A circus is scheduled to appear in a city on a given date. The profits obtained are heavily dependent on the weather which can be classified as “good” or” bad”. The circus owners may choose to setup operations in a large open field that is centrally located or rent a small building to stage a small version of the circus. The small building is not expected to be adversely affected by bad weather – thus will not affect the circus for it is well secure and has covered parking for the guests. The following shows the profits of the options and states of nature: States of nature Decision alternatives good bad Set up in field $14,500 -$15,000 Rent small building $5000 $4,000 Probability P(G)=0.5 P(B)=0.5 The circus owners may choose to delay the decision until the day before the event is due. At this time they can obtain the one-day weather report (free) which is usually reliable. This delay will however increase their set up cost by $1000.00 or if they choose to rent, the rental cost will go up by $1500. The following is the reliability of the weather forecasters who will report that the weather will be either rainy or sunny: Reliability of forecast Forecast report good bad Sunny 0.7 0.2 Rainy 0.3 0.8 That is P(S/G) =0.7; P(R/G) =0.3; P(S/B) =0.2; P(R/B) =0.8 After you have computed the revised probabilities round to two decimal places a) Construct the appropriate decision tree to help the circus make the appropriate decisions. This tree must be constructed in logical order with labels and net payoffs. It also includes the revised probabilities b) Fold back the decision tree to determine the best strategy for the circus; you must state this strategy . What is the final expected profit? c) What is the expected value of sample information (EVSI)- the most that the weather forecast values? d) Calculate the expected value of perfect information (EVPI)- the most that should be paid to an expert for perfect prediction of the uncertain outcomes. e) What is the efficiency of sample information?
A circus is scheduled to appear in a city on a given date. The profits obtained are heavily dependent on
the weather which can be classified as “good” or” bad”. The circus owners may choose to setup
operations in a large open field that is
of the circus. The small building is not expected to be adversely affected by bad weather – thus will not
affect the circus for it is well secure and has covered parking for the guests. The following shows the
profits of the options and states of nature:
| States of nature | ||
| Decision alternatives | good | bad |
| Set up in field | $14,500 | -$15,000 |
| Rent small building | $5000 | $4,000 |
| Probability | P(G)=0.5 | P(B)=0.5 |
The circus owners may choose to delay the decision until the day before the event is due. At this time
they can obtain the one-day weather report (free) which is usually reliable. This delay will however
increase their set up cost by $1000.00 or if they choose to rent, the rental cost will go up by $1500. The
following is the reliability of the weather forecasters who will report that the weather will be either
rainy or sunny:
| Reliability of forecast | ||
| Forecast report | good | bad |
| Sunny | 0.7 | 0.2 |
| Rainy | 0.3 | 0.8 |
That is P(S/G) =0.7; P(R/G) =0.3; P(S/B) =0.2; P(R/B) =0.8
After you have computed the revised probabilities round to two decimal places
a) Construct the appropriate decision tree to help the circus make the appropriate decisions. This
tree must be constructed in logical order with labels and net payoffs. It also includes
the revised probabilities
b) Fold back the decision tree to determine the best strategy for the circus; you must state
this strategy . What is the final expected profit?
c) What is the expected value of sample information (EVSI)- the most that the weather forecast
values?
d) Calculate the expected value of perfect information (EVPI)- the most that should be paid to an
expert for perfect prediction of the uncertain outcomes.
e) What is the efficiency of sample information?
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