decision theory

UNIT – III : DECISION THEORY

TYPES OF DECISION MAKING ENVIRONMENTSDECISION MAKING UNDER CERTAINTYDECISION MAKING UNDER UNCERTAINTYDECISION MAKING UNDER RISK SIX STEPS IN DECISION MAKING : CLEARLY DEFINE THE PROBLEM IN HAND LIST THE POSSIBLE ALTERNATIVES IDENTIFY THE POSSIBLE OUTCOMES OR STATE OF NATURE LIST THE PAYOFF OR PROFIT OF EACH COMBINATION OF ALTERNATIVES & OUTCOMES SELECT ONE OF THE MATHEMATICAL DECISION THEORY MODELS APPLY THE MODEL AND MAKE YOUR DECISION

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DECISION THEORY DECISION MAKING UNDER CERTAINTY : DECISION MAKERS KNOW

WITH CERTAINTY THE CONSEQUENCE OF EVERY ALTERNATIVE OR DECISION CHOICE. NATURALLY THEY WILL CHOOSE THE ALTERNATIVE THAT WILL RESULT IN THE BEST OUTCOME. EXAMPLE IS MAKING A FIXED DEPOSIT IN A BANK.

DECISION MAKING UNDER UNCERTAINTY :

SEVRAL CRITERIA EXIST FOR MAKING DECISION UNDER THESE CONDITIONS :

1. MAXIMAX (OPTIMISTIC)2. MAXIMIN (PESSIMISTIC)3. CRITERION OF REALISM (HURWICZ)4. EQUALLY LIKELY (LAPLACE)5. MINIMAX REGRET

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DECISION THEORY

A CASE STUDY•JOHN THOMPSON IS THE PRESIDENT OF STEWARTS & LLOYDS OF INDIA LTD.•JOHN THOMPSON’S PROBLEM IS TO IDENTIFY WHETHER TO EXPAND HIS PRODUCT LINE BY MANUFACTURING AND MARKETING A NEW PRODUCT : WASHING MACHINE.•IN ORDER TO MAKE A PROPOSAL FOR SUBMITTING TO HIS BOARD OF DIRECTORS, THOMPSON THOUGHT OF FOLLOWING THREE ALTERNATIVES THAT ARE AVAILABLE TO HIM. •TO CONSTRUCT A LARGE NEW PLANT TO MANUFACTURE THE WASHING MACHINE •TO CONSTRUCT A SMALL PLANT TO MANUFACTURE THE WASHING MACHINE• NO PLANT AT ALL ( THAT IS HE HAS THE OPTION OF NOT DEVELOPING THE NEW PRODUCT LINE).

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DECISION THEORY

• THOMPSON DETERMINES THAT THERE ARE ONLY TWO POSSIBLE STATE OF NATURES :

1. THE MARKET FOR THE WASHING MACHINE COULD BE FAVOURABLE, MEANING THAT THERE IS A HIGH DEMAND FOR THE PRODUCT

2. IT COULD BE UNFAVOURABLE, MEANING THAT THERE IS A LOW DEMAND FOR THE WASHING MACHINE.

JOHN THOMPSON EVALUATED THE PROFITS ASSOCIATED WITH VARIOUS OUTCOMES. HE THINKS :

WITH A FAVOURABLE MARKET, A LARGE FACILITY WOULD RESULT IN A PROFIT OF Rs.200,000 TO HIS FIRM. BUT Rs.200,000 IS A CONDITIONTAL VALUE BECAUSE THOMPSON’S RECEIVING THE MONEY IS CONDITIONAL UPON BOTH HIS BUILDING A LARGE FACTORY AND HAVING A GOOD MARKET.

THE LARGE FACILITY AND UNFAVOURABLE MARKET WOULD RESULT IN NET LOSS OF Rs.180,000.

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DECISION THEORY

A SMALL PLANT WITH A FAVOURABLE MARKET WOULD RESULT IN A NET PROFIT OF Rs.100,000 .

A SMALL PLANT WITH UNFAVOURABLE MARKET WOULD RESULT IN A NET LOSS OF Rs.20,000 .

DOING NOTHING, THAT IS NEITHER TO MAKE LARGE FACILITY NOR A SMALL PLANT, IN EITHER MARKET WOULD RESULT IN ZER0 PROFIT.

THE DECISION TABLE OR PAYOFF TABLE FOR THOMPSON’S CONDITIONAL VALUES IS SHOWN IN TABLE ON NEXT SLIDE .

