decisiontheory.pptx Decision Theory represents a general approach to decision making which is suitable for a wide range of management decisions, including:

A decision problem is characterized by decision alternatives, states of nature, and resulting payoffs.
The decision alternatives are the different possible strategies the decision maker can employ.
The states of nature refer to future events, not under the control of the decision maker, which will ultimately affect decision results.
States of nature should be defined so that they are mutually exclusive and contain all possible future events that could affect the results of all potential decisions.

1. Decision Theory

2. Contents Fundamentals of decision theory Decision environment Decision making under uncertainty Decision making under risk Decision tree

3. Decision Theory represents a general approach to decision making which is suitable for a wide range of management decisions, including: product and service design equ i pme n t selection lo c a tion pl a nn i ng Decisio n Theory Capacity planning Product –mix Credit policies

4. 4 Problem Formulation A decision problem is characterized by decision alternatives, states of nature, and resulting payoffs. The decision alternatives are the different possible strategies the decision maker can employ. The states of nature refer to future events, not under the control of the decision maker, which will ultimately affect decision results. States of nature should be defined so that they are mutually exclusive and contain all possible future events that could affect the results of all potential decisions.

5. 5 Payoff Tables The outcomes resulting from a specific combination of a decision alternative and a state of nature is a payoff . A table showing payoffs for all combinations of decision alternatives and states of nature is a payoff table . Payoffs can be expressed in terms of profit , cost , time , distance or any other appropriate measure.

6. Fundamentals of decision theory Decision al t ern a ti v es States of nature Payoff Courses of action or strategies An occurrence over which decision maker has no control Quantitative measure of the outcome

7. Three-egg omelette Problem You are preparing a three-egg omelette. Having already broken two , good eggs into the pan, you are suddenly assailed by doubts about the quality of the third. As yet unbroken.egg, two things may happen: either the egg is good or it is rotten.

8. Egg omelette problem E v ents Probability Break 3 rd egg into pan Break 3 rd egg into saucer & inspect Throw away 3 rd egg Thi r d e g g is g oo d 0.9 3-egg omlette 3-egg omelette, one saucer to wash 2-egg omelette, one good egg destroyed Thi r d e g g is r o tt en 0.1 No egg omlette 2 good eggs destroyed 2-egg omelette, one saucer to wash 2-egg omelette S t a t es of nature Acts (strategies) P a y- o f f s

9. Certainty - Environment in which relevant parameters have known values Risk - Environment in which certain future events have probable outcomes Uncertainty - Environment in which it is impossible to assess the likelihood of various future events Decisio n Environme n ts

10. Risk vs. Uncertainty Risk Must make a decision for which the outcome is not known with certainty Can list all possible outcomes & assign probabilities to the outcomes Uncertainty - Cannot list all possible outcomes Cannot assign probabilities to the outcomes Certainty - is an environment in which future outcomes or state of nature are known. Eg: Investment in Bank FD, there is CERTAINTY regarding FUTURE PAYMENTS on maturity Investment in shares is risky Investment in shares FETCHING returns higher than FD in another 2 years, is uncertain

11. TYPES OF DECISION –MAKING : Decision making under certainty Decision making under uncertainty Decision making under risk

12. DECISION MAKING UNDER CERTAIN TY: The decision maker knows with certainty the consequences of selecting every course of action or decision choice. Technique Used: System of equations Linear programming Integer programming etc

13. DECISION MAKING UNDER UNCERTAINTY: Under this condition , There is no historical data available or no relative frequency which could indicate the probability of the occurrence of a particular state of nature. In other words , The decision maker has no way of calculating the expected payoff for the courses of action. Example: When a new product is introduce in the market.

14. Criteria of decision making under uncertainity 0ptimism(Maximax or Minimin ) Pessimism(Maximin or Minimax) Equal probabilities(Laplace) Coefficient of optimism(Hurwicz) Regret(Salvage)

15. THE CRITERION OF OPTIMISM OR MAXIMAX (Risk Lover) It was suggested by Leonid Hurwitz . The decision criterion locates the alternative strategy with the highest possible gain. Steps: Determine the best outcome for each alternative. Choose the alternative associated with the best of these. Strategies States of nature N1 N2 N3 ROW MAX I M UM S1 7000 3000 1500 7000 S2 5000 4500 5000 S3 3000 3000 3000 3000

16. THE CRITERION OF PESSIMISM OR MAXIMIN: (Risk Averse) It was suggested by Arabham Wald. The decision criterion locates the alternative strategy that has the least possible loss. Steps: Determine the lowest outcome for each alternative. Choose the alternative associated with the best of these. Strategies States of nature N1 N2 N3 Row Minimum S1 7000 3000 1500 1500 S2 5000 4500 S3 3000 3000 3000 3000

17. Decision table and tree 1 Outcome 1 2 outcome2 Outcome 3 outcome 4 States of nature Strategies State 1 State 2 Strategy 1 Outcome 1 Outcome2 Strategy 2 Outcome 3 Outcome 4

18. Decision tree Decision tree is a network which exhibits graphically the relationship between the different parts of the complex decision process. It is a graphical model of each combination of various acts and states of nature along with their payoffs, probability distribution It is extremely useful in multistage situations which involve a number of decisions ,each depending on the preceding one. A decision tree analysis involves the construction of a diagram that shows , at a glance, when decisions are expected to be made- in what sequence, their possible outcomes, & corresponding payoffs.

19. Decision tree example Stay comfortable and dry Bear unnecessary trouble of carrying umbrella Get wet and uncomfortable Remain dry and comfortable

20. 24 Elements of Decision Theory • • States of nature: The states of nature could be defined as low demand and high demand. Al t ern a ti v es : V GK c ou l d deci d e t o b u i ld a smal l , medium, or large Flour processing mill . Payoffs: The profit for each alternative under each potential state of nature is going to be determined. We develop different models for this problem on the following slides.

21. 25 VGK Flour mill : Payoff Table Alternatives Small Medium Large Low 8 5 - 11 High 8 15 22 States of Nature (Profits in LAKHS of Rs ) THIS IS A PROFIT PAYOFF TABLE

22. Laplace criterion(Equal probabilities) Under this assumption ,all states of nature are equally likely. D ecision maker can compute the average payoff for each row (the sum of the possible consequences of each alternative is divided by the number of states of nature) and, then, select the alternative that has the highest row average

23. LAPLACE CRITERION States of nature ROW Strategies N1 N2 N3 Avg. S1 7000 3000 1500 3,833.33 S2 5000 4500 3166.66 S3 3000 3000 3000 3000 The largest expected return is from Strategy S1, THE EXECUTIVE MUST SELECT S1

24. Regret (Salvage rule) This rule represents a pessimistic approach . The opportunity loss reflects the difference between each payoff and the best possible payoff in a column (it can be defined as the amount of profit foregone by not choosing the best alternative for each state of nature). For each course of action identify the maximum regret value, record this no in a row Select the course of action with Smallest anticipated opportunity loss value

25. States of nat u r e Row max The company should adopt minimum opportunity loss strategy S1 Strategies N1 States N2 of nature N3 S1 7000 3000 1500 S2 5000 4500 S3 3000 3000 3000 Column max 7000 4500 3000 Strategies N1 N2 N3 S1 7000 – 7000 = 4500-3000= 1500 3000-1500=1500 1500 S2 7000- 5000 = 2000 4500-4500=0 3000-0=3000 3000 S3 7000-3000 = 4000 4500-3000= 1500 3000-3000=0 4000 Col max 7000 4500 3000