```! 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); ```