Questions:
Q1) Suppose there are two variables whose value we are unsure of. What are the benefits and limitations of each of two one-way sensitivity plots, a tornado diagram, a two way sensitivity plots compared to the others?
Q2) Consider the card tournaments with values reproduced below:
- Bingo single prize $100 (20% chance)
- Poker single prize $30 (40% chance)
- Blackjack 1st place: $20 (30% chance)
2nd place: $10 (30% chance)
Suppose you are not entirely sure of those values. Specifically, you think the probability of winning at Bingo could be as low as 0.05 and as high as 0.20. You also think the first place prize money for Blackjack could be as low as $20 or as high as $40. For these two variables, draw two one-way sensitivity plots (one plot for each variable; plot all alternatives) and a two-way sensitivity plot.
Q3) An orange grower in Florida faces a dilemma. The weather forecast is for cold weather, and there is a 20% to 60% chance p that the temperature will be cold enough to destroy a portion β of the entire crop, which is worth $50k in total. He estimates β is between 50% and 100%.
He can take two possible actions to try and alleviate his loss. First, he could set burners in the orchard; this would cost $8k, but he would still expect to incur damage of 0.4 β of his crop.
Second, he could set up sprinklers to spray the trees. If the temperature drops, the water would freeze on the fruit, providing some insulation. This method is cheaper, costing $4k, but less effective. With the sprinklers, he could expect to incur damage of 0.6 β of his crop.
Draw the decision tree and a two-way sensitivity plot for this problem. Would you make a recommendation to the farmer based on this result? If you later found out p was between 0.3 and 0.5 and that β was between 0.6 and 0.8, would you make a different recommendation?
[Note: The formulas you (should) get for the boundary lines are non-linear. You can use plotting software or calculate a few points along the curve to plot by hand (like if you had a linear formula y=3x+2 and you plugged in a few values of x to get the corresponding y coordinate)]
Q4) Describe the "philosophy" of each of the following criteria for making decisions:
a) Expected value
b) Risk profile dominance (stochastic or deterministic)
c) Most likely outcome
d) (Uniform) Average over outcomes
e) Maximin
f) Maximax
g) Hurwicz
h) Minimax regret
i) Expected regret
j) Going with your gut instinct
Q5) Two bettors at a race crack both believe in using the Laplace principle. They are considering a bet on a horse which carries the number I and wondering whether to bet $2 on this horse or not to bet on the race at all. If number I wins he is expected to pay $6, yielding a profit of $6-$2 = $4. One bettor argues that there are two possible futures, the horse either wins or loses. The other bettor feels that there are six possible futures since one of the six horses in the race will win. What conclusions will they reach?
Q6) A retailer is wondering how many units of a perishable item to stock. The demand for the item during a stocking period could, in his opinion be 0, 1, 2, 3, or 4 units, but he does not feel able to estimate the probabilities. He will suffer a loss of $1 for each unit stocked but not sold, and make a profit of $10 on each unit sold. Would you advise a policy of minimizing the maximum loss? (For this, since there is one decision and one uncertain node makes a table like in Morris 8.07; also calculate the table of regrets and from that determine the maximum regrets of each alternative).
Q7) Case Study: Clemen Reilly "Dumond International, Part I" on pages 211-213.
Question: Explain why Nancy believes that DuMond should go with the new product.
Assignment Reading -
https://www.dropbox.com/s/byck2rfmhhf586v/Assignment%20Reading.rar?dl=0