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DECISION THEORY

ALTERNATIVE STATE OF NATUREFAVOURABLEMARKET (Rs.)

UNFAVOURABLE MARKET (Rs.)

CONSTRUCT ALARGE PLANT

200,000 - 180,000

CONSTRUCT A SMALL PLANT

100,000 - 20,000

DO NOTHING 0 0

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DECISION THEORY MAXIMAX : THE MAXIMAX CRITERION IS USED TO FIND THE ALTERNATIVE THAT MAXIMISES THE MAXIMUM PAYOFF. FIRST LOCATE THE MAXIMUM PAYOFF FOR EACH ALTERNATIVE, AND THEN PICK THAT ALTERNATIVE WITH THE MAXIMUM NUMBER. IT LOCATES THE ALTERNATIVE WITH THE HIGHEST POSSIBLE GAIN : THEREFORE IT IS CALLED AN OPTIMISTIC DECISION CRITERIA. THOMPSON’S MAXIMAX CHOICE IS THE FIRST ALTERNATIVE “CONSTRUCT A LARGE PLANT”.TABLE 1 : THOMPSON’S MAXIMAX DECISION

ALTERNATIVE STATE OF NATURE MAXIMUM IN A ROW (Rs.)FAVOURABLE

MARKET(Rs.)

UNFAVOURABLE MARKET

(Rs.)CONSTRUCT A LARGE PLANT

200,000 -180,000 200,000MAXIMAX


100,000 -20,000 100,000

DO NOTHING 0 0 07

DECISION THEORY MAXIMIN : THE MAXIMIN CRITERION IS USED TO FIND THE ALTERNATIVE THAT MAXIMISES THE MINIMUM PAYOFF OR CONSEQUENCE FOR EVERY ALTERNATIVE. FIRST LOCATE THE MINIMUM PAYOFF FOR EACH ALTERNATIVE AND THEN PICK THAT ALTERNATIVE WITH THE MAXIMUM PAYOFF. THIS DECISION CRITERION LOCATES THE ALTERNATIVE THAT GIVES THE BEST OF THE WORST (MINIMUM) PAYOFFS, AND THUS IT IS CALLED A PESSIMISTIC DECISION CRITERION. THIS CRITERION GUARANTEES THAT THE PAYOFF WILL BE AT LEAST THE MAXIMIN VALUE. THOMPSON’S MAXIMIN CHOICE IS “DO NOTHING”. TABLE 2 : THOMPSON’S MAXIMIN DECISION

ALTERNATIVE

STATE OF NATURE

MINIMUM IN A ROW(Rs.)

FAVOURABLE MARKET

(Rs.)

UNFAVOURABLE MARKET

(Rs.)

CONSTRUCT A LARGE PLANT

200,000 - 180,000 - 180,000


100,000 - 20,000 - 20,000

DO NOTHING 0 0 0MAXIMIN 8

DECISION THEORY CRITERON OF REALISM (HURWICZ CRITERION)THE CRITERION OF REALISM IS A COMPROMISE BETWEEN AN OPTIMISTIC AND A PESSIMISTIC DECISION. A COEFFICIENT OF REALISM (α ) IS USED TO MEASURE THE DEGREE OF OPTIMISM OF THE DECISION MAKER. THIS COEFFICIENT, α LIES BETWEEN O AND 1. THE WEIGHTED AVERAGE IS COMPUTED AS FOLLOWS :WEIGHTED AVERAGE = (α) x (MAXIMUM IN ROW) + (1 – α) x (MINIMUM IN ROW)IN THE GIVEN CASE, JOHN THOMPSON SETS α = 0.80 AND THUS THE BEST DECISION WOULD BE TO CONSTRUCT A LRAGE PLANT AS SHOWN IN TABLE 3 BELOW.TABLE 3 : THOMPSON’S CRITERION OF REALISM DECISION

ALTERNATIVE

STATE OF NATURE CRITERON OF REALISMOR WEIGHTED AVERAGE

(α = 0.80)FAVOURABLE MARKET

(Rs.)UNFAVOURABLE MARKET

(Rs.)


