Part G: Approximating Probability Distributions
One possible approximation is obtained by the "stair-step" method yields the following:
Here is the "10-50-90" approximation, which we use to solve the decision tree:
These two approximations are very close. We will use the second one, the "10-50-90" approach, because it has the three values actually assessed from our decision maker. The difference in expected value between these two approximations is only $0.025k ($25).
1. Using the full "stair-step" method, approximate the cumulative distribution you assessed in Part F with a tree containing three branches. This is a more accurate method than using the "10-50-90" approximation.
2. Compare the approximation you created in Step 1 to the results obtained from the "10-50-90" approximation method. Although less accurate, this is the approximation you should use in the decision tree in Part H.
Part H: Decision Tree and Decision Tree Analysis
1. (Optional) Draw Freemark Abbey's decision tree for the choice between harvesting now or waiting. The influence diagram from Part D will help. Include in your tree an analysis of what Jaeger should do if it rains but the mold does not form. Discuss the decision tree with your coach.
2. A completed decision tree, with branch structure and labels, is attached. Calculate the value for each endpoint of the tree, based on information provided previously. You may use some of the information from Part E, the tornado diagram calculations. Places prices, any reputation values, and calculated net revenues in the columns of the table and the right side of the tree. The table on the next pages summarizes the data you need. Save the last column of the tree for Part I.
3. Assign probabilities to the tree, again relying on data provided previously (and summarized on the next page)
4. Evaluate the decision tree.
a) "Roll back" Freemark Abbey's decision tree.
b) Should Jaeger harvest now or wait? Why?
c) Plot the cumulative probability distribution for the Harvest Now and Wait alternatives. Then sketch below the graph the flying bars and expected values for these two alternatives.
d) Discuss these results with your coach.
Please make the following assumptions in the event of no rain:
- If the acid level stays above 0.7%, the grapes will either ripen to 20% or 25% sugar content, with equal probability.
- If the acid level drops below 0.7%, the grapes must be harvested immediately at a sugar content of 19%
Questions to answer about your decision tree analysis:
1. Alice is really pushing the concept of bottling a thin wine and advertising it as Freemark Abbey "Lite." Is this a good idea or not?
2. What's the best decision-harvest now or wait? Why?
3. If Murray were to get a perfect forecast of Rain/No Rain, how would that improve our decision-making? What is the most the winery should pay for a better forecast?
4. Given that Jaeger Waits (i.e., not harvest now), does Jaeger prefer rain or no rain?
5. How much financial risk is involved in waiting? Specifically, what is the probability that if he waits, William will have an outcome lower than harvesting now? (To answer this question, you need to draw the cumulative probability distribution.) What could Jaeger do to try to minimize the down side and maximize the up side?
6. Barney thinks the winery should apply mold spores now to ensure the mold if it rains. What would it be worth to spread spores now and guarantee mold if it rains (i.e., what is the most the winery should pay for spores)?
Part I: Value of Information and Control
1. On weekday evenings, the Napa Valley SuperStation rents its SuperDoppler weather detector to vineyards throughout the valley. The detector is portable and can be brought right to the vineyard. This results in very accurate local forecasts (you can assume "perfect"). The SuperStation charges $1,000 per use. Should Wm. Jaeger rent it? Murray the Meteorologist is eager to rent the radar.
2. Barney the Botanist gave a call to Harvey Borz of Borz's Overnight Mold Spores. Harvey sells Botrytis spores and guarantees that if you use his spores and it rains, Botrytis mold will develop.
One application would be enough to treat Freemark Abbey's Riesling grapes and would cost $10,000. Wm. Jaeger must pay the $10,000 up front (before the storm), but if he does that 24 hours before the predicted storm, the spores will arrive and can be applied just before the rain starts, thereby ensuring that Botrytis mold will form immediately after the warm rain. Should Wm. Jaeger buy the spores? Barney strongly advocates that he should.
3. After you arrive at recommendations, discuss them with your coach. Update the cumulative probability distribution and flying bars for your recommended strategy.
Part J: Final Presentation
It is likely that your analysis has produced significant insights for Freemark Abbey and its managers; it is now time to present them to Wm. Jaeger.
- Prepare for a dialogue with Jaeger on whether Freemark Abbey should harvest the Riesling grapes now or wait. Also, give your recommendations regarding the improved weather forecast, the spores, and any superior hybrid strategies that you have identified.
- Prepare simple graphics that tell your story and make the best course of action clear. You do not have to (in fact you should not) use all of the graphics you have learned in this course. Choose the ones that illustrate the quantitative insights behind your recommended strategy.
- Your team should ensure that they have addressed all of the important issues in the case? Ask yourself if you have left anything out. What information could change before your meeting with Jaeger? Would such changes alter your recommendation?
- A common mistake is to focus on "the steps we took" rather than "the insights and conclusions we reached." Ask yourself what matters most to the decision makers, and plan the best way to communicate that.
Attachment:- Assignment.rar