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Operations Research II Course,, September 20131 Part 5: Decision Models Operations Research II Dr. Aref Rashad.

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Presentation on theme: "Operations Research II Course,, September 20131 Part 5: Decision Models Operations Research II Dr. Aref Rashad."— Presentation transcript:

1 Operations Research II Course,, September 20131 Part 5: Decision Models Operations Research II Dr. Aref Rashad

2 Operations Research II Course,, September 2013 2 Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information Utility Chapter Topics

3 Operations Research II Course,, September 2013 3 Payoff Table A state of nature is an actual event that may occur in the future. A payoff table is a means of organizing a decision situation, presenting the payoffs from different decisions given the various states of nature. Decision Analysis Components of Decision Making

4 Operations Research II Course,, September 2013 4 Decision situation: Decision-Making Criteria: maximax, maximin, minimax, minimax regret, Hurwicz, and equal likelihood Payoff Table for the Real Estate Investments Decision Analysis Decision Making without Probabilities

5 Operations Research II Course,, September 2013 5 Payoff Table Illustrating a Maximax Decision In the maximax criterion the decision maker selects the decision that will result in the maximum of maximum payoffs; an optimistic criterion. Decision Making without Probabilities Maximax Criterion

6 Operations Research II Course,, September 2013 6 Payoff Table Illustrating a Maximin Decision In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion. Decision Making without Probabilities Maximin Criterion

7 Operations Research II Course,, September 2013 7 Regret Table Illustrating the Minimax Regret Decision Regret is the difference between the payoff from the best decision and all other decision payoffs. The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret. Decision Making without Probabilities Minimax Regret Criterion

8 Operations Research II Course,, September 2013 8 The Hurwicz criterion is a compromise between the maximax and maximin criterion. A coefficient of optimism, , is a measure of the decision maker’s optimism. The Hurwicz criterion multiplies the best payoff by  and the worst payoff by 1- ., for each decision, and the best result is selected. Decision Values Apartment building $50,000(.4) + 30,000(.6) = 38,000 Office building $100,000(.4) - 40,000(.6) = 16,000 Warehouse $30,000(.4) + 10,000(.6) = 18,000 Decision Making without Probabilities Hurwicz Criterion

9 Operations Research II Course,, September 2013 9 The equal likelihood ( or Laplace) criterion multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of nature are equally likely to occur. Decision Values Apartment building $50,000(.5) + 30,000(.5) = 40,000 Office building $100,000(.5) - 40,000(.5) = 30,000 Warehouse $30,000(.5) + 10,000(.5) = 20,000 Decision Making without Probabilities Equal Likelihood Criterion

10 Operations Research II Course,, September 2013 10 A dominant decision is one that has a better payoff than another decision under each state of nature. The appropriate criterion is dependent on the “risk” personality and philosophy of the decision maker. Criterion Decision (Purchase) MaximaxOffice building MaximinApartment building Minimax regretApartment building HurwiczApartment building Equal likelihoodApartment building Decision Making without Probabilities Summary of Criteria Results

11 Operations Research II Course,, September 2013 11 Decision Making without Probabilities Solution with QM for Windows (1 of 3)

12 Operations Research II Course,, September 2013 12 Decision Making without Probabilities Solution with QM for Windows (2 of 3)

13 Operations Research II Course,, September 2013 13 Decision Making without Probabilities Solution with QM for Windows (3 of 3)

14 Operations Research II Course,, September 2013 14 Expected value is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence. EV(Apartment) = $50,000(.6) + 30,000(.4) = 42,000 EV(Office) = $100,000(.6) - 40,000(.4) = 44,000 EV(Warehouse) = $30,000(.6) + 10,000(.4) = 22,000 Payoff table with Probabilities for States of Nature Decision Making with Probabilities Expected Value