200,000 - 180,000


100,000 -20,000 76,000

DO NOTHING 0 0 0

Rs. 124,000REALISM

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DECISION THEORY EQUALLY LIKELY (LAPLACE) :THIS CRITERION USES ALL THE PAYOFFS FOR EACH ALTERNATIVE . THIS IS ALSO CALLED LAPLACE, DECISION CRITERION. THIS CRITERIA FINDS THE AVERAGE PAYOFF FOR EACH ALTERNATIVE AND SELECT THE ALTERNATIVE WITH HIGHEST AVERAGE. THIS CRITERION ASSUMES THAT ALL PROBABILITY OF OCCURANCE FOR THE STATE OF NATURES ARE EQUAL, AND THUS EACH STATE OF NATURE IS EQUALLY LIKELY. THOMPSON’S CHOICE AS PER THIS CRITERION IS THE SECOND ALTERNATIVE, “CONSTRUCT A SMALL PLANT”.TABLE 4 : THOMPSON’S EQUALLY LIKELY DECISION

ALTERNATIVE

STATE OF NATUREROW AVERAGE

(Rs.)FAVOURABLE MARKET(Rs.)

UNFAVOURABLE MARKET(Rs.)


200,000 - 180,000 10,000


100,000 - 20,000

DO NOTHING 0 0 0

40,000EQUALLY LIKELY

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DECISION THEORY MINIMAX REGRETTHIS DECISION CRITERION IS BASED ON OPPORTUNITY LOSS OR REGRET. THE OPPORTUNITY LOSS OR REGRET IS THE AMOUNT LOST BY NOT PICKING THE BEST ALTERNATIVE IN A GIVEN STATE OF NATURE. THE FIRST STEP IS TO CREATE THE OPPORTUNITY LOSS TABLE. OPPORTUNITY LOSS FOR ANY STATE OF NATURE , OR ANY COLUMN, IS CALCULATED BY SUBTRACTING EACH PAYOFF IN THE COLUMN FROM THE BEST PAYOFF IN THE SAME COLUMN.THOMPSON’S OPPORTUNITY LOSS TABLE IS SHOWN IN TABLE 5. USING THE OPPORTUNITY LOSS TABLE, THE MINIMAX REGRET CRITERION FINDS THE ALTERNATIVE THAT MINIMISES THE MAXIMUM OPPORTUNITY LOSS WITHIN EACH ALTERNATIVE.FIRST FIND THE MAXIMUM OPPORTUNITY LOSS FOR EACH ALTERNATIVE. NEXT, LOOKING AT THESE MAXIMUM VALUES, PICK THAT ALTERNATIVE WITH MINIMUM NUMBER. WE CAN SEE THAT MINIMAX REGRET CHOICE IS THE SECOND ALTERNATIVE, “CONSTRUCT A SMALL PLANT”. TABLE 5 : OPPORTUNITY LOSS

TABLE 3.7 OPPORTUNITY LOSS TABLE FOR THOMPSON

ALTERNATIVE

STATE OF NATURE STATE OF NATURE

FAVOURABLE MARKET(Rs.)


MAXIMUM IN A ROW


0[200,000 – 200,000]

180,000[0 - ( - 180,000)]

180,000


100,000[200,000 – 100,000]

20,000[0 - ( - 20,000)]

100,000MINIMAX

DO NOTHING 200,000[200,000 - 0]

0[0 - 0]

200,000 11

DECISION THEORY DECISION MAKING UNDER RISKDECISION MAKING UNDER RISK IS A DECISION SITUATION IN WHICH SEVERAL POSSIBLE

STATE OF NATURE MAY OCCUR AND THE PROBABILITIES OF THESE STATES OF NATURE ARE KNOWN. THE DECISION UNDER RISK ARE TAKEN BASED ON FOLLOWING :

EXPECTED MONETARY VALUE OR EXPECTED VALUE (EMV) EXPECTED VALUE OF PERFECT INFORMATION (EVPI) EXPECTED OPPORTUNITY LOSS (EOL)

EXPECTED MONETARY VALUE THE EXPECTED MONETARY VALUE (EMV) FOR AN ALTERNATIVE IS JUST THE SUM OF

PRODUCTS OF PAYOFFS AND PROBABILITY OF EACH STATE OF NATURE.EMV (Alternative ,i) = (Payoff of first state of nature) x ( Probability of first state of nature) + (Payoff of second state of nature) x (Probability of second state of nature) + (Payoff of third state of nature) x (Probability of third state of nature) + …………..+ (Pay of last state of nature) x (Probability of last state of nature)THE ALTERNATIVE WITH MAXIMUM EMV IS THEN CHOSEN.

