The CEO of CNY, a large car manufacturer, has confided in you that there is some evidence that either model T, or model X or both car models have a significant design defect. An initial estimate of the probability of the defect being only in model T is 18%, only in model X is 8% and in both models is 72%. The CEO is considering three alternative actions. The first alternative is to recall all units of both models immediately. The recall of both models will have a significant cost but no impact on sales, since the company will be seen as pro-active. The second alternative is to hide the evidence gathered so far. If the potential defects are never discovered, there will be no costs for the company. However, there is a 10% chance that the collusion to hide the evidence will be found out, which will mean a complete recall of all units of both models and a predicted 90% loss in sales due to the public outcry. Moreover, everyone involved in the cover-up will be legally liable. Finally, the third alternative is to mandate an internal investigation that will determine with certainty which model is defective and recall only those units. If the investigation is completed before becoming public, there will be no impact on sales. However, there is an 80% chance that the ongoing investigation will become public before it finishes. In that case, the company may either wait for the investigation to finish and find out which model (if any) is actually defective or decide to recall all units of both models immediately. If it waits, the impact on sales because of the uncertainty will be a loss of 60%, whereas if it acts as soon as the ongoing investigation becomes public and recalls both models, the damage will be limited to a loss of 10% of sales. The CEO wants you to look at the available data and alternative actions and advise her in the best course of action.
Table 1: Cost of recalls
Units recalled
(thousands) Cost (£M)
20 1
30 3
40 5
Table 2: Profit according to sales
Sales (thousands of units) Profit (£M)
0 0
1 6
11 11
1. The first step in the analysis is to visualise and understand the data given to you. Let us focus on Table 1 first. For this, represent the data in Table 1 using a suitable chart. Correctly label the axes. In addition, fit a linear and a quadratic model. Plot each model, the model equation and its ð‘… 2 value on the corresponding chart and include the final chart in your report. Discuss which model would be more appropriate in this case.
2.: Now let us focus on Table 2. Represent the data using a suitable chart with correctly labelled axes. Assuming that the model is of the form Profit = ð‘Ž − ð‘ (Sales+1) , find the values of ð‘Ž and ð‘ that fit the data in Table 2. Plot the model and the model equation in the chart and include the final chart in your report. Discuss the relationship (i.e. trends you can observe) between sales and profit. Does it make sense to calculate the R2 value of this model?
3.The second step in the analysis is to find out the impact of each event and decision using the models in Q1 and Q23. Given that there are 25,000 units in the market of model T and 15,000 units of model X, calculate the cost of recalling all units of model T, all units of model X and all units of both models using the best model from Q1. Knowing that the predicted volume of sales is 11 thousands of units, calculate the loss in profit if the volume of sales was reduced to by 10%, 60% and 90% of this predicted volume of sales, using the model calculated in Q2. Include in your report two tables with the values estimated by you.
4.: Draw a decision tree representing the potential decisions and possible events faced by the company. Use the correct symbols for decision and chance nodes, label each branch with a few words explaining its meaning, and also label the branches going out from chance nodes with their corresponding probabilities. Finally, calculate the total cost for the company (recall cost plus profit loss) of each potential outcome (leaf branches) in the tree.
5. Using the tree in Q4, calculate what is the strategy that minimises the expected total cost according to expected value. Would you recommend this strategy to the CEO? If not, please explain why and determine the second best strategy according to expected value.
6. Using the tree in Q4, ignore any probabilities given in the tree and calculate what would be the recommended strategy according to each of Wald’s and Laplace’s criteria. Given the results, give a very brief commentary (one sentence is enough) of the risk characteristics (optimistic/pessimistic, likely/unlikely) of each strategy.
