Decision making under uncertainty
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1) The document discusses several criteria for decision making under uncertainty including maximax, maximin, minimax, minimin, and Laplace. 2) The maximax criterion is optimistic and chooses the alternative with the highest possible payoff. Maximin is pessimistic and chooses the alternative with the highest minimum payoff. 3) Minimax regret considers the maximum regret for each alternative and chooses the one with the minimum maximum regret. This accounts for opportunity loss across states of nature.
Decision making under uncertainty
- 2. Decision Making Under Uncertainty In this case the decision maker has the complete knowledge of the consequences of every alternative or decision choice. Here the decision maker presumes that only one state of nature is relevant for this purpose. He identifies this state of nature , takes it for granted and presumes complete knowledge as to its occurrence.
- 4. Maximax This is the OPTIMISTIC type of criterion In this criterion the decision maker does not want to miss the opportunity to achieve the largest possible profit. Procedure 1) Locate the maximum payoff values corresponding to each act 2) From among the maximums choose the highest value 3) The act corresponding to the highest value will be the decision
- 5. Example 1) maximum payoff values corresponding to act 𝐴1=120 i.e. maximum in 1st column maximum payoff values corresponding to act 𝐴2=80 i.e. maximum in 2nd column maximum payoff values corresponding to act 𝐴3=100 i.e. maximum in 3rd column 2) From among the maximums choose the highest value maximum payoff values out of (120,80,100)=120 3) The act corresponding to the highest value 120 is 𝐴1 will be the decision State of Nature Acts 𝐴1 𝐴2 𝐴3 𝑆1 40 80 100 𝑆2 70 30 80 𝑆3 120 10 20
- 6. Maximin This is the PESSIMISTIC type of criterion. This is a conservative approach. Here the decision maker attempts in maximizing the minimum possible profit Procedure 1) Locate the minimum payoff values corresponding to each act 2) From among the minimum choose the maximum value 3) The act corresponding to the maximum value will be the decision
- 7. Example 1) minimum payoff values corresponding to act 𝐴1=40 i.e. maximum in 1st column minimum payoff values corresponding to act 𝐴2=10 i.e. maximum in 2nd column minimum payoff values corresponding to act 𝐴3=20 i.e. maximum in 3rd column 2) From among the minimum choose the maximum value maximum payoff values out of (40,10,20)=40 3) The act corresponding to the highest value 40 is 𝐴1 will be the decision State of Nature Acts 𝐴1 𝐴2 𝐴3 𝑆1 40 80 100 𝑆2 70 30 80 𝑆3 120 10 20
- 8. Minimin This is the PESSIMISTIC type of criterion. Procedure 1) Locate the minimum payoff values corresponding to each act 2) From among the minimum choose the minimum value 3) The act corresponding to the minimum value will be the decision
- 9. Example 1) minimum payoff values corresponding to act 𝐴1=40 i.e. maximum in 1st column minimum payoff values corresponding to act 𝐴2=10 i.e. maximum in 2nd column minimum payoff values corresponding to act 𝐴3=20 i.e. maximum in 3rd column 2) From among the minimum choose the minimum value minimum payoff values out of (40,10,20)=10 3) The act corresponding to the minimum value 10 is 𝐴2 will be the decision State of Nature Acts 𝐴1 𝐴2 𝐴3 𝑆1 40 80 100 𝑆2 70 30 80 𝑆3 120 10 20
