To determine the best decision alternative using the MINIMAX regret method, we first need to calculate the regret values for each decision alternative based on the worst payoffs for each state of nature.
- Identify the maximum payoffs for each state:
- For the first state of nature: \( \text{Max}(200, 300, 600) = 600 \)
- For the second state of nature: \( \text{Max}(335, 334, 333) = 335 \)
- For the third state of nature: \( \text{Max}(223, -100, -120) = 223 \)
- Calculate the regret for each alternative:
The regret is calculated as the maximum payoff minus the payoff of the chosen alternative for each state of nature.
-
Sell Company:
- Regret for state 1: \( 600 - 200 = 400 \)
- Regret for state 2: \( 335 - 335 = 0 \)
- Regret for state 3: \( 223 - 223 = 0 \)
- Total Regret: 400 + 0 + 0 = 400
-
Form Joint Venture:
- Regret for state 1: \( 600 - 300 = 300 \)
- Regret for state 2: \( 335 - 334 = 1 \)
- Regret for state 3: \( 223 - (-100) = 323 \)
- Total Regret: 300 + 1 + 323 = 624
-
Sell Software on Own:
- Regret for state 1: \( 600 - 600 = 0 \)
- Regret for state 2: \( 335 - 333 = 2 \)
- Regret for state 3: \( 223 - (-120) = 343 \)
- Total Regret: 0 + 2 + 343 = 345
- Compare Total Regrets:
- Sell Company: 400
- Form Joint Venture: 624
- Sell Software on Own: 345
- Choose the alternative with the minimum regret:
The lowest total regret is 345, which corresponds to the decision to Sell Software on Own.
Thus, the best decision alternative using the MINIMAX regret method is: c) Sell Software on own.