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DECISION & RISK ANALYSIS
FINAL EXAM
Part I: Decision Analysis
Gucci, a luxury brand, is trying to decide whether to launch a new product globally or focus on the production of the Gucci Chloe handbag. If Gucci decides to continue producing Chloe Handbag, its total profit will be £2M, where M stands for a million. On the other hand, if Gucci decides to launch the new product and no longer produce Chloe Handbag, it has to make £4M initial investment. However, there is significant uncertainty about whether the new product will eventually succeed in the global market. Specifically, there are three possible outcomes in the global market, namely, great, normal and bad. The global market outcome is great, normal, and bad with probabilities 0.4, 0.3 and 0.3 respectively. When the global market outcome is great, normal and bad, units sold in the global market is, respectively, 60K, 30K, and 10K, where K stands for a thousand. Gucci’s unit margin (i.e., price minus variable cost) from the new product in the global market is £180.
Concerned with the uncertainty, Gucci looks for ways to increase its chances of success from launching the new product in the global market. Its design team believes that after launching the product, their chances of succeeding in the global market will increase if they hire a world- known designer. Hiring the famous designer will cost Gucci £3M, where M stands for a million. Gucci believes that once the new product is designed by the famous designer, the global market outcome will be either great or normal with probabilities 0.6 and 0.4, respectively. In this case, the total units sold in the global market will still be 60K and 30K when the market outcome is great and normal, respectively.
Question 1. Decision Tree
(i) Construct the decision tree and recommend an optimal strategy for Gucci. What is Gucci’s expected profit under the optimal strategy.
Question 2. Risk Profiles and Value of Control
(i) State the risk profiles associated with Gucci’s decision whether to hire the famous designer or not.
(ii) What is the maximum amount Gucci will be willing to pay to hire the famous designer?
Question 3. Value of Perfect Information
Assume that Gucci decides not to hire the famous designer any more. Gucci’s marketing experts believe that because of its international nature, London represents the global market fairly well. Hence, in order to get more information about the global market, Gucci considers testing the new product in London first and then decide whether to launch the new product in global market or not.
Similar to the global market, there are three possible outcomes in London market: great, normal and bad. Using past data for similar products, Gucci estimates the probability that the London market will be great, normal and bad for the new product with probabilities 0.35, 0.3 and 0.35, respectively.
Assuming London perfectly represents global market (i.e., the global market outcome is great (respectively, normal and bad) if the London market outcome is great (respectively, normal and bad) with probability 1), answer the following question.
(i) Construct the decision tree and recommend an optimal strategy for Gucci if the cost of testing the new product in London is £1M.
Question 4. Value of Imperfect Information
Continue using information in question 3, i.e., hiring the famous designer is no longer an option, and Gucci considers testing the new product first in London before deciding whether to launch it in global market. Now suppose that London market imperfectly represents the global market. Specifically,
● if the London market outcome is great, the global market outcome will be great, normal, and bad with probabilities 0.8, 0.1, and 0.1, respectively.
● if the London market outcome is normal, the global market outcome will be great, normal, and bad with probabilities 0.25, 0.5, and 0.25, respectively.
● if the London market outcome is bad, the global market outcome will be great, normal, and bad with probabilities 0.1, 0.1, and 0.8, respectively.
(i) Construct the decision tree for the case where Gucci decides to test the new product in London Market.
(ii) How much would Gucci be willing to pay to test the new product in London the most in this case?
Part II: Optimization
Question 5. True or False
Circle “T” if the statement is true and “F” if the statement is false. Each question is worth 2.5 points.
(i) (T/F) A binary variable takes only values of 0,1 or 2.
(ii) (T/F) The shadow price of a binding constraint will always be positive.
(iii) (T/F) Increasing the right hand side of a constraint will always change the objective function.
(iv) (T/F) A linear optimization model has always one single solution.
Question 6. Setting up the Optimization Model
Gucci needs to produce exactly one of each type of five different bags in its factory in Milan for the Vogue Fashion Show that will take place one week from now. Gucci factory in Milan has three work stations A, B and C. The cost per hour in all three stations is the same but the time required to produce the required number of each bag type is different in each station. Each station can operate at most 40h/week. The time (in hours) for the stations to produce the required number of each bag type are shown in the table.