MSINM014/MSING014/MSING014B
DECISION & RISK ANALYSIS ─ 2015
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.
The values in the cells assume that each bag type is produced entirely by a single station. For example, if workstation B operates for 18 hours it can produce all the required quantity for briefcases and station C can work on another bag type. However, the production of each bag type can be shared with completion times being determined proportionally. For example, work station B can operate 9 hours for briefcases (and the rest 31 on another bag type) and work station C can operate 10 hours for briefcases (and the rest 30 on another bag type) and the required amount of one briefcase will be produced. If no entry exists in a particular cell it means that the corresponding bag type cannot be produced in the corresponding work station. The goal of Gucci is to minimize total production time.
|
Work Station/Bag Type
|
Briefcase
|
Backpack
|
Clutch
|
Handbag
|
Purse
|
|
A
|
-
|
20
|
17
|
21
|
34
|
|
B
|
18
|
23
|
-
|
28
|
31
|
|
C
|
20
|
-
|
15
|
26
|
37
|
Set up the optimization model. Make sure to specify the objective function, the decision variables, and the constraints.
Part III: Simulation
Many of Gucci hand bags are produced in a cluster of small factories in Italy, called “ manufacturing clusters” . Many of these factories are boutique manufacturers that specialize in making a few specific high-end product for small number of clients.
Mr. Arzignano’s family has been running a factory that specializes in high-end leather handbags for 5 generations. For the past decade, his factory has been responsible for manufacturing one type of high-end Gucci handbag. The high-quality leather for the bags are processed, colored, and sewn together with other materials to produce a bag. Production of these bags are extremely labour-intensive, and also capital intensive requiring many sophisticated machinery (e.g. to process the high volume of leather).
In the past few years, the industry in general has been struggling with economic recessions and is facing steep competition from China. Mr. Arzignano’s company has also been losing orders for their high-end items to Chinese companies. As a result, the company is struggling to maintain profitability with profit being practically zero. To maintain profitability and utilize his company’s high-end expertise, Mr. Arzignano is considering to downsize some of his workforce, and redistribute the rest of the workforce for production of one ultra-high margin product for Gucci. If he were to do so, the annual profit can be estimated by computing the annual revenue and cost (Annual Profit = Revenue – Cost).
The price to charge Gucci depends on many factors and would need to be negotiated with Gucci. Each handbag sold to Gucci (which Gucci sells retail for £8,000) earned Mr. Arzignano and estimated £1,500. The order quantity was on average 600 annually (50 bags/month). The variable cost, consisting of paying skilled artisans and leather, is £800, and the fixed cost is £300,000 mainly consisted of rent and annual operating license. Based on these estimates Mr. Arzignano would earn a positive profit of £120,000.
However, he does not feel comfortable with his calculation because he cannot afford to lose more than £100,000 - if so, he will have to close down the factory all together. He says that the price per bag he can charge has to be negotiated and can in fact be any number between £1,200 and £1,800. The order quantity from Gucci can also vary significantly between 360 and 800, though he feels 600 is most likely. Variable cost can also vary between £800 and £1000, though £800 is most likely.
The Italian government is working to re-vitalize the manufacturing cluster by providing a discount on rent and licensing fees. If this occurs, the fixed cost would decrease by 33%. However, whether it would take effect, Mr. Arzignano is unsure and would put a 50-50% probability.
He is keen to understand whether that would be a good strategy to improve profitability and has consulted you for advice.
Question 7. Setting up the Model
(i) Formally state the objective(s) and the necessary equations.
(ii) Determine the uncertain quantities and determine their distributions
(iii) Based on his range of values, is there a theoretical chance that Mr Arzignano will not be profitable? In other words, state the worst case scenario.
Question 8. Simulation Analysis
Based on the model created above, you perform. a simulation analysis (1,000 iterations) using @Risk, which produced the following output.
Annual profit
(i) Determine the average profit, and provide explanation of its meaning
(ii) What is the probability of being unprofitable?
(iii) Suppose the current profitability of the company (without downsizing) would result in £0 profit. Would you recommend Mr. Arzignano to proceed with downsizing? Explain your rationale.
Question 9. Alternative Strategy
You propose an alternative strategy: instead of specializing and downsizing the firm, you consider what would happen Mr. Arzignano makes the decision to diversify the product line and increase the workforce.
You perform. simulation analysis of this strategy and compare the resulting cumulative probability distribution of the profit of the alternative strategy with that of the downsizing strategy. The cumulative probability distribution of alternative strategy’s profit is represented by the dotted curve (the cumulative of probability distribution of the profit of the original downsizing strategy is represented by the solid line).
Annual profit
(i) What is the probability that the alternative strategy does better than the downsizing strategy?
(ii) What is the realistic downside (VaR 5%) of the alternative strategy? What is the realistic upside (VaR 95%) of the alternative strategy?
(iii) Based on the simulation analysis, which of the two strategies would you
recommend to Mr. Arzignano?
Question 10. True or False
Circle “T” if the statement is true and “F” if the statement is false. Each question is worth 2 points.
(i) (T/F) Average outcome is associated with the most likely outcome.
(ii) (T/F) When running simulation, the average is likely to significantly change between
10 iterations and 100 iteration.
(iii) (T/F) Suppose that you simulate the profits from two different alternatives, A and B. If alternative A results in higher average profit and smaller downside than alternative B, then following alternative A will lead to higher profit more often than following alternative B.
(iv) (T/F) A tornado diagram is useful for identifying which risks to focus on.
(v) (T/F) Sensitivity analysis informs us about the probability of an event.