Microsoft Office Tutorials and References

In Depth Information

and a circle. The rectangle represents a step or decision in the process, e.g. the arrival

of attendees or the accumulation of revenue. The circle represents an
uncertain

event and the outputs of the circle are the anticipated results of the event. These

are the symbols that are also used in
decision trees
, but our use of the symbols is

slightly different from those of decision trees. Rectangles in decision trees represent

decisions, actions, or strategies. In our use of these symbols, we will allow rectan-

gles to also represent some state or condition, for example the collection of entry fee

revenue or the occurrence of some weather condition like rain. Exhibit 7.6 shows

the model for this new IFD modeling approach.

In Exhibit 7.6, the ﬂow of the IFD proceeds from top to bottom. The ﬁrst event

that occurs in our problem is the resolution of the uncertainty related to weather.

How does this happen? Imagine that Fr. Eﬁa awakens early on October 6th and looks

out his kitchen window. He notices the weather for the day. Then he assumes that

the weather he has observed will persist for the entire day. All of this is embodied

in the circle marked
Weather Condition
and the resulting arrows. The three arrows

represent the possible resolution of
weather condition
uncertainty, each of which

leads to an assumed, deterministic number of participants. In turn, this leads to a

corresponding entry fee revenue varying from a low of $15,000 to a high of $40,000.

For example, suppose Fr. Eﬁa observes
sunshine
out of his kitchen window. Thus,

weather condition
uncertainty is resolved and 4000 attendees are expected to attend

Vegas Night at OLPS
, resulting in $40,000 in entry fees.

7.4.4 Attendees Play Games of Chance

Next, the number of attendees determined earlier will participate in each of the three

games. The attendees either win or lose in each game; an attendee win is bad news

for OLPS and a loss is good news for OLPS. Rather than concerning ourselves with

the outcome of each individual attendee’s gaming results, an
expected
outcome of

revenues can be determined for each game and for each weather/attendee situation.

An
expected value
in decision analysis has a special meaning. Consider an indi-

vidual playing the WOD. On each play the player has a 35% chance of winning.

Thus, the average or expected winnings on any single play are $17.50 ($50
∗
0.35)

and the losses are $32.50 ($50
∗
[1–0.35]). Of course, we know that an attendee

either wins or loses and that the outcomes are either $50 or $0. The expected values

represent a weighted average; outcomes weighted by the probability of winning or

losing. Thus, if a player plays WOD 100 times, the player can
expect
to win $1750

(100
∗
$17.50) and Fr. Eﬁa can
expect
to collect $3250 (100
∗
32.50). The expected

values should be relatively accurate measures of long term results, especially given

the large quantity of attendees, and this should permit the averages for winning (or

losing) to be relatively close to odds set by Fr. Eﬁa.

At this point we have converted some portions of our probabilistic model into a

deterministic model; the probabilistic nature of the problem has not been abandoned,

but it has been modiﬁed to permit the use of a deterministic model. The weather

Search JabSto ::

Custom Search