Answer:
The question is about making use of Decision Tree to evaluate the options. The choice is between the existing gasoline powered cars and electric cars. There are three possibilities 1. savings of $1.5 million, 2. loss of $700,000 and 3. breakeven ( no savings no loss). A consultant hired by the city estimated the probabilities as 30%, 30% and 40% respecvtively for the above mentioned possibilities.
Further city has the opportunity to have a pilot project costing $75,000 for a period of three months with rented small number of electric cars. The results ( three outcomes) of pilot project will not be conclusive but provide crucial information about probabilities of likely output of the main project. Relationships between outcomes of pilot project and that of main project are given in the form of a table in terms of probabilities.
Therefore the problem has three options to begin with(Decision box 1) namely 1. no action (no change) 2. Act and go for change of existing cars with electric cars 3. First Pilot Program followed by two options ( Decision boxes ) no action and Act... as mentioned earlier [ Problem of two stage decision making]
First option of no action has net inflow/outflow zero.
Second option of Act will have expected value = .30*1,500,000 + .30* (-700,000) + .40*0 = 240,000
Third Option may result in three outcomes: savings, loss and breakeven and on these outcomes there will be decision box having options of no change and Act for change which will have outcomes similiar to above
The probabilities of savings, loss and breakeven of project program are .37 (.6*.3+.1*.3+.4*.4), .23(.1*.3+.4*.3+.2*.4) and .40(.3*.3+.3*.5+.4*.4)
The option of no action after project program will have loss of cost of project (75,000) whereas the other branches of act gives values of .37*240,000, .23*240,000 and .40*240,000 for outcomes savings, loss and breakeven