SUPPOSE THOMPSON NOW BELIEVES THAT THE PROBABILITY OF A FAVOURABLE MARKET IS EXACTLY THE SAME AS THE PROBABILITY OF AN UNFAVOURABLE MARKET. NOW REFERRING TO THOMSON’S PAYOFF TABLE 1, WHAT DECISION IS EXPECTED TO BE TAKEN BY THOMPSON USING EMV METHOD ?

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DECISION THEORY SOLUTION BY USING EMV METHOD :EMV (LARGE PLANT) = (0.50) x (Rs.200,000) + (0.50) x (-Rs.180,000) = Rs.10,000EMV ( SMALL PLANT) = (0.50) x (Rs.100,000) + (0.50) x (-Rs.20,000) = Rs.40,000EMV (DO NOTHING) = (0.50) x (Rs.0) + (0.50) x (Rs.0) = Rs.0THE LARGEST EXPECTED VALUE OF Rs.40,000 RESULTS FROM THE SECOND ALTERNATIVE “CONSTRUCT A SMALL PLANT”. THUS THOMPSON WOULD PROCEED TO SET UP SMALL PLANT. TABLE 6 : Decision Table with Probabilities and EMVs for John Thompson

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Alternatives State of Nature EMV

FavourableMarket

UnfavourableMarket

Construct Large Plant

200,000 - 180,000 10,000

Construct Small Plant

100,000 - 20,000 40,000

Do Nothing 0 0 0

Probability 0.50 0.50

DECISION THEORY EXPECTED VALUE OF PERFECT INFORMATION (EVPI)SUPPOSE, JOHN THOMPSON HAS BEEN APPROACHED BY A MARKETING CONSULTANT THAT

THEY ARE WILLING TO HELP JOHN WITH SOME PERFECT INFORMATION WHETHER THE MARKET IS FAVOURABLE FOR THE PROPOSED PRODUCT ENABLING JOHN TO TAKE CORRECT DECISION AND PREVENT HIM FROM MAKING A VERY EXPENSIVE MISTAKE. MARKETING CONSULTANT WOULD CHARGE JOHN THOMPSON Rs.65,000 FOR PROVIDING SUCH INFORMATION. WHAT JOHN SHOULD DO IN THIS SITUATION ?

1. SHOULD HE HIRE THE MARKETING CONSULTANT FOR MAKING THE MARKET STUDY ?2. EVEN IF THE INFORMATION PROVIDED IS PERFECTLY ACCURATE, IS IT WORTH TO PAY

Rs.65,000 TO MARKETING CONSULTANT?3.IF NOT, WHAT WOULD IT BE WORTH ? IN THIS CASE, TWO RELATED TERMS ARE INVESTIGATED :1. THE EXPECTED VALUE OF PERFECT INFORMATION (EVPI), AND2. THE EXPECTED VALUE WITH PERFECT INFORMATION (EVwPI)EVwPI = (Best payoff for first state of nature) x (Probability of first state of nature) + (Best payoff for second state of nature) x (Probability for second state of nature) + ……………+ (Best payoff for last state of nature) x (Probability for last state of

nature)EVPI = EVwPI - Maximum EMV

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DECISION THEORY EVPI WITH RESPECT TO TABLE 6 IS CALCULATED AS FOLLOWS :1. THE BEST PAYOFF FOR THE STATE OF NATURE “FAVOURABLE MARKET” IS Rs.200,000. THE BEST PAYOFF FOR THE STATE OF NATURE “UNFAVOURABLE MARKET” IS Rs.0.NOW, EVwPI = (Rs.200,000) (0.50) + (Rs.0) (0.50) = Rs.100,000THUS, IF JHOHN HAD PERFECT INFORMATION, THE PAYOFF WOULD AVERAGE Rs.100,0002.THE MAXIMUM EMV WITHOUT ADDITIONAL INFORMATION IS Rs.40,000(FROM TABLE 6)SO, EVPI = (Expected value with perfect information) – (Maximum EMV) = Rs.100,000 - Rs.40,000 = Rs.60,000THUS, AT BEST JOHN THOMPSON WOULD BE WILLING TO PAY FOR PERFECT INFORMATION IS Rs.60,000 BASED ON ASSUMPTION THAT THE PROBABILITY OF EACH STATE OF NATURE IS 0.50. EXPECTED OPPORTUNITY LOSSAN ALTERNATIVE APPROACH IS TO MAXIMISE EMV BY MINIMISING EXPECTED OPPORTUNITY LOSS. FIRST AN OPPORTUNITY LOSS TABLE IS CONSTRUCTED. THEN THE EOL IS COMPUTED FOR EACH ALTERNATIVE BY MULTIPLYING THE OPPORTUNITY LOSS BY THE PROBABILITY AND ADDING THESE TOGETHER.

