Company Case

DECISION MODELS

Decisions Making Under Uncertainty                          Decisions Making Under Risk

1. Max-Min Criteria (pessimist)                                1. Expected Payoff (Average)

- Best of the worst        A. Multiply payoffs by probabilities and

-Becomes (Min-Max) if loss table                              add up. (For each action separately)  

A. Find min (max) in each row                                B. Pick best action

B. Pick the best of the Max (Min)                        

                                                        2. Expected Opportunity Loss

                                                        A. Set up loss matrix

                                                        -Subtract all numbers in each column Criteria Max-Max Criterion (Optimist)                        from the largest number in that column

-Best of the best                                        B. Find average opportunity loss Becomes (min-min) if loss table                                 for each action.

A. Find max (min) in each row                                - multiply the probability time loss and B. B. Pick the largest (smallest)                                add up.

C. Pick smallest number (want to min loss)

3. Most Probable State of Nature

3. Weighted Average Criterion                                                                                                                                 A. Determine the most probable state of nature - Coef. of Optimism = α                                        (one with highest probability)

- Optimistic=1, pessimistic=0                        

A. Calculate weighted value                                 B. Pick the action with the highest expected

   α (best) + (1 - α) (worst)                                       payoff.

   B. Pick best value                                             C. Good criteria for a non-repetitive

 Decision

4. Minimizing Regret                                5. Expected Value of Perfect Information

- Savage opportunity loss criteria                        A. Fix a state of nature.                          

A. Set up opportunity loss matrix                                B. Pick largest value in each column

- subtract the largest number in

each column from all other numbers                        C. Multiply prob. X largest values

  in that column                                                  and add up = ERPI                                                                                        ERPI=Expected Return of Perfect Info)

B. Find max regret in each row                                D. EVPI = ERPI - Average expected payoff

C. Pick the action with min. regret.                        E. EVPI is always equal to Expected                                                                 opportunity loss.

6. Equal Likely Strategy (Laplace Criterion)

   - Best on Average

   A. Expected payoffs for each row

   B. Pick the largest (max problem) (Smallest for min problems)

Numerical Example

                              State of Nature          

                (0.5)**                (0.3)**                (0.2)**              **Use Probabilities for Decision                                                                         Under Risk Problems only.

Action                Growth                No Change        Inflation

Bonds                 12%                  6%                   3%

Stocks                 15%                  3%                  -2%

Deposit                 6.5%                  6.5%                   6.5%                                

Note: Objective is to Maximize

DECISION MAKING UNDER PURE UNCERTAINTY

1. Max-Min (Pess)        2. Max-Max (Opt)        3. Weighted Average                                     

   Min/Row                   Max/Row                Action        Weighted Value (α = 0.7)