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

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

Operations Research II Course,, September 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

Operations Research II Course,, September 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

Operations Research II Course,, September 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

Operations Research II Course,, September 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

Operations Research II Course,, September 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

Operations Research II Course,, September 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

Operations Research II Course,, September 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

Operations Research II Course,, September 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

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

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

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

Operations Research II Course,, September 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

Operations Research II Course,, September 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

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

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

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

Operations Research II Course,, September 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

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

Operations Research II Course,, September 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 = $28,000 EOL(office) = $0(.60) + 70,000(.4) = $28,000 Decision Making with Probabilities EVPI Example (2 of 2)

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

Operations Research II Course,, September 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)

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

Operations Research II Course,, September 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)

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

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

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

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

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

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

Operations Research II Course,, September 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:

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

Operations Research II Course,, September 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.

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

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

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

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

Operations Research II Course,, September 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)

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

Operations Research II Course,, September 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.

Operations Research II Course,, September 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)

Operations Research II Course,, September 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)

Operations Research II Course,, September 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)

Operations Research II Course,, September 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 = $195,000 Decision Analysis Example Problem Solution (6 of 9)

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