15 Operations Research II Course,, September 2013 15 The expected opportunity loss is the expected value of the regret for each decision. The expected value and expected opportunity loss criterion result in the same decision. EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000 EOL(Office) = $0(.6) + 70,000(.4) = 28,000 EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000 Regret (Opportunity Loss) Table with Probabilities for States of Nature Decision Making with Probabilities Expected Opportunity Loss

16 Operations Research II Course,, September 2013 16 Expected Value Problems Solution with QM for Windows

17 Operations Research II Course,, September 2013 17 Expected Value Problems Solution with Excel and Excel QM (1 of 2)

18 Operations Research II Course,, September 2013 18 Expected Value Problems Solution with Excel and Excel QM (2 of 2)

19 Operations Research II Course,, September 2013 19 The expected value of perfect information (EVPI) is the maximum amount a decision maker would pay for additional information. EVPI equals the expected value given perfect information minus the expected value without perfect information. EVPI equals the expected opportunity loss (EOL) for the best decision. Decision Making with Probabilities Expected Value of Perfect Information

20 Operations Research II Course,, September 2013 20 Payoff Table with Decisions, Given Perfect Information Decision Making with Probabilities EVPI Example (1 of 2)

21 Operations Research II Course,, September 2013 21 Decision with perfect information: $100,000(.60) + 30,000(.40) = $72,000 Decision without perfect information: EV(office) = $100,000(.60) - 40,000(.40) = $44,000 EVPI = $72,000 - 44,000 = $28,000 EOL(office) = $0(.60) + 70,000(.4) = $28,000 Decision Making with Probabilities EVPI Example (2 of 2)

22 Operations Research II Course,, September 2013 22 Decision Making with Probabilities EVPI with QM for Windows

23 Operations Research II Course,, September 2013 23 A decision tree is a diagram consisting of decision nodes (represented as squares), probability nodes (circles), and decision alternatives (branches). TPayoff Table for Real Estate Investment Example Decision Making with Probabilities Decision Trees (1 of 4)

24 Operations Research II Course,, September 2013 24 Decision Tree for Real Estate Investment Example Decision Making with Probabilities Decision Trees (2 of 4)

25 Operations Research II Course,, September 2013 25 The expected value is computed at each probability node: EV(node 2) =.60($50,000) +.40(30,000) = $42,000 EV(node 3) =.60($100,000) +.40(-40,000) = $44,000 EV(node 4) =.60($30,000) +.40(10,000) = $22,000 Branches with the greatest expected value are selected. Decision Making with Probabilities Decision Trees (3 of 4)

26 Operations Research II Course,, September 2013 26 Decision Tree with Expected Value at Probability Nodes Decision Making with Probabilities Decision Trees (4 of 4)

27 Operations Research II Course,, September 2013 27 Decision Making with Probabilities Decision Trees with QM for Windows

28 Operations Research II Course,, September 2013 28 Decision Making with Probabilities Decision Trees with Excel and TreePlan (1 of 4)

29 Operations Research II Course,, September 2013 29 Decision Making with Probabilities Decision Trees with Excel and TreePlan (2 of 4)

30 Operations Research II Course,, September 2013 30 Decision Making with Probabilities Decision Trees with Excel and TreePlan (3 of 4)

31 Operations Research II Course,, September 2013 31 Decision Making with Probabilities Decision Trees with Excel and TreePlan (4 of 4)

32 Operations Research II Course,, September 2013 32 Decision Making with Probabilities Sequential Decision Trees (1 of 4) A sequential decision tree is used to illustrate a situation requiring a series of decisions. Used where a payoff table, limited to a single decision, cannot be used. Real estate investment example modified to encompass a ten-year period in which several decisions must be made:

33 Operations Research II Course,, September 2013 33 Sequential Decision Tree Decision Making with Probabilities Sequential Decision Trees (2 of 4)

34 Operations Research II Course,, September 2013 34 Decision Making with Probabilities Sequential Decision Trees (3 of 4) Decision is to purchase land; highest net expected value ($1,160,000). Payoff of the decision is $1,160,000.

