Decision Analysis

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?

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

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

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

Decision Criteria • Maximax • Maximin • Minimax Regret • Hurwicz • Equal Likelihood

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

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

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

Minimax Regret • The calculations for the example States Decisions Good Bad Apartment $100,000 - 50,000 = 50,000 $30,000 - 30,000 = 0 Office $100,000 - 100,000 = 0 $30,000 - (-40,000) = 70,000 Warehouse $100,000 - 30,000 = 70,000 $30,000 - 10,000 = 20,000 • Chose the decision which minimizes this regret • Purchase the apartment building • Decision maker experiences the least amount of regret

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

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

Hurwicz Criterion • Given  = 0.4, then 1- = 0.6, Decisions Values 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

Equal Likelihood or LaPlace • Hurwicz Criterion when  = 0.5 Decisions Values 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

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 ?

Summary of Techniques Criterion Decision Maximax Office Building Maximin Apartment Minimax regret Apartment Hurwicz Apartment Equal Likelihood Apartment

Decision Analysis