Resource Allocation Problem
I worked the attached Resource Allocation Problem, but I am not sure I worked it correctly. I used intuition more than mathematical constructs. Will you take a look and let me know know the right way to do the problem?
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- Dynamic Programming Problem2.doc
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- Dynamic Programming Problem2.doc
J. R. Carrington has $4 million to invest in 3 oil well sites. The revenue earned
from each site depends on the amount invested in the individual site. See the table
below for the investment/revenue matrix.
Amount Invested Revenue ($ millions)
($ millions) Site 1 Site 2 Site 3
0 4 3 3
1 7 6 7
2 8 10 8
3 9 12 13
4 11 14 15
Assume that the amount invested must be an exact multiple of $ 1 million, and
determine by dynamic programming to determine the investment policy that will
maximize the revenue J. R. will earn from the three wells.
Solution:
Stage 1:
x1 *
S=x1 F1(s1) x1(s1)
Site10 4 4 Site10 Site10
Site11 7 7 Site11 Site11
Site12 8 8 Site12 Site12
Site13 9 9 Site13 Site13
Site14 11 11 Site14 Site14
Stage 2:
S=x2
x1 *
Site10 Site11 Site12 Site13 Site14 F1(s1) x1(s1)
4 7 8 9 11
Site20 3 7 10 11 12 14 14
Site21 6 10 13 14 15 17 17
Site22 10 14 17 18 19 21 21
Site23 12 16 19 20 21 23 23
Site24 14 18 21 22 23 25 25
Stage 3:
S=x2
x2 *
Site20 Site21 Site22 Site23 Site24 F2(s2) x2(s2)
3 6 10 12 14
Site30 3 10 13 17 19 21 21
Site31 7 12 15 19 21 23 23
Site32 9 16 19 23 25 27 27
Site33 13 18 21 25 27 29 29
Site34 15 10 13 17 19 21 21
Invest 3 million in Site 3 and 1 million in Site 1
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