35 Operations Research II Course,, September 2013 35 Sequential Decision Tree with Nodal Expected Values Decision Making with Probabilities Sequential Decision Trees (4 of 4)

36 Chapter 12 - Decision Analysis 36 Sequential Decision Tree Analysis Solution with QM for Windows

37 Operations Research II Course,, September 2013 37 Sequential Decision Tree Analysis Solution with Excel and TreePlan

38 Operations Research II Course,, September 2013 38 Payoff Table for Auto Insurance Example Decision Analysis with Additional Information Utility (1 of 2)

39 Operations Research II Course,, September 2013 39 Expected Cost (insurance) =.992($500) +.008(500) = $500 Expected Cost (no insurance) =.992($0) +.008(10,000) = $80 Decision should be do not purchase insurance, but people almost always do purchase insurance. Utility is a measure of personal satisfaction derived from money. Utiles are units of subjective measures of utility. Risk averters forgo a high expected value to avoid a low-probability disaster. Risk takers take a chance for a bonanza on a very low-probability event in lieu of a sure thing. Decision Analysis with Additional Information Utility (2 of 2)

40 Operations Research II Course,, September 2013 40 Decision Analysis Example Problem Solution (1 of 9)

41 Operations Research II Course,, September 2013 41 Decision Analysis Example Problem Solution (2 of 9) a.Determine the best decision without probabilities using the 5 criteria of the chapter. b.Determine best decision with probabilities assuming.70 probability of good conditions,.30 of poor conditions. Use expected value and expected opportunity loss criteria. c.Compute expected value of perfect information. d.Develop a decision tree with expected value at the nodes.

42 Operations Research II Course,, September 2013 42 Step 1 (part a): Determine decisions without probabilities. Maximax Decision: Maintain status quo DecisionsMaximum Payoffs Expand $800,000 Status quo1,300,000 (maximum) Sell 320,000 Maximin Decision: Expand DecisionsMinimum Payoffs Expand$500,000 (maximum) Status quo -150,000 Sell 320,000 Decision Analysis Example Problem Solution (3 of 9)

43 Operations Research II Course,, September 2013 43 Minimax Regret Decision: Expand DecisionsMaximum Regrets Expand$500,000 (minimum) Status quo 650,000 Sell 980,000 Hurwicz (  =.3) Decision: Expand Expand $800,000(.3) + 500,000(.7) = $590,000 Status quo$1,300,000(.3) - 150,000(.7) = $285,000 Sell $320,000(.3) + 320,000(.7) = $320,000 Decision Analysis Example Problem Solution (4 of 9)

44 Operations Research II Course,, September 2013 44 Equal Likelihood Decision: Expand Expand $800,000(.5) + 500,000(.5) = $650,000 Status quo $1,300,000(.5) - 150,000(.5) = $575,000 Sell $320,000(.5) + 320,000(.5) = $320,000 Step 2 (part b): Determine Decisions with EV and EOL. Expected value decision: Maintain status quo Expand $800,000(.7) + 500,000(.3) = $710,000 Status quo $1,300,000(.7) - 150,000(.3) = $865,000 Sell $320,000(.7) + 320,000(.3) = $320,000 Decision Analysis Example Problem Solution (5 of 9)

45 Operations Research II Course,, September 2013 45 Expected opportunity loss decision: Maintain status quo Expand $500,000(.7) + 0(.3) = $350,000 Status quo 0(.7) + 650,000(.3) = $195,000 Sell $980,000(.7) + 180,000(.3) = $740,000 Step 3 (part c): Compute EVPI. EV given perfect information = 1,300,000(.7) + 500,000(.3) = $1,060,000 EV without perfect information = $1,300,000(.7) - 150,000(.3) = $865,000 EVPI = $1.060,000 - 865,000 = $195,000 Decision Analysis Example Problem Solution (6 of 9)

46 Operations Research II Course,, September 2013 46 Step 4 (part d): Develop a decision tree. Decision Analysis Example Problem Solution (7 of 9)

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