Weather forecasts in construction. A company is to carry out a rain-sensitive component or a construction project. One option is to hire a subcontractor (sub) to do the work at a fixed cost, c. regardless of weather conditions. Another option is for the company to rent equipment and do the job itself. If it does the job itself and it does not rain during the construction period, a savings of 25% will result. However, if it does rain the company is not prepared for all the modifications that would be necessary, and the final cost would be twice that of hiring the work done. Since this situation comes up frequently, the company has analyzed weather data for the construction period as shown in the table below. It is now 30 days from the beginning of the construction period, and the company has four options: (1) hire the subcontractor immediately, (2) rent (reserve) the equipment immediately in order to do the work itself, (3) wait until the seven-day weather report to decide, or (4) wait until the one-day weather report to decide. No equipment rental penalties are incurred for waiting but if the company waits until one day before the construction period, the cost of hiring a subcontractor will be 25% higher.
| Joint Probabilities | |||
Seven-Day Forecast | One-Day Forecast | |||
Actual Outcome | Rain | No rain | Rain | No rain |
Rain | 0.08 | 0.12 | 0.12 | 0.08 |
No rain | 0.17 | 0.63 | 0.18 | 0.62 |
(a) Are there biases in the weather forecast? If so,what are they?
(b) Draw the complete decision tree for tile contractor and determine the optimal action and associated cost (carry probability calculations out to the third decimal place when necessary). What is the expected percentage cost savings?
(c) Assuming that the two Forecasts are independent, if the seven-day forecast is for rain should the contractor wait for the one-day forecast before deciding what to do, or should he take immediate action?
(d) What is the EMVI gained from knowing only the marginal probabilities of rain and no rain for the construction period? What is the EMVI gained from knowing the joint probabilities for the seven-day and one-day weather forecasts?
(e) What is the EMVPI for this problem, assuming that the company knows the marginal probabilities for rain and no rain?
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