Question

12. (a) The design of a system is to be pursued from one of two available alternatives. Each alternative has a life-cycle cost associated with an expected future. The costs for the corresponding futures are given in the following table (in millions of dollars). If the probabilities of the occurrence of the optimistic, expected and pessimistic futures are 30%, 50%, and 20%, respectively, which alternative is most desirable from an expected cost viewpoint. Use an interest rate of 10% and show an equivalent cost comparison to support your answer. (10 marks) | | 1 0.5 1.0 1.0 2 1.0 5.0 7.0 3 0.8 1.0 1.2 4 0.8 1.0 1.2 7 0.8 1.0 1.2 8 0.8 1.0 1.2 9 0.8 1.0 1.2 10 0.8 1.0 1.2 Design 1 Future Optimistic Expected Pessimistic Design 2 Future Optimistic Expected Pessimistic Years 5 6 0.8 0.8 1.0 1.0 1.2 1.2 Years 5 6 0.3 0.3 0.8 0.8 1.0 1.0 1 1.0 3.0 5.0 2 3.0 6.0 6.0 3 0.3 0.8 1.0 4 0.3 0.8 1.0 7 0.3 0.8 1.0 8 0.3 0.8 1.0 9 0.3 0.8 1.0 10 0.3 0.8 1.0 (b) Which alternative should be chosen if the Laplace decision rule is used? Provide numerical results to support your answer. (2 mark) (c) Which alternative should be chosen if the maximax decision rule is used? Provide numerical results to support your answer. (2 mark) (d) Which alternative should be chosen if the maximin decision rule is used? Provide numerical results to support your answer. (2 mark) (e) Which alternative should be chosen if the Hurwicz decision rule is used with a = 0.6? Provide numerical results to support your answer. (4 marks)