Decision Trees Case Study

Decent Essays
Decision Trees - Chelst Chapter 10 Exercises – Kimberly Matthews
10.1 – Sequential decisions: Present an example of a sequence of two or more decisions followed by an uncertainty.
Should we open a bakery or a diner? If we open a bakery, should we sell specialty items, like wedding cakes, or sell a variety of baked goods? If we open a diner, should we be open from 6am – 11pm daily or should we be open 24 hours? 10.2 – Information gathering and decisions: Think of a decision scenario where decisions are interspersed with random events. Avon wants to invent their own line of long-wearing lipstick (8+ hours). * Other companies already offer long-wearing lipstick, so will this just saturate the market? * Can Avon come up with the chemical components to make the lipstick stay in place for 8+ hours? Do a test panel with women to see if they like the product and would use it. * Is Avon offering too many / too few shades? Avon initiates a line of long-wearing lipstick. * How should Avon market their new product line? (offer an introduction sale for the line / have samples for women to try / have their sales associates “talk up” the new lipstick line with a 10% bonus commission for each item sold 10.3 – Refer to Figure 10.26: Interpret sensitivity analysis – the variable cost of high investment +10%. a) How sensitive is the optimal solution to changes in this variable? It is sensitive enough that when adding 10% to the variable cost of the high investment strategy that the optimal strategy shifts from high automation investment to low automation investment. b) What do you notice with regard to the slope? The slope of the high investment option is negative, which tells us that as we increase the variable cost of the high investment option, our expected value decreases. The slope of the low investment option is zero (meaning it’s not changing, as it is not affected by the variable cost of the high investment option). 10.4 – Refer to Figure 10.27: Interpret sensitivity analysis – the variable cost of low investment -5%. a) How sensitive is the optimal solution to changes in this variable? It is sensitive enough that a 5% decrease in the variable cost of the low investment strategy will cause a shift in the optimal strategy at
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The current store price is $50. Construct a decision tree to determine whether or not she should buy the dress now or gamble and wait to try to buy it next week if it remains unsold (If she comes back next week and finds the dress has been sold, Laila will buy it online).
Buy now = $50 expected value
Wait = (50% x $60) + (50% x $37.50) = $48.75 expected value, therefore she should wait a week. b) Just before analyzing her decision, she found another place online that sells the same dress for $55. Why might a lower price online affect her purchase decision in this store? This should definitely sway her to decision to wait a week. Should she buy the dress now or gamble and wait to buy it in the second week if available? She should wait and take a
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These more expensive dresses have only a 30% chance of being sold each week and again they tell the customers that every week they reduce the price buy 25%. She checked and found a similar dress for $90 online. Construct a decision tree for 3 weeks of possible discounts.

10.9 a and d a) Draw a decision tree to determine the number of questions to attempt to maximize expected earnings. What is the best decision and what are the expected earnings? They should stop after two questions to win $2200.00 d) The smart Quiz show is considering changing the reward for answering the third question correctly. Let m represent the amount of money a contestant will earn for correctly answering the third question. Write an equation to calculate the expected value for the last decision as a function of m (assume a 50-50 chance). (2,200 + m) x .5

10.10 b, c, d and e b) Based on your decision tree, do you recommend they bid, and if so, what should they bid per installation? Yes, they should bid $95. c) Under the optimal policy, what is the probability they will win the contract?

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