assignment Decision tree analysis, Schemes and Mind Maps of Quantitative Techniques

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Decision Tree Analysis

Assignment No. (1): Decision Tree

Name: Samar Mohamed Ahmed Fouad

Group: C

Supervised by DR: Adel Sakr

• Path to node ( 1 3), we will have an enhanced chance of significant metal deposits where purchase and explore costs 4£m, but decide to abandon, total profit (- 1 £m)

➢ In the case of conducting 3 days test at cost (750000£+ 250000 £):

• Path to node ( 1 4), we will have reduced chance of significant metal deposits where purchase and explore costs 4£m, Manganese will have revenue 30 £M, Total profit (25£m)
• Path to node ( 1 5), we will have reduced chance of significant metal deposits where purchase and explore costs 4£m, Gold will have revenue 250 £M, Total profit (2 45 £m)
• Path to node ( 1 6), we will have reduced chance of significant metal deposits where purchase and explore costs 4£m, Silver will have revenue 150 £M, Total profit ( 145 £m)
• Path to node ( 1 7), we will have reduced chance of significant metal deposits where purchase and explore costs 4£m, we will Find Nothing, total profit (- 5 £m)
• Path to node ( 1 8), we will have reduced chance of significant metal deposits where purchase and explore costs 4£m, but decide to abandon, total profit (- 1 £m)

The second step:

Starting from right to left: a) EMV for node ( 8 ) with its branches to nodes ( 14 - 17 ): = 0.0075(25) + 0.0004(245) + 0.00175(145) + 0.99035(-5) = - 4. So, the best decision for (S&E) at node 6 is to abandon where EMV= - 1 b) EMV for node ( 7 ) with its branches to nodes ( 9 - 12 ): = 0.03(25) + 0.02(245) + 0.01(145) + 0.94(-5) = 2. So, the best decision for (S&E) at node 5 is to purchase where EMV= 2. c) EMV for node (4): = 0.5(2.4) + 0.5(-1) = 0. d) EMV for node ( 3 ) = 0.01(26) + 0.0005(246) + 0.002(146) + 0.9875(-4) = - 3. So, the decision for (S&E) at node 1 is to abandon with EMV= 0, purchase & explore with EMV= - 3.275 or to perform 3 days test with EMV= 0.7, So I recommend (S&E) to go for 3 days test as it has the greatest EMV. Question two: I think it will be a good offer to accept sharing the revenues & costs at a 50:50 basis as in the case of loss will decrease the amount of loss for each & in case of revenue, the revenue will be divided between them on a 50:50 basis too but with sharing all the risks together.