My Math Forum need help with creating a decision tree plan

 September 28th, 2012, 12:22 AM #1 Newbie   Joined: Mar 2012 Posts: 8 Thanks: 0 need help with creating a decision tree plan The City of Ohio is considering whether or not to replace its fleet of gasoline?powered automobiles with electric cars (true!!!). The manufacturer of electric cars claims that the city will experience significant cost savings over the life of the fleet if it chooses to pursue the conversion. If the manufacturer is correct, the city will save an estimated $1.2 million dollars. If the new technology within the electric cars is faulty, as some critics suggest, the conversion to electric cars will cost the city$525,000. A third possibility is that less serious problems will arise and the city will break even with the conversion. A consultant hired by the city estimates the probabilities of these 3 outcomes are 0.40, 0.30 and 0.30 respectively. The city has an opportunity to implement a pilot program that would indicate the potential cost or savings resulting from a switch to electric cars. The pilot program involves renting a small number of electric cars for 3 months and running them under typical conditions. The pilot program would cost the city \$50,000. The city’s consultant believes that the results of the pilot program would be significant but not conclusive; she provides the city with the following compilation of probabilities based on her past experience consulting with other cities under the same conditions. According to the consultant, the reliability for the pilot program in the past has been: Actual City Outcomes of Electric Car Conversions ------------------------------Savings Loss Breakeven Pilot Predicted: Savings---- 0.60 0.10 0.40 Pilot Predicted: Loss---------0.10 0.40 0.20 Pilot Predicted: Breakeven 0.30 0.50 0.40 so what I've been told to do is create a decision tree based on the info above, but Im not sure how to proceed right now I have the first decision is to decide whether to switch to electric or stick with gasoline, if we switch to electric then there are the 3 outcomes of saving, loss, or break even but I don't know how to work in the pilot study information .. any help is greatly apreciated.
 September 28th, 2012, 08:01 PM #2 Senior Member   Joined: Aug 2012 Posts: 229 Thanks: 3 Re: need help with creating a decision tree plan Hey TJ44. Are you only dealing with a decision tree that assumes you are going to do the pilot test anyway or do you have the choice of not doing it?
 September 29th, 2012, 12:30 AM #3 Newbie   Joined: Mar 2012 Posts: 8 Thanks: 0 Re: need help with creating a decision tree plan hey chiro, to be honest I don't know, the assignment just says to develope a decision tree using the info above, though I would assume that the option of going ahead without a pilot and even not switching over and staying with gasoline cars being an option, I should have been more clear sorry about it.
 September 29th, 2012, 12:41 AM #4 Senior Member   Joined: Aug 2012 Posts: 229 Thanks: 3 Re: need help with creating a decision tree plan Well the first choice will be whether you include a pilot or not and then consider each option and what the final net cost (i.e. negative means city loses money, positive means it saves money). Then after you have done this attach probabilities to them. The skeleton of the tree won't need probabilities straight away: the best thing to do first is to just get the tree description down and then add the probabilities later by using the information given to you by the expert.
 September 29th, 2012, 09:44 AM #5 Newbie   Joined: Mar 2012 Posts: 8 Thanks: 0 Re: need help with creating a decision tree plan yeah I think I got the first bit half of the decision tree down, but the 2nd half involving the pilot results is where I'm confused I don't know how to finish my tree basically.
 September 29th, 2012, 06:35 PM #6 Senior Member   Joined: Aug 2012 Posts: 229 Thanks: 3 Re: need help with creating a decision tree plan Well with regards to pilot test, this should be at the root of the tree if you have a choice of doing the test or not doing it. So the root node will be "Pilot" vs "Non-Pilot" and you will have the same sub-trees for each of them. If you have the entire tree for all the options that can occur not considering the pilot test, then the only main thing is to consider duplicating this tree for the two branches off the root node corresponding to "pilot" and "no-pilot".

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# a city in ohio is considering replaceing its fleet of gasoline powered automobiles with electric cars. The mnufacturer of the electric cars claims that this municipality will experience significant cost saving over the life of the fleet

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