Draw a decision tree to represent tc problem

Question

Assignment Task 1:

Problem (a) Draw a decision tree to represent TC's problem

Problem (b) Determine the optimal policy for TC, assuming that their objective is to minimize expected costs. (Note: ignore time preferences for money.)

Assignment Task 2:

Problem (a) Utility functions for the mean numbers of passengers carried and the profit have been obtained from the rail operator's Managing Director (MD), as below.

Plot the above utility functions - and provide an interpretation of the plots.

Problem (b) An elicitation session* revealed that, for the MD, mean number of passengers and profit are mutually utility independent. You are reminded that, in this case, a two-attribute utility function can be obtained from:

u(x₁, x₂) = k1u(x₁) + k₂u(x₂) + k₃u(x₁)u(x₂) Where k₃ = 1 - k₁ - k₂

The elicitation session also revealed that k₁ = 0.9 and k₂ = 0.6, where the attribute number 1 is the mean number of passengers.

Given the above utilities, [i] determine the policy that the rail operators should undertake; and [ii] comment on your answer.

Assignment Task 3:

A UK construction company has estimated their profits over the next 12 months; depending on their business development strategy (A to L) & the economic outlook. Table 1.

Problem (a) For each of (i) to (v) which option should they choose and why

i. Maximin rule

ii. Minimax regret

iii. Maximax rule

iv. Laplace equation

v. Hurwicz Rule or Principle of realism (index = 0.4)

Option	Economic outlook
	Excellent	Very	Good	Moderate	Average	Poor	Recession
		good
A	45	35	30	20	20	0	-5
B	12	12	12	12	12	12	12
C	35	32	30	25	10	5	-10
D	45	30	30	40	30	5	-30
E	30	30	20	20	10	10	-10
F	18	18	18	18	15	15	12
G	45	35	25	20	10	-5	-15
H	25	20	20	15	10	5	0
I	40	30	20	20	20	-10	-10
J	30	20	20	20	20	-10	-15
K	25	20	20	15	10	10	5
L	10	10	10	12	12	12	15

Table 1: Estimated profits (£ million) dependent on economic outlook and eight options business development (A to L)

Problem (b) Which option(s) are insensitive to changes in economic outlook?

Problem (c) Plot a sensitivity analysis "spider diagram" for Options A,B, C & L.

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