Question: An orange grower in Florida faces a dilemma. The weather forecast is for cold weather, and there is a 50% chance that the temperature tonight will be cold enough to freeze and destroy his entire crop, which is worth some $50,000. He can take two possible actions to try to alleviate his loss if the temperature drops. First, he could set burners in the orchard; this would cost $5,000, but he could still expect to incur damage of approximately $15,000 to $20,000. The estimated loss is $17,500. Second, he could set up sprinklers to spray the trees. If the temperature drops, the water would freeze on the fruit and provide some insulation. This method is cheaper. The cost is $2,000, but it is less effective. With the sprinklers, he could expect to incur as much as $25,000 to $30,000 of the loss with no protective action. The estimated loss is $27,500.
Complete the following tasks.
(1) Construct a decision tree to capture the above scenario.
Note that your tree should include the following considerations if any.
- We use the negative sign (-) for the cost, the expenses, cash outflow, etc.
- We use the positive sign (+) for the revenue, profit, cash inflow, etc.
- Your tree will be able to generate the Cumulative Chart that includes the curves of all the possible decision strategies.
(2) Write down the number of decision strategies that you can find from your tree.
(3) Write down the expected loss for each decision strategy.
(4) Generate the risk profile for the decision tree. The risk profile only includes the Cumulative Chart.
(5) Generate the two-way sensitivity analysis between the burners and the sprinklers. Set the steps = 50.
(6) Explain which optimal decision strategy between the burners and the sprinklers should be chosen based upon the results from (3) to (5).