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

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

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

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

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

Decision Making Under Risk n 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 n EMV(Large F.) = ( 0.50)($200,000)+(0.5)(-180,000)= $10,000 n n EMV(Small F.) = ( 0.50)($100,000)+(0.5)(-20,000)= $ 4 0,000 n n EMV(Do Nothing) = ( 0.50)($0)+(0.5)(0)= $0

Thompson Lumber 200, , , ,000 0 Favorable ($)Unfavorable ($) Alternatives Large Plant Small Plant Do Nothing State of Nature (Market) EMV ($) Probabilities ,000 40,000

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

Thompson Lumber Thompson Lumber Expected Value of Perfect Information n n Best Outcome For Each SN Favorable: Large plant, Payoff = $200,000 Unfavorable: Do Nothing, Payoff = $0 n n So Expected Value with Perfect Info. = ( 0.50)($200,000)+(0.5)(0)= $100,000 n n The Max. EMV = $ 40,000 n n EVPI = $100,000 - $40,000 = $ 60,000

Decision Table Example Low ($)High ($)Alternative Small Facility Large Facility Do Nothing Possible Future Demand

Example A Low ($)High ($) Alternatives Small Large Do Nothing Demand EMV ($) Probabilities

Example A.8 Example A.8 Expected Value of Perfect Information n n Best Outcome For Each SN High Demand: Large, Payoff = $800 Low Demand : Small, Payoff = $200 n n So Expected Value with Perfect Info. = ( 0.60)($800)+(0.4)(200)= $560 n n The Max. EMV = $ 544 n n EVPI = $ $ 544 = $ 16

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

Opportunity Loss : Thompson Lumber 0 100, , ,000 20,000 0 Favorable ($)Unfavorable ($) Alternatives Large Plant Small Plant Do Nothing State of Nature (Market) EOL ($) Probabilities0.5 90,000 60, ,000

Sensitivity Analysis EMV, $ ,000 1 Values of P -200, , ,000 EMV(LF) EMV(DN) EMV(SF) Point 2, p=0.62 Point 1 p=0.167

One Time Decision

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

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

Decision Tree: Example Small Large Do Nothing Unfavorable (0.5) F. (0.5) Favorable (0.5) U. (0.5) F. (0.5)

A Decision Tree for Capacity Expansion (Payoff in thousands of dollars) Low demand [0.40] $70 High demand [0.60] ($135) 2 Low demand [0.40] $40 High demand [0.60] $220 ($109) ($148) 1 Don’t expand $90 Expand $135 Small expansion Large expansion

Decision Tree for Retailer Low demand [0.4] $200 Don’t expand $223 Expand $270 Do nothing $40 Advertise Modest response [0.3] $20 Sizable response [0.7] $220 High demand [0.6] $800 ($544) ($160) ($270) ($242) Large facility Low demand [0.4] Small facility High demand [0.6]