decision theory

1. UNIT – III : DECISION THEORY
TYPES OF DECISION MAKING ENVIRONMENTS
DECISION MAKING UNDER CERTAINTY
DECISION MAKING UNDER UNCERTAINTY
DECISION 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
1

2. 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
2

3. 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).
3

4. 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.
4

5. 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 .
5

6. DECISION THEORY
ALTERNATIVE STATE OF NATURE
FAVOURABLE
MARKET (Rs.)
UNFAVOURABLE
MARKET (Rs.)
CONSTRUCT A
LARGE PLANT
200,000 - 180,000
CONSTRUCT A
SMALL PLANT
100,000 - 20,000
DO NOTHING 0 0
6

7. 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 -180,000 200,000
MAXIMAX
CONSTRUCT A
SMALL PLANT
100,000 -20,000 100,000
DO NOTHING 0 0 0
7

8. 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
CONSTRUCT A
SMALL PLANT
100,000 - 20,000 - 20,000
DO NOTHING 0 0 0
MAXIMIN
8

9. 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 REALISM
OR WEIGHTED AVERAGE
(α = 0.80)
FAVOURABLE MARKET
(Rs.)
UNFAVOURABLE MARKET
(Rs.)
CONSTRUCT A LARGE
PLANT
200,000 - 180,000
CONSTRUCT A SMALL
PLANT
100,000 -20,000 76,000
DO NOTHING 0 0 0
Rs. 124,000
REALISM
9

10. 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 NATURE
ROW AVERAGE
(Rs.)FAVOURABLE MARKET
(Rs.)
UNFAVOURABLE MARKET
(Rs.)
CONSTRUCT A LARGE
PLANT
200,000 - 180,000 10,000
CONSTRUCT A SMALL
PLANT
100,000 - 20,000
DO NOTHING 0 0 0
40,000
EQUALLY LIKELY
10

11. DECISION THEORY
MINIMAX REGRET
THIS 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.)
UNFAVOURABLE MARKET
(Rs.)
MAXIMUM IN A ROW
CONSTRUCT A LARGE
PLANT
0
[200,000 – 200,000]
180,000
[0 - ( - 180,000)]
180,000
CONSTRUCT A SMALL
PLANT
100,000
[200,000 – 100,000]
20,000
[0 - ( - 20,000)]
100,000
MINIMAX
DO NOTHING 200,000
[200,000 - 0]
0
[0 - 0]
200,000 11

12. DECISION THEORY
 DECISION MAKING UNDER RISK
DECISION 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 ?
12

13. DECISION THEORY
SOLUTION BY USING EMV METHOD :
EMV (LARGE PLANT) = (0.50) x (Rs.200,000) + (0.50) x (-Rs.180,000) = Rs.10,000
EMV ( SMALL PLANT) = (0.50) x (Rs.100,000) + (0.50) x (-Rs.20,000) = Rs.40,000
EMV (DO NOTHING) = (0.50) x (Rs.0) + (0.50) x (Rs.0) = Rs.0
THE 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
13
Alternatives State of Nature EMV
Favourable
Market
Unfavourable
Market
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

14. 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), AND
2. 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
14

15. 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.100,000
THUS, IF JHOHN HAD PERFECT INFORMATION, THE PAYOFF WOULD AVERAGE
Rs.100,000
2.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.60,000
THUS, 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 LOSS
AN 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. 15

16. 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.90,000
EOL (CONSTRUCT A SMALL PLANT) = (0.50) (Rs.100,000) + (0.50) (Rs.20,000) = Rs.60,000
EOL (DO NOTHING) = (0.50) (Rs.200,000) + (0.50) (Rs.0) = Rs.100,000
FROM 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.)
UNFAVOURABLE MARKET
(Rs.)
CONSTRUCT A LARGE
PLANT
0 180,000 90,000
CONSTRUCT A SMALL
PLANT
100,000 20,000 60,000
DO NOTHING 200,000 0 100,000
PROBABILITIES 0.50 0.50
16

17. 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 :
17
STRATEGIES STATE OF NATURE
N1 N2 N3
S1 700000 300000 150000
S2 500000 450000 0
S3 300000 300000 300000

18. 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
18

19. DECISION THEORY
19
STRATEGIES STATE OF NATURE
N1 N2 N3
S1 700000 300000 150000
S2 500000 450000 0
S3 300000 300000 300000

20. 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.
20

21. DECISION THEORY
21
COURSE OF
ACTION
(ALTERNATIVES)
STATE OF NATURE
PRICE OF “X”
INCREASES
PRICE OF “X”
DOES NOT
INCREASE
USE “X”
USE “Y & Z”

22. 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.
22

23. DECISION THEORY
Solution :
EMV(Bus) =
EMV(Stay at hotel) =
EMV(Taxi) = 23
State of Nature
Course of
Action
Catches the flight
Probability Payoff
Miss the flight
Probability Payoff
Bus 0.92 0.08
Stay in
hotel
0.96 0.04
Taxi 0.99 0.01

24. 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.
24
Strategy
Low Medium High
Regular
shares
7% 10% 15%
Risky
shares
- 10% 12% 25%
Property - 12% 18% 30%

25. 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 CHOSEN
STATE-OF-NATURE NODES ARE REPRESENTD BY CIRCLES OUT OF WHICH ONE OR
MORE STATE-OF-NATURE WILL OCCUR
IN 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 PROBLEM
2.DRAW THE DECISION TREE
3.ASSIGN PROBABILITIES TO THE STATE OF NATURE
4.ESTIMATE PAYOFFS FOR EACH POSSIBLE COMBINATION OF ALTERNATIVE AND STATE OF NATURE
5.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.
25

26. 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) - 180,000
CONSTRUCT 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.40,000
SO, A SMALL PLANT SHOULD BE BUILT
1
2
EMV FOR NODE
2=Rs.40,000
EMV FOR NODE 1 =
Rs.10,000
26

27. 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. 27

28. 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 tests
Without prior test
100
120
Failure With prior test -50
Without prior test - 40
Sale of exploitation
rights
Prior test show “success”
Prior test show “Failure”
Without prior test
65
15
45

29. 29