To determine which decision alternative to choose using the Expected Opportunity Loss (EOL) method, we first need to calculate the opportunity loss for each decision alternative based on the outcomes provided.
Step 1: Calculate the Maximum Payoff for Each State of Nature.
- Success: The maximum payoff is 210 (Form Joint Venture).
- Moderate Success: The maximum payoff is 229 (Sell Software on own).
- Failure: The maximum payoff is 100 (Sell Software on own).
Step 2: Calculate the Opportunity Loss for Each Decision Alternative.
The opportunity loss (OL) is calculated as follows:
\[ \text{Opportunity Loss} = \text{Maximum Payoff} - \text{Actual Payoff} \]
| Decision Alternative | Success OL | Moderate Success OL | Failure OL | |-----------------------------|----------------------|-----------------------|------------------| | Sell Company | 210 - 96 = 114 | 229 - 50 = 179 | 100 - 0 = 100 | | Form Joint Venture | 210 - 210 = 0 | 229 - 0 = 229 | 100 - 44 = 56 | | Sell Software on own | 210 - 0 = 210 | 229 - 229 = 0 | 100 - 100 = 0 |
Step 3: Multiply by Their Probabilities.
Next, multiply each opportunity loss by the probability of each state of nature.
Probability of Success = 0.3
Probability of Moderate Success = 0.3
Probability of Failure = 0.4
| Decision Alternative | Success OL | Moderate Success OL | Failure OL | EOL Calculation | |-----------------------------|----------------------|-----------------------|------------------|-----------------------------------| | Sell Company | 114 × 0.3 = 34.2 | 179 × 0.3 = 53.7 | 100 × 0.4 = 40 | EOL = 34.2 + 53.7 + 40 = 127.9 | | Form Joint Venture | 0 × 0.3 = 0 | 229 × 0.3 = 68.7 | 56 × 0.4 = 22.4 | EOL = 0 + 68.7 + 22.4 = 91.1 | | Sell Software on own | 210 × 0.3 = 63 | 0 × 0.3 = 0 | 0 × 0.4 = 0 | EOL = 63 + 0 + 0 = 63 |
Step 4: Compare EOL for Each Alternative.
- Sell Company EOL: 127.9
- Form Joint Venture EOL: 91.1
- Sell Software on own EOL: 63
Conclusion: The alternative with the lowest expected opportunity loss (EOL) is to Sell Software on own with an EOL of 63. Thus, that is the recommended decision alternative to choose based on the EOL method.