1 DSCI 3223 Decision Analysis Decision Making Under Uncertainty –Techniques play an important role in business, government, everyday life, college football rankings –How can a manager provide a rational methodology for decision making and analysis in the face of uncertainty? –How does a manager chose among alternatives in an optimal fashion when those alternatives may be numerous and conflicting?

2 DSCI 3223 Components of Decision Making State –An actual event that may occur in the future Decision –Options from which a decision maker can chose Outcomes –The result of a combination of states and decisions

3 DSCI 3223 Payoff Table A means to organize states, decisions, and outcomes e.g., States Decisions a b 1payoff 1apayoff 1b 2 payoff 2apayoff 2b

4 DSCI 3223 Payoff Table Example An investor must decide among an apartment building, an office building, and a warehouse. States Decisions Good Bad Apartment $50,000$30,000 Office 100,000-40,000 Warehouse 30,000 10,000

5 DSCI 3223 Decision Criteria Maximax Maximin Minimax Regret Hurwicz Equal Likelihood

6 DSCI 3223 Maximax Decision maker selects the decision that will result in the maximum of the maximum payoffs Decisions Good Apartment $50,000 Office 100,000 Warehouse 30,000 Decision would be to purchase the office Decision completely ignores down side, loss of $40,000 Assumes a very optimistic future

7 DSCI 3223 Maximin Decision maker selects the decision that will result in the maximum of the minimum payoffs Decisions Bad Apartment $30,000 Office -40,000 Warehouse 10,000 Decision would be to purchase the apartment Decision is relatively conservative Assumes a very pessimistic future

8 DSCI 3223 Minimax Regret Decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret Select the maximum payoff under each state: –Good ----> $100,000 –Bad > 30,000 Regret is then calculated as follows: –Good ----> $100,000 - payoff for each decision –Bad > 30,000 - payoff for each decision

9 DSCI 3223 Minimax Regret The calculations for the example States DecisionsGood Bad Apartment $100, ,000 = 50,000 $30, ,000 = 0 Office$100, ,000 = 0 $30,000 - (-40,000) = 70,000 Warehouse $100, ,000 = 70,000 $30, ,000 = 20,000 Chose the decision which minimizes this regret Purchase the apartment building Decision maker experiences the least amount of regret

10 DSCI 3223 Hurwicz Criterion A compromise between the maximax and maximin criterions Payoffs are weighted using a coefficient of optimism,  A measure of the decision maker’s optimism regarding the outcome of the events 0 <  < 1

11 DSCI 3223 Hurwicz Criterion The  is multiplied by the best payoff and (1-  ) is multiplied by the worst payoff and these values are added together This criterion is a simple weighting scheme However,  must be determined by the decision maker and is completely subjective The Hurwicz Criterion is completely subjective

12 DSCI 3223 Hurwicz Criterion Given  = 0.4, then 1-  = 0.6, DecisionsValues Apartment $50,000*(0.4) + $30,000*(0.6) = $38,000 Office$100,000 *(0.4) - $40,000*(0.6)= $16,000 Warehouse $30,000 *(0.4) + $10,000*(0.6) = $18,000 Hurwicz criterion specifies selection corresponding to the maximum weighted average Apartment building

13 DSCI 3223 Equal Likelihood or LaPlace Hurwicz Criterion when  = 0.5 DecisionsValues Apartment $50,000*(0.5) + $30,000*(0.5) = $40,000 Office$100,000 *(0.5) - $40,000*(0.5)= $30,000 Warehouse $30,000 *(0.5) + $10,000*(0.5) = $20,000 Equal likelihood criterion specifies selection corresponding to the maximum weighted average Apartment building

14 DSCI 3223 Limitations of Weighting Methods Regardless of how a is determined it is a subjective measure, even with equal likelihood The degree of the decision maker’s optimism is reflected in  Untrained decision maker’s generally choose  incorrectly How would you choose  ?

15 DSCI 3223 Summary of Techniques CriterionDecision MaximaxOffice Building MaximinApartment Minimax regretApartment HurwiczApartment Equal LikelihoodApartment