INEN435 Stochastic Operations Research Homework 3 - Due Date on Blackboard Probl
ID: 2073820 • Letter: I
Question
INEN435 Stochastic Operations Research Homework 3 - Due Date on Blackboard Problem 2 You are given the following payoff table (in units of thousands of dollars) for a decision analysis probl Consider the following payoff matrix. Decision em. State of Nature S1 220 200 0.6 A1 170 180 0.3 150 0.1 Prior Probability a. Which alternative should be chosen under the maximin payoff criterion? b. Which alternative should be chosen under the maximax payoff criterion? c. Which alternative should be chosen under the expected value criterion? d. Which alternative should be chosen under the minimax regret payoff criterion? e. Do sensitivity analysis graphically with respect to the prior probabilities of states S1 and S2 (without changing the prior probability of state S3) to determine the crossover point where the decision shifts from one alternative to the other. Then use algebra to determine this crossover point. Repeat (e) for prior probabilities of states Si and S3. Repeat (e) for prior probabilities of states S2 and S3. If you feel that the true probabilities of the states of nature are within 10 percent of the given prior probabilities, which alternative would you choose? f. g. h.Explanation / Answer
The given payoff matrix is analysizes as follows:
Maximum likely is 194 corresponding to A1 (Ans.2)
Also maximum probaility is for state S1 under which alternative A1 gives the maximum expected gain,
Under Bayes' decision rule it is assumed that all states have the same probabilities and decision maker first calculate the average outcome for every option and then selects that with the maximum value.
States Sigma-pixi Alternatives S1 S2 S3 Expected A1 220 170 110 194 220*.6+170*.3+110*.1 A2 200 180 150 189 200*.6+180*.3+150*.1 Prior Probability 0.6 0.3 0.1 Minimum 200 170 110 MaxiMin is 200 corresponding to A2 (Ans.1)Maximum likely is 194 corresponding to A1 (Ans.2)