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DECISION THEORY USING TABLE 5, WE COMPUTE THE EOL FOR EACH ALTERNATIVE AS FOLLOWS :EOL(CONSTRUCT LARGE PLANT) = (0.50) (Rs.0) + (0.50) (Rs.180,000) = Rs.90,000EOL (CONSTRUCT A SMALL PLANT) = (0.50) (Rs.100,000) + (0.50) (Rs.20,000) = Rs.60,000EOL (DO NOTHING) = (0.50) (Rs.200,000) + (0.50) (Rs.0) = Rs.100,000FROM THE EOL TABLE 7 , WE SEE THAT THE BEST DECISION WOULD BE THE SECOND ALTERNATIVE : “CONSTRUCT A SMALL PLANT”.

TABLE 7 : EOL TABLE FOR JOHN THOMPSON

ALTERNATIVE

STATE OF NATURE

EOLFAVOURABLE MARKET(Rs.)



0 180,000 90,000


100,000 20,000 60,000

DO NOTHING 200,000 0 100,000

PROBABILITIES 0.50 0.50

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DECISION THEORY

Q1. A food products company wants to introduce a new product by replacing the existing product with new packaging at much higher price (S1). The company may even make a moderate change in the composition of the existing product with a new packaging at a small increase in price (S2), or the company may make a small change in the composition of the existing product by labeling the product “new” and making a negligible increase in price (S3). The three possible state of nature are : (i)High increase in sales (N1), (ii) No change in sales (N2) and (iii)Decrease in sales (N3). The payoffs computed by the company in terms of yearly net profit for each of the strategies are given in table below :

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STRATEGIES STATE OF NATUREN1 N2 N3

S1 700000 300000 150000

S2 500000 450000 0

S3 300000 300000 300000

DECISION THEORY

Which strategy the concerned executive choose on the basis of (a) MAXIMIN Criteria(b) MAXIMAX Criteria(c) MINIMAX REGRET Criteria(d) LAPLACE Criteria

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DECISION THEORY

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STRATEGIES STATE OF NATUREN1 N2 N3

S1 700000 300000 150000

S2 500000 450000 0

S3 300000 300000 300000

DECISION THEORY

Q2. A Pharmaceutical company manufactures a drug which requires a chemical “X”. At the moment, the company spends Rs.1000 per year on procurement of “X”, but there is a possibility that the price may soon increase to four times of its present price because of a world shortage of the chemical “X”. There is another chemical “Y”, which the company could use in conjunction with a third chemical “Z”, in order to give the same effect as chemical “X”. The chemical “Y” and “Z” would together cost the company Rs.3000 per year, but their prices are unlikely to change. What action should the company take? Apply the Maximin and Minimax criteria for decision-making and give two sets of solutions. If the coefficient of optimism is 0.4, then find the course of action that minimizes the cost.

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DECISION THEORY

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COURSE OF ACTION (ALTERNATIVES)

STATE OF NATURE

PRICE OF “X” INCREASES

PRICE OF “X” DOES NOT INCREASE

USE “X”

USE “Y & Z”

DECISION THEORY

Q3. Mr.Amit Gupta flies quite often from Delhi to Chennai. Mr. Gupta can use the Airport bus which costs Rs.25.00. But if he avails it, there is a 0.08 chance of missing the flight. The stay in his company’s hotel costs him only Rs.270.00 with special discount for the employee and there is 0.96 chance of being on time for the flight. For Rs.350.00 he can use a taxi which will make 99% chance of being on time for the flight. If Mr.Gupta catches the flight on time, he will conclude a business transaction that will produce a profit of Rs.10,000.00, otherwise he will loose it. Which mode of transport Mr.Gupta should use ? Answer on the basis of EMV criteria.

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DECISION THEORY

Solution :

EMV(Bus) =

EMV(Stay at hotel) =

EMV(Taxi) = 23

State of Nature

Course of Action

Catches the flightProbability Payoff

Miss the flight Probability Payoff

Bus 0.92 0.08

Stay inhotel

0.96 0.04

Taxi 0.99 0.01

DECISION THEORY

Q. An investor is given the following investment alternatives and percentage rate of returns :

Over the past 300 days, 150days have been medium market condition and 60 days have had high market increases. On the basis of these data, state optimum investment strategy for the invvestment.

