Cairo University
Faculty of Computers and Information
Decision Support System Applications
Dr. Mohamed Saleh
Team members:
Eman Adel Mahmoud 20130088
Mahmoud Samir Farag 20130228
Mostafa Mahmoud Mohamed 20130243
Hala Samir Khalil 20130284
Following is the video illustrating our problem. You can watch it here.
Faculty of Computers and Information
Decision Support System Applications
Dr. Mohamed Saleh
Team members:
Eman Adel Mahmoud 20130088
Mahmoud Samir Farag 20130228
Mostafa Mahmoud Mohamed 20130243
Hala Samir Khalil 20130284
The Vector Project
The General Ford Motors Corporation (GFMC) is
planning the introduction of a brand-new SUV—the Vector. There are four options
for production.
- Building the Vector at the company’s existing plant in Indiana
- Opening a new plant in Georgia.
- Building a new plant in London.
- Maybe Berlin would be better.
Due to the uncertainty in expected sales for the
Vector, GFMC is considering conducting a marketing survey to determine customer
attitudes toward the Vector which will give 2 attitudes that are likely to happen equally:
- Positive with high sales 30%, moderate sales of 54% and low sales of 16%.
- Negative with high sales 36%, moderate sales of 24% and low sales of 40%.
On our way through the solution, we'll be adding some important information for all we have.
First of all, we'll start drawing the decision tree with the information we have, the 2 probabilities, 4 cities and 3 choices in each.
and the same goes with the negative attitude information as follows and of course the same goes with London and Berlin:
to calculate the profit for each option, GFMC needs some input such as:
- The average revenue based on each Vector is $30,000.
- The annual sales of:
- High sales -> $100,000
- Moderate sales -> $50,000
- Low sales -> $30,000
- Fixed costs to be spent per city are:
- Indiana -> $200 million
- Georgia -> $400 million
- London -> $300 million
- Berlin -> $100 million
- Production cost of each city and high, moderate and low sale respectively (in thousands):
- Indiana (24,16,15)
- Georgia (20,22,12)
- London (23,17,10)
- Berlin (25,20,10)
profit = annual sales * (average revenue - production cost) - fixed cost
so going through the 4 cities and the given probabilities within each option we get these following steps, equations and values:
for the first event node (3 - positive + Indiana):
given high sales:
= 100,000 * (30,000 - 24,000) = 600 million - 200 million = $400 million
given moderate sales:
= 50,000 * (30,000 - 16,000) = 700 million - 200 million = $500 million
given low sales:
= 30,000 * (30,000 - 15,000) = 450 million - 250 million = $250 million
therefore 0.3*400 + 0.54*500 + 0.16*250 = $430 million (node 3)
doing the same calculations through the rest of the nodes:
Georgia (4) = 0.3*600 + 0.54*0 + 0.16*140 = $202.4 million
given high sales:
= 100,000 * (30,000 - 20,000) = 1000 million - 400 million = $600 million
given moderate sales:
= 50,000 * (30,000 - 22,000) = 400 million - 400 million = $0 million
given low sales:
= 30,000 * (30,000 - 12,000) = 540 million - 400 million = $140 million
London (5) = 0.3*400 + 0.54*350 + 0.16*300 = $357 million
given high sales:
= 100,000 * (30,000 - 23,000) = 700 million - 300 million = $400 million
given moderate sales:
= 50,000 * (30,000 - 17,000) = 650 million - 300 million = $350 million
given low sales:
= 30,000 * (30,000 - 10,000) = 600 million - 300 million = $300 million
Berlin (6) = 0.3*400 + 0.54*400 + 0.16*500 = $416 million
given high sales:
= 100,000 * (30,000 - 25,000) = 500 million - 100 million = $400 million
given moderate sales:
= 50,000 * (30,000 - 20,000) = 500 million - 100 million = $400 million
given low sales:
= 30,000 * (30,000 - 10,000) = 600 million - 100 million = $500 million
now back to decision node (2), choose the maximum of the previous 4 nodes and you get Indiana as the best choice if it's a positive attitude from the survey with EMV of $430 million.
now repeating all the previous steps but in the negative part of our problem which will give the same profit for each but will differ in the EMV as the probability of negative differs than that of the positive:
Indiana (8) = 0.36*400 + 0.24*500 + 0.4*250 = $364 million
Georgia (9) = 0.36*600 + 0.24*0 + 0.4*140 = $272 million
London (10) = 0.36*400 + 0.24*350 + 0.4*300 = $348 million
Berlin (11) = 0.36*400 + 0.24*400 + 0.4*500 = $440 million
now back to decision node (7), choose the maximum of the previous 4 nodes and you get Berlin as the best choice if it's a negative attitude from the survey with EMV of $440 million.
now for node 1, it has 2 possible profits from the positive and negative nodes with an equal probability to happen, therefore:
Possible profit = 0.5*430 + 0.5*440 = $435 million
Summing up:
Over all the possible profit could be $435 million, however if GFMC chose to go with the:
- Positive attitude it'll go with the option of building the Vector in Indiana with a profit of: $430 million.
- Negative attitude it'll go with the option of opening a plant in Berlin to build our great Vector with a profit of: $440 million.
Following is the video illustrating our problem. You can watch it here.
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