Assume an investor wants to build a hotel in an area where hurricanes occasional

Question

Assume an investor wants to build a hotel in an area where hurricanes occasionally hit. Suppose that hurricanes could be strong, medium or weak. The investor has to decide how much to reinforce the buildings at the hotel complex. Hotel can be reinforced to withstand a strong, medium or weak hurricane. Probabilities of having a strong, medium, and weak hurricane in the area are 5%, 30%, and 65%. If hotel is built to withstand a strong hurricane, it will cost 30 million dollars and it will not be damaged in any kind of hurricane. .If hotel is built to withstand a medium hurricane, it will cost 20 million dollars and it will not be damaged in a medium and weak hurricane, but it will take 5 million dollars damage in a strong hurricane. If hotel is built to withstand a weak hurricane, it will cost 15 million dollars, it will take 10 and 15 million dollars damage in a medium and strong hurricane, but it will not be damaged in a weak hurricane. . The investor can buy a hurricane forecast service from National Hurricane Center (NHC) that predicts hurricane strength. If the hurricane is strong: NHC predicts a strong hurricane correctly in 80% of the time NHC predicts a medium hurricane incorrectly in 10% ofthe time NHC predicts a weak hurricane incorrectly in 10% of the time If the hurricane is medium: NHC predicts a strong hurricane incorrectly in 20% of the time NHC predicts a medium hurricane correctly in 70% of the time NHC predicts a weak hurricane incorrectly in 10% of the time o If the hurricane is weak: NHC predicts a strong hurricane incorrectly in 10% of the time NHC predicts a medium hurricane incorrectly in 20% of the time NHC predicts a weak hurricane correctly in 70% of the time a) Calculate all the required probabilities. b) Draw the decision tree (optional). c) Calculate the EMV without information. d) Calculate the EMV with perfect information.

Explanation / Answer

Let ES, EM and EW be an event of a strong, medium and weak hurricanes respectively and AS, AM, AW be events that NHC predicts strong, medium and weak hurricanes respectively.

According to the problem, P(ES)=0.05, P(EM)=0.3, P(EW)=0.65, P(AS|ES)=0.8, P(AM|ES)=0.1, P(AW|ES)=0.1,

P(AS|EM)=0.2, P(AM|EM)=0.7, P(AW|EM)=0.1, P(AS|EW)=0.1, P(AM|EW)=0.2, P(AW|EW)=0.7.

P(AS)=P(AS|ES)XP(ES)+P(AS|EM)XP(EM)+P(AS|EW)XP(EW)=0.165

P(AM)=P(AM|ES)XP(ES)+P(AM|EM)XP(EM)+P(AM|EW)XP(EW)=0.345

P(AW)=P(AW|ES)XP(ES)+P(AW|EM)XP(EM)+P(AW|EW)XP(EW)=0.49

P(ES|AS)=(P(AS|ES)XP(ES))/P(AS)=0.24, P(ES|AM)=0.01, P(ES|AW)= 0.01,

P(EM|AS)=0.36, P(EM|AM)=0.61, P(EM|AW)=0.06,

P(EW|AS)=0.40, P(EW|AM)=0.38, P(EW|AW)=0.93.

c) Calculation the EMV without information:

The expected monetary value is how much money you can expect to make from a certain decision.

Since there is no damaged in any kind of hurricane when hotel is build to withstand a strong hurricane, then

EMV for this type of hotel=30 million dollars,

Since there is no damaged in a medium and weak hurricane when hotel is build to withstand a medium hurricane, then

EMV for this type of hotel=(20-5xP(ES)) million dollars=(20+5x0.05) million dollars=20.25 million dollars

Since there is no damaged in a weak hurricane when hotel is build to withstand a weak hurricane, then

EMV for this type of hotel=(15-(10xP(EM)+15xP(ES))) million dollars=(15-(10x0.3+15x0.05)) million dollars=18.75 million dollars

EMV without information=(30+20.25+18.75) million dollars=69 million dollars

d) Calculation the EMV with information:

Since there is no damaged in any kind of hurricane when hotel is build to withstand a strong hurricane, then

EMV for this type of hotel=30 million dollars.

Since there is no damaged in a medium and weak hurricane when hotel is build to withstand a medium hurricane, then EMV for this type of hotel=(20+5x(P(ES|AM)+P(ES|AW))) million dollars=(20-5x0.02) million dollars=20.1 million dollars

Since there is no damaged in a weak hurricane when hotel is build to withstand a weak hurricane, then

EMV for this type of hotel=(15+(10xP(EM|AW)+15x(P(ES|AM)+P(ES|AW)))) million dollars=(15+(10x0.06+15x0.02)) million dollars=15.9 million dollars

EMV without information=(30+20.1+15.9) million dollars=66 million dollars

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