Decision Analysis
hurwicz approach
- a compromise between optimistic and conservative approaches - uses a coefficient of optimism (0 < α <1) that measure relative optimism
minimax regret approach
- choose the decision alternative that minimizes the maximum possible regret - requires calculation of the associated 'regrets' for each possible payoff
when formulating a decision analysis problem, characterize 3 components:
- decision alternatives (di): different possible strategies that decision makers can employ - states of nature (Si): chance or random events which may occur - payoffs (Pij): consequence resulting from a given decision alternative and state of nature
calculating regret
- for a max, for each state of nature, we take the absolute difference between the largest (best) payoff for that state of nature and the individual payoffs for each decision alternative - for min, for each state of nature, we take the absolute difference between the smallest (best) payoff for that state of nature and the individual payoffs for each decision alternative
optimistic approach or criterion ("best" or the "best")
- for a maximization problem: maximum of the maximum (maximax) - for a minimization problem: minimum of the minimum (minimin)
pessimistic or conservative approach ("best" of the "worst")
- for a maximization problem: maximum of the minimum (maximin) - for a minimization problem: minimum of the maximum (minimax)
to determine the associated hurwicz value for this criterion:
- multiply the best payoff by α and the worst payoff by 1-α for each decision alternative, and the alternative with the BEST result is selected - both the optimistic and conservative approaches are special cases of the hurwicz criterion, with α = 1 equivalent to the optimistic approach with α = 0 being the conservative appraoch
two categories of decision situations:
- probabilities cannot OR can be assigned to future occurrences
to determine the preferred decision using this criteria (equal likelihood)
- the payoffs for each decision at each state of nature is multiplied by an equal weight (the likelihood of each state of nature) and summed - the weights or likelihoods (assuming equal likelihoods) is simply 1/number of states of nature - the decision alternative with the BEST weighted payoff is then selected note: applying equal weights (likelihood) to each payoff for a given decision alternative and summing them to get the total is equivalent to taking the average payoff for each decision alternative
payoff table
a table showing payoffs for all combinations of decision alternatives and state of nature - can be expressed in terms of profit, cost, time, or any other appropriate measure
equal likelihood (laplace) approach
assumes that each state has the same likelihood of occurring
calculate the average
equal likelihood approach
Hurwicz Value = α("best" payoff) + (1- α)("worst" payoff)
hurwicz approach equation
R = | best payoff for S - P |
minimax regret approach
decision analysis
refers to methods of evaluating decision alternatives whose outcomes cannot be anticipated with certainty but depend on which of multiple possible random future events occur