- 10. Laplace In this criteria it is assumed that all states of nature will occur with equal probability. Here the decision maker finds the average outcome for each act and picks up the act corresponding to maximum value Procedure 1) Find the average payoff values corresponding to each act 2) From among the averages choose the maximum value 3) The act corresponding to the maximum value will be the decision
- 11. Example 1) average payoff values corresponding to act 𝐴1 = 40+70+120 3 = 230 3 = 76.67 i.e. average in 1st column average payoff values corresponding to act 𝐴2 = 80+30+10 3 = 120 3 = 40 i.e. average in 2nd column average payoff values corresponding to act 𝐴3 = 100+80+20 3 = 200 3 = 66.67 i.e. average in 3rd column 2) From among the averages choose the maximum value minimum payoff values out of (76.67,40,66.67)=76.67 3) The act corresponding to the maximum value 76.67 is 𝐴1 will be the decision State of Nature Acts 𝐴1 𝐴2 𝐴3 𝑆1 40 80 100 𝑆2 70 30 80 𝑆3 120 10 20
- 12. Minimax Regret In this criteria the decision maker identifies the maximum regret for each act and selects the act for which maximum regret is minimum. Procedure 1) Convert conditional profit matrix into regret matrix i.e. opportunity loss table 2) Find the maximum values corresponding to each act 2) From among the averages choose the minimum value 3) The act corresponding to the minimum value will be the decision
- 13. Opportunity Loss Table The Opportunity Loss is defined as the difference between the highest possible profit for a state of nature and the actual profit obtained for the particular action taken. Maximum pay of 𝑆1=Max{𝑃11, 𝑃12, 𝑃13, … 𝑃1𝑛} = Max{S1} State of Nature Acts 𝐴1 𝐴2 𝐴3 --- 𝐴 𝑛 𝑆1 𝑃11 𝑃12 𝑃13 𝑃1𝑛 𝑆2 𝑃21 𝑃22 𝑃23 𝑃2𝑛 𝑆3 𝑃31 𝑃32 𝑃33 𝑃3𝑛 ---- 𝑆 𝑚 𝑃 𝑚1 𝑃 𝑚2 𝑃 𝑚3 𝑃𝑚𝑛 Conditional Profit Matrix State of Nature Acts 𝐴1 𝐴2 𝐴3 --- 𝐴 𝑛 𝑆1 Max S1 − 𝑃11 Max S1 − 𝑃12 Max S1 − 𝑃13 Max S1 − 𝑃1𝑛 𝑆2 Max S2 − 𝑃21 Max S2 − 𝑃22 Max S2 − 𝑃23 Max S2 − 𝑃2𝑛 𝑆3 Max S3 − 𝑃31 Max S3 − 𝑃32 Max S3 − 𝑃33 Max S3 − 𝑃3𝑛 ----- 𝑆 𝑚 Max S 𝑚 − 𝑃 𝑚1 Max S 𝑚 − 𝑃 𝑚2 Max S 𝑚 − 𝑃 𝑚3 Max S 𝑚 − 𝑃𝑚𝑛 Opportunity Loss Table or Regret Table
- 14. Example Maximum of 𝑆1=Max{𝑆1}=Max{40,80,100}=100 Maximum of 𝑆2=Max{𝑆2}=Max{70,30,80}=80 Maximum of 𝑆3=Max{𝑆3}=Max{120,10,20}=120 State Nature Acts 𝐴1 𝐴2 𝐴3 𝑆1 40 80 100 𝑆2 70 30 80 𝑆3 120 10 20 Conditional Payoff Matrix State of Nature Acts 𝐴1 𝐴2 𝐴3 𝑆1 100-40 100-80 100-100 𝑆2 80-70 80-30 80-80 𝑆3 120-120 120-10 120-20 Opportunity Loss Table State of Nature Acts 𝐴1 𝐴2 𝐴3 𝑆1 60 20 0 𝑆2 10 50 0 𝑆3 0 110 100 Opportunity Loss Table
- 15. Example Step 2) Maximum of 𝐴1=Max{60,10,0}=60 Maximum of 𝐴2=Max{20,50,110}=110 Maximum of 𝐴3=Max{0,0,100}=100 Step 3) From among the averages choose the minimum value i.e. min{60,110,100}=60 Step 4) The act corresponding to the minimum value 60 will be the decision i.e. 𝐴1 State of Nature Acts 𝐴1 𝐴2 𝐴3 𝑆1 60 20 0 𝑆2 10 50 0 𝑆3 0 110 100 Opportunity Loss Table