Property Development on Flood Plains - Optimal Policy for TC - French Local Authority - Management Assignment Help

Assignment Task:

Question One
The risk of flooding in the land next to the River Scheldt has increased. This is because of: 
[i] climate change 
[ii] more property development on flood plains 
[iii] spring high-tides. Sea barrier gates are being constructed at the mouth of the river (Vissingen). However, downstream Terneuzen Council (TC) has to decide how to provide flood protection to their town for the next 2 years (i.e. before the sea barrier gates are completed). 

Flooding is only likely during the spring high-tide period, and the height of the river at this time cannot be accurately predicted (i.e. it is uncertain). However, if flooding occurs in any one year, TC will have to pay out compensation of about €2 million. 
TC is considering three options. 
[1] Do nothing 
[2] Build a temporary barrier 
[3] Build a more robust barrier 
More details of options 
[1] Do nothing and hope that flooding will not occur in either of the next 2 years. The river’s natural banks will stop any flooding as long as the water height is less than 3 meters. There is a probability of 0.37 that the height of the river will exceed this 3-meter figure in any one year. 
[2] TC could build a temporary barrier (at a cost of €0.5 million) to a height of 5 m, and there is a probability of 0.09 that the height of the river would exceed this barrier. However, if the water did rise above the barrier in the first year, there is a 30% chance that the barrier would be damaged. (Therefore, making it totally ineffective for the second year and a return to the situation as [1] above). TC would then have to decide whether to repair the barrier at a cost of €0.5 million, or whether to leave the river unprotected for the second year (i.e. a return to the situation as [1]). 
[3] Building a more robust barrier. The fixed cost of erecting this type of barrier would be €0.8million, with an additional cost of €0.1 million for each metre in the barrier’s height. For design reasons, the height of this barrier must be either be 4 or 5 m. These barriers 
[a] would not be damaged if flooding occurred and 
[b] would change the probability of the river’s height exceeding (in any one year) 4m or 5m. These new probabilities are 5 m barrier(0.004) and 4m barrier (0.08). 
Questions 
(a) Draw a decision tree to represent TC’s problem 
(b) Determine the optimal policy for TC, assuming that their objective is to minimize expected costs. (Note: ignore time preferences for money.) (20 marks) 

Question Two 
A French local authority owns a well-established light rail system, but the rail operators are being asked to increase passenger numbers. They have to make a decision on whether to lower fares in an effort to increase passenger numbers. 
If they decide to reduce fares, they will then have to decide whether to launch a social media advertising campaign to increase awareness of the fare reduction. 
If fares remain the same then it is estimated that there is a 0.68 probability that the mean number of passengers carried per day over the next year will equal 20 000 . In addition, a 0.32 probability that the number will fall to 14 000. 
The annual profits associated with these passenger numbers are estimated to be €3million and €1million, respectively. 
If the fares are reduced, but advertising is not used, then it is thought that there is a 0.6 probability that the mean number of passengers carried will increase to 25 000 . In addition, a 0.4 probability that the number will increase to 22 000. The resulting profits generated by these passenger numbers are estimated to be €2million and €1.7 million, respectively. 

Social media advertising of the fare reduction would further the probability of an increase to a mean of 25 000 passengers to 0.8; and reduce the probability that the mean will be 22 000 to 0.2. However, it would reduce the profits associated with these mean passenger numbers by €0.58 million. The tram operating company’s objectives are to 
[A] maximize passenger numbers and 
[B] maximize profit. 
Note Objective [A] is present as the local authority has secondary objectives to introduce social & environmental benefits {e.g. more people walking, lower carbon footprint, improved air quality, reduced traffic congestion}. 
(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. 
Mean number of passengers Utility 
15 000 0.00 16 200 0.20 17 000 0.30 17 500 0.40 19 000 0.60 20 000 0.75 21 000 0.90 22 000 0.95 25 000 1.00 
Profit (€ million) Utility 
1.0 0.00 1.1 0.20 1.3 0.50 1.4 0.60 1.5 0.65 1.7 0.75 2.0 0.90 2.2 0.92 2.5 0.95 2.8 0.98 3.0 1.00 
Plot the above utility functions - and provide an interpretation of the plots.  
(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. 
 
[Note * Elicitation = the process of producing data ] 

Question Three 
A UK construction company has estimated its profits over the next 12 months; depending on its business development strategy (A to L) & the economic outlook. 
 
3(a) For each of (i) to (v) which option should they choose and why 
i. Maximin rule (2 marks) 
ii. Minimax regret (4 marks) 
iii. Maximax rule (2 marks) 
iv. Laplace equation 
v. Hurwicz Rule or Principle of realism (index = 0.4) 

3 (b) Which option(s) are insensitive to changes in economic outlook?
3 (c) Plot a sensitivity analysis “spider diagram” for Options A,B,C & L.

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