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Strategy

Low Medium High

Regular shares

7% 10% 15%

Risky shares

- 10% 12% 25%

Property - 12% 18% 30%

DECISION THEORY DECISION TREES ANY PROBLEM THAT CAN BE PRESENTED IN A DECISION TABLE CAN ALSO BE GRAPHICALLY ILLUSTRATED BY A DECISION TREE. ALL DECISION TREES CONTAINS DECISION NODES AND STATE OF NATURE NODES.DECISION NODES ARE REPRESENTED BY SQUARES FROM WHICH ONE OR SEVERAL ALTERNATIVES MAY BE CHOSENSTATE-OF-NATURE NODES ARE REPRESENTD BY CIRCLES OUT OF WHICH ONE OR MORE STATE-OF-NATURE WILL OCCURIN DRAWING THE TREE, WE BEGIN AT THE LEFT AND MOVE TO THE RIGHT. BRANCHES FROM THE SQUARES (DECISION NODES) REPRESENT ALTERNATIVES, AND BRANCHES FROM THE CIRCLES (STATE-OF-NATURE NODE) REPRESENT THE STATE OF NATURE.FIGURE 3.2 GIVES THE BASIC DECISION TREE OF JOHN THOMPSON PROBLEM.FIVE STEPS OF DECISION TREE ANALYSIS :1.DEFINE THE PROBLEM2.DRAW THE DECISION TREE3.ASSIGN PROBABILITIES TO THE STATE OF NATURE4.ESTIMATE PAYOFFS FOR EACH POSSIBLE COMBINATION OF ALTERNATIVE AND STATE OF NATURE5.SOLVE THE PROBLEM BY COMPUTING EXPECTED MONETARY VALUES (EMVs) FOR EACH STATE OF NATURE NODE. THIS IS DONE BY STARTING AT THE RIGHT OF THE TREE AND WORKING BACK TO DECISION NODE ON THE LEFT. AT EACH DECISION NODE, THE ALTERNATIVE WITH BEST EMV IS SELECTED.

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DECISION THEORY FIGURE 3.2 THOMPSON’S DECISION TREE PAYOFFS (Rs.) FAVOURABLE MARKET (0.50) 200,000 A STATE-OF-NATURE NODE

CONSTRUCT LARGE PLANT UNFAVOURABLE MARKET(0.50) - 180,000CONSTRUCT SMALL PLANT FAVOURABLE MARKET (0.50) 100,000

DECISION NODE UNFAVOURABLE MARKET (0.50) - 20,000 DO NOTHING

0

EMV FOR NODE 1 = (0.50) (200,000) + (0.50) (- 180,000) = Rs.10,000 EMV FOR NODE 2 = (0.50) (100,000) + (0.50) (- 20,000) = Rs.40,000SO, A SMALL PLANT SHOULD BE BUILT

1

2

EMV FOR NODE 2=Rs.40,000

EMV FOR NODE 1 = Rs.10,000

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DECISION THEORY

Q. ONGC has recently acquired the rights in a certain area to conduct surveys and test drilling to lead to lifting oil if it is found in commercially exploitable quantities. At the outset, the company has the choice to conduct further geological tests or to carryout a “drilling programme” immediately. On the known conditions, the company estimates that there is a 70 : 30 chance of further tests showing a “success”.Whether the tests show the possibility of ultimate success or not or even if no tests are undertaken at all, the company could still pursue its “drilling programme” or alternatively consider selling its rights to other agency to drill in the area. Thereafter, however, if it carries out the “drilling programme”, the likelihood of final success or failure is considered dependent on the foregoing stages. Thus : •If “successful tests” have been carried out, the expectation of success in drilling is given as 80 : 20.

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DECISION THEORY • If the tests indicate “failure” then the expectation of success in drilling is given

as 20 : 80. • If no tests have been carried out at all, the expectation of success in drilling is

given as 55 : 45. Costs and revenues have been estimated for all possible oucomes and Net Present

Value of each is as follows :

(a)Draw a decision Tree diagram to represent above information’(b)Evaluate the tree to advice management for best course of action28

Success

Outcome Net Present Value

With prior testsWithout prior test

100120

Failure With prior test -50

Without prior test - 40

Sale of exploitation rights

Prior test show “success”Prior test show “Failure” Without prior test

651545

decision theory

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