! Oil Drilling Decision tree from Hillier & Lieberman, Chapter 15;
! Keywords: Decision tree, Petroleum, Hillier & Lieberman,
Decisionmaking under uncertainty;
! An oil exploration company faces the sequence of decisions
and random events:
SRV = Do a survey, or
NOS = No survey,
FAV = Favorable result from survey, or
UNF = Unfavorable,
SEL = Sell rather than drill,
DRL = Drill,
OIL = Hit Oil, or
DRY = Dry hole.
We must decide to make the survey or not, and then drill or sell
so as to maximize expected profits;
! In the model below, each variable of the form ijk
is the probability of the sequence of events i, j, k, e.g.,
SRVFAVDRL means: we did the survey, it turned out favorable,
and we drilled;
! In the solution, any decision we should take will have a positive
probability. E.g., if SRV > 0 in the solution, it means we should
take the survey. If SRVFAVDRL > 0 it means if the survey turns out
favorable, then we should drill;
!Stage 1 decision. With probability 1, we do something;
1 = SRV + NOS; ! Do survey or no survey;
!Stage 1 nature's decision. Prob{Survey unfavorable} = .7;
SRV*.7 = SRVUNF; ! Do survey, turns out unfavorable;
SRV*.3 = SRVFAV; ! Do survey, turns out favorable;
! Stage 2, our decision;
SRVUNF = SRVUNFDRL + SRVUNFSEL; ! Survey unfavorable, either drill or sell;
SRVFAV = SRVFAVDRL + SRVFAVSEL; ! Survey favorable, either drill or sell;
NOS = NOSDRL + NOSSEL; ! No Survey, either drill or sell;
! Stage 2 nature's decision;
!Prob{Hit oil | Survey unfavorable} = .143;
!Prob{survey & unfav & drill & hit oil};
SRVUNFDRL*.143 = SRVUNFDRLOIL;
!Prob{survey & unfav & drill & dry};
SRVUNFDRL*.857 = SRVUNFDRLDRY;
SRVFAVDRL*.5 = SRVFAVDRLOIL;
SRVFAVDRL*.5 = SRVFAVDRLDRY;
NOSDRL*.25 = NOSDRLOIL;
NOSDRL*.75 = NOSDRLDRY;
! Expected revenue from oil;
MAX= 800*(SRVUNFDRLOIL + SRVFAVDRLOIL + NOSDRLOIL)
! Expected revenue from selling;
+ 90*(SRVFAVSEL + SRVUNFSEL + NOSSEL)
! Cost of survey;
- 30*SRV
! Expected cost of drilling;
- 100*(SRVUNFDRL + SRVFAVDRL + NOSDRL);
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