  simulation, see the website of Sam Savage at
  Stanfordhttp//www.stanford.edu/dept/MSandE/facu
  lty/savage/including, in particular, a tutorial
  on uncertaintyhttp//analycorp.com/uncertainty/

2

• This is the screen that pops up automatically,
  once you have run the simulation
• It lists a number of statistics, such as the
  mean, maximum, and minimum value for each input
  and output parameter

• You can always return to this screen by clicking
  on the Summary Statistics icon

3

• You can obtain additional statistics for each of
  the parameters by selecting the Detailed
  Statistics report
• This report includes, e.g. the standard
  deviation, variance, and selected cumulative
  probabilities for each parameter

For example this number indicates that the
probability that the net result is smaller or
equal to 119953 equals 10
4

• You can also visualize the simulation output
  graphically
• To this end, select an output parameter, click
  on the Graph icon, and select the type of
  graph you would like to generate for example a
  histogram

5

• This is a histogram representation of the
  probability distribution of the net result

The sidebar lists again the summary statistics
The ruler refers to the cumulative
distributionfor example, these numbers indicate
again that the probability that the net result is
smaller or equal to 119953 is 10
6

• Another useful graph. representation is the
  Ascending Cumulative Line
• It plots for each value of the output (here the
  net result) the probability that the output is
  smaller or equal to this value

This point indicates that the probability that
the net result is smaller or equal to 175000 is
(approximately) 20
You can use this output to determine the risk
that the result will be below a certain value or,
conversely, the potential that the result will be
above a certain value
7

• By means of the function Risksimtable() you can
  run multiple simulations successively for
  different choices of a decision variable (such
  as different production quantities in the
  Dynatron case)
• You can then compare the performance of the
  different choices based on their output
  statistics (in particular, mean and standard
  deviation)
• You can also plot the output distributions for
  the different choices in a single graph
• To this end, plot the results for one of the
  outputs as before then right- click the graph
  select Format Graph select Variables to Graph
  check the outputs you want to add

8

• In this way, you can, for example, compare the
  risk of having a net result below 100,000 for
  the three strategies

Strategy I (Sales)Prob. of net result
below100,000 is 23
Strategy III (Gassman)Prob. of net result
below100,000 is 13
Strategy II (Production)Prob. of net result
below100,000 is 8
9

• Which strategy you should eventually select
  depends on your risk attitude
• If you are risk-neutral you should pick the
  strategy with the highest mean ( expected
  output)
• If you are risk-avoiding, you may be willing to
  pick a strategy with a slightly lower mean, if it
  also carries a smaller risk
• There are many ways to measure the risk related
  to a strategy, in particular the standard
  deviation of its output, its minimum output (max.
  downside risk), its maximum output (max. upside
  potential),
• but also the kind of threshold probabilities
  analyzed in the previous slides (probability of
  output below a certain value)
• If you are risk-seeking you may be willing to
  pick a strategy with a slightly lower mean, if it
  also offers a higher upside potential