An office building is being constructed during the summer rainy season. It rains one out of every six days during the 3 months of rain. On the days that it rains, the rain accumulation is classified as less than half an inch, between a half inch and one inch, and greater than one inch. Each of these three categories is equally likely. Small, Medium, and Large pumps are able to remove the rain from the project site. The small pumps can handle less than a half inch of rain and can be rented for $100 dollars per day. The medium pumps can handle one inch of rain and can be rented for $150 dollars per day. The large pumps can handle more than one inch of rain and can be rented for $200 dollars per day. The project site is closed for 1 day, if less than a half inch of rain accumulates. The project site is closed for 2 days, if a half inch to one inch of rain accumulates. The project site is closed for 3 days, if more than one inch of rain accumulates. Additionally, $6,000 is the cost for each day that the project site is closed due to overhead. Draw a decision tree. Should the pumps be rented and if so which ones? The following are summarized steps to take in solving the problem:
1) Calculate the probability of rain occurring on a day.
2) Determine the probability for the type of rain event on a day (less than 1/2, 1/2 to 1, and >1)
3) Calculate each of the different Poisson probability for each k occurrences for the different rain event categories (i.e k=1 day, k=2 days, k=3 days, etc.). Note that the calculations will end up being the same for each type of event since each event is equally likely.
4) Calculate the probable contingency cost of rain for each category. This will be the sum of each of the k occurrence probabilities calculated multiplied by the downtime impact cost of the event
5) Determine the pump rental costs for the different types of pumps
6) Compare the pump rental costs to the probable contingency costs calculated to see what is best alternative.