Decision Analysis A A Elimam College of Business

Decision Analysis A. A. Elimam College of Business San Francisco State University

Characteristics of a Good Decision Based on Logic n Considers all Possible Alternatives n Uses all Available Data n Applies Quantitative Approach n Decision Analysis Frequently results in a favorable outcome

Decision Analysis (DA) Steps n Clearly define the problem n List all possible alternatives n Identify possible outcomes n Determine payoff for each alternative/outcome n Select one of the DA models n Apply model to make decision

Types of Decision Making (DM) n DM under Certainty: Select the alternative with the Maximum payoff n DM under Uncertainty: Know nothing about probability n DM under Risk: Only know the probability of occurrence of each outcome

Decision Table Example State of Nature (Market) Alternatives Favorable($) Unfavorable($) Large Plant 200, 000 -180, 000 Small Plant 100, 000 -20, 000 Do Nothing 0 0

Decision Making Under Risk n Expected Monetary Value (EMV) EMV (Alternative i) = (Payoff of first State of Nature-SN) x (Prob. of first SN) + (Payoff of second SN) x (Prob. of Second SN) + (Payoff of third State of Nature-SN) x (Prob. of third SN) +. . . + (Payoff of last SN) x (Prob. of last SN)

Thompson Lumber Example n EMV(Large F. ) = (0. 50)($200, 000)+(0. 5)(-180, 000)= $10, 000 n EMV(Small F. ) = (0. 50)($100, 000)+(0. 5)(-20, 000)= $40, 000 n EMV(Do Nothing) = (0. 50)($0)+(0. 5)(0)= $0

Thompson Lumber State of Nature (Market) Alternatives Favorable ($) Unfavorable ($) EMV ($) Large Plant 200, 000 -180, 000 10, 000 Small Plant 100, 000 -20, 000 40, 000 Do Nothing 0 0 Probabilities 0. 5

Expected Value of Perfect Information (EVPI) n Expected Value with Perfect Information = (Best Outcome for first SN) x (Prob. of first SN) + (Best Outcome for second SN) x (Prob. of Second SN) +. . . + (Best Outcome for last SN) x (Prob. of last SN)

Expected Value of Perfect Information (EVPI) n EVPI = Expected Outcome with Perfect Information - Expected Outcome without Perfect Information n EVPI = Expected Value with Perfect Information - Maximum EMV

Thompson Lumber Expected Value of Perfect Information n Best Outcome For Each SN • Favorable: Large plant, Payoff = $200, 000 • Unfavorable: Do Nothing, Payoff = $0 So Expected Value with Perfect Info. = (0. 50)($200, 000)+(0. 5)(0)= $100, 000 n The Max. EMV = $ 40, 000 n EVPI = $100, 000 - $40, 000 = $ 60, 000 n

Decision Table Example Possible Future Demand Alternative Low ($) High ($) Small Facility 200 270 Large Facility 160 800 0 0 Do Nothing

Example A. 5 Demand Alternatives Low ($) High ($) EMV ($) Small 200 270 242 Large 160 800 544 0 0 0. 4 0. 6 Do Nothing Probabilities

Example A. 8 Expected Value of Perfect Information n Best Outcome For Each SN • High Demand: Large , Payoff = $800 • Low Demand : Small , Payoff = $200 So Expected Value with Perfect Info. = (0. 60)($800)+(0. 4)(200)= $560 n The Max. EMV = $ 544 n EVPI = $ 560 - $ 544 = $ 16 n

Opportunity Loss : Thompson Lumber State of Nature (Market) Favorable ($) Unfavorable($) 200, 000 -200, 000 0 -(-180, 000) 200, 000 -100, 000 0 -(-20, 000) 200, 000 -0

Opportunity Loss : Thompson Lumber State of Nature (Market) Alternatives Favorable ($) Unfavorable ($) EOL ($) Large Plant 0 180, 000 90, 000 Small Plant 100, 000 20, 000 60, 000 Do Nothing 200, 000 0 100, 000 Probabilities 0. 5

Sensitivity Analysis EMV, $ 200, 000 Point 1 p=0. 167 Point 2, p=0. 62 EMV(LF) EMV(SF) 100, 000 EMV(DN) 0 1 -100, 000 -200, 000 Values of P

One Time Decision

Decision Trees n Decision Table: Only Columns-Rows n Columns: State of Nature n Rows: Alternatives- 1 Decision ONLY n For more than one Decision n Decision Trees can handle a sequence of one or more decision(s) Trees

Decision Trees n Two Types of Nodes n Selection Among Alternatives n State of Nature n Branches of the Decision Tree

Decision Tree: Example ) 5. 0 ( e orabl Fav e g r La Small Unfavora F. (0. 5) U. (0. 5 ) Do No th ing F. (0. 5) U. (0. 5) ble (0. 5)

A Decision Tree for Capacity Expansion (Payoff in thousands of dollars) Low demand [0. 40] ll a m S 1 ($148) a exp n nsio ($109) Lar ge e xpa nsio n ($148) $70 Don’t expand $90 High demand [0. 60] 2 ($135) Low demand [0. 40] $40 High demand [0. 60] $220 Expand $135

Decision Tree for Retailer Low demand [0. 4] $200 Hi gh de [0. ma 6] nd Don’t expand $223 al Sm 2 Expand $270 ($270) Do nothing 1 L ar $40 Modest response [0. 3] nd 3 ge a ($544) fac em ] $20 d Advertise ilit w 4 ($160) y Lo [0. Sizable response [0. 7] ($160) $220 ty i l ci ($242) a lf ($544) High demand [0. 6] $800