【正文】 ?Event nodes and branches represent uncontrollable factors. Decision nodes and event nodes are arranged in order of subjective chronology. For example, the position of an event node corresponds to the time when the decision maker learns the oute of the event (not necessarily when the event occurs). 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Other Terms Decision tree models include such concepts as nodes, branches, terminal values, strategy, payoff distribution, probability distribution, and the rollback method. The following problem illustrates the basic concepts. ?Nodes:(1) Decision Node(2) Event Node(3) Terminal Node ?Branch:(1) Decision Branch (2) Event Branch (Probability) ?Profit (Payoff/Oute) 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Type of Node Written Symbol Computer Symbol Node Successor Decision square square decision branches Event circle circle event branches Terminal endpoint triangle or vertical line terminal value 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Sometimes, the nodes of the decision tree are referred to as forks, and the arcs are called branches. ?A decision fork, represented by a square, indicates that a decision needs to be made at that point in the process. ?A chance fork, represented by a circle, indicates that a random event occurs at that point. 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Pro b a b i l i t yEv e n t n a m eT e rm i n a l v a l u eC a s h f l o wPro b a b i l i t yD e ci s i o n n a m e Ev e n t n a m eT e rm i n a l v a l u eC a s h f l o w C a s h f l o wPro b a b i l i t yEv e n t n a m eT e rm i n a l v a l u eC a s h f l o wD e ci s i o n n a m eT e rm i n a l v a l u eC a s h f l o w重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING The prototype example involves a sequence of two decisions: 1. Should a seismic survey be conducted before an action is chosen? 2. Which action (drill for oil or sell the land) should be chosen? The corresponding decision tree (before adding numbers and performing putation) is displayed in Fig. . Constructing the Decision Tree 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Do Seismic No Seismic Unfavorable Favorable Drill Sell Drill Sell Sell Drill Oil Dry Oil Oil Dry Dry 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING 0 . 2 5Wi n S e c o n d Co n t ra c t0 . 1 5 $ 1 0 , 5 0 0Wi n F i rs t Co n t ra c t $ 7 , 0 0 0 $ 1 0 , 5 0 0$ 4 , 2 0 0 $ 5 , 2 5 0 0 . 7 50 . 7 1 S u b l i c e n s eL i c e n s e A g re e m e n t $ 3 , 5 0 0$0 $ 3 , 5 0 0 $ 5 7 5 $1930 . 8 5P u rc h a s e O p t i o n N o Co n t ra c t $ 7 0 0 $ 1 2 5 $100 $0 $ 7 0 00 . 2 9N o L i c e n s e A g re e m e n t1 $ 1 2 5$100 $0 $ 1 2 5Re j e c t P u rc h a s e$0$0 $0Al l d o l l ar am o u n ts ar e th o u s an d s ( $ 0 0 0 ) .De ci s i o n T r ee b as ed o n AI L E x am p l e i n U l v i l a an d B r o wn , De ci s i o n An al y s i s C o m es o f Ag e , Ha r va r d B u s i n es s R ev i ew , S ep tem b er Oc to b er 1 9 8 2P R O B A B IL IT IES : E n t e r n u m b e r s o r f o r m u l a s i n t h e s e c e l l .D E CI S IO N NO D E : T h e n u m b e r i n t h e n o d e i n d i c a t e s E V E NT T E R M IN A L NO D E S P A R T IAL CAS H F L O W S : E n t e r n u m b e r s o r f o r m u l a s i n t h e s e c e l l .B R A NC H L A B E L S : T y p e t e x t i n t h e s e c e l l sT E R M IN A L V A L U E S : E q u a l t o s u m o f p a r t i a l c a s h f l o w s a l o n g p a t h .R O L L B A CK E V s : E q u a l t o t h e e x p e c t e d v a l u e a t t h i s p o i n t i n t h e t r e e .重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING Performing the Analysis Having constructed the decision tree, including its numbers, we now are ready to analyze the problem by using the following procedure. 1, Start at the right side of the decision tree and move left one column at a time. For each column, perform either step 2 or step 3 depending upon whether the forks in that column are chance forks or decision forks. 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING 2. For each chance fork, calculate its expected payoff by multiplying the expected payoff of each branch (shown in boldface to the right of the branch) by the probability of that branch and then summing these products. Record this expected payoff for each decision fork in boldface next to the fork, and designate this quantity as also being the expected payoff for the branch leading to this fork. 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING 3. For each decision fork, pare the expected payoffs of its branches and choose the alternative whose branch has the largest expected payoff. In each case, record the choice on the decision tree by inserting a double dash as a barrier through each rejected branch. 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING To begin the procedure, consider the rightmost column of forks, namely, chance forks f, g, and h. Applying step 2, their expected payoffs (EP) are calculated as EP= 1/7 (670) + 6/7 (130) = , for fort f, EP = 1/2 (670)+ 1/2 (130) = 270, for fork g, EP = 1/4 (700) + 3/4 (100) = 100, for fork h. 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING 重慶大學(xué)制造工程研究所副所長 鄢萍 博士 ?2022 SYSTEMS ENGINEERING These expected payoffs then are placed above these forks, as shown in Fig. . Next, we move one column to the left, which consists of decision forks c, d, and e. The expected payoff for a branch that leads to