Questions and Answers > MATH 451 Decision Making Under Uncertainty

Colorado Technical University MATH 451 Math 451 decision making under uncertainty Learning Materials Decision Making Under Uncertainty Decision making under uncertainty is made according to the following criteria: ...

Colorado Technical University MATH 451 Math 451 decision making under uncertainty Learning Materials Decision Making Under Uncertainty Decision making under uncertainty is made according to the following criteria:  Maximax  Maximin  Criterion of realism  Equally likely  Minimax regret Maximax Maximax criterion selects the decision alternative that maximizes the maximum payoff over all alternatives. This is the best outcome a manager can wish for to have the highest profit or payoff. It can also be called optimistic criterion. Maximin The opposite of maximax criterion is maximin criterion. It maximizes the minimum payoff over all decision alternatives. It is also called pessimistic criterion because it takes an extremely conservative view of the future. Criterion of Realism Criterion of realism or Hurwicz is somewhere between extreme optimists and extreme pessimists. You use the coefficient of realism denoted by alpha (α) to measure the decision maker’s level of optimism regarding the future. Coefficient of realism is bounded by 0 and 1 where 0 represents that the decision maker is totally pessimistic and the value of 1 suggests the decision maker is totally optimistic about the future. The realism payoff for alternatives can be calculated by: α * Maximum payoff for alternative + (1 - α) * Minimum payoff for alternative Equally Likely Equally likely criterion determines the decision alternative that has the highest average payoff. Minimax Regret Minimax regret criterion is based on opportunity loss which is defined as the difference between the optimal payoff and the actual payoff received. It determines the alternative that minimizes the maximum opportunity loss within each alternative. Example Consider the following company’s outcomes for four different decisionmaking options they have. The following table shows the payoff of each alternative: Create Decision-Making Criteria Using Excel Using Excel’s program, create all the mentioned decision-making criteria. Figure 1 clearly establishes all the Excel functions used to calculate the results. Click here for an enlarged image. Figure 1: Excel Program Used to Solve the Decision Making Under Uncertainty Figure 2 shows the numerical value for the decision-making criterion. Figure 2: Results of the Application Using Excel Program A company has outcomes for four different decision-making options they have. The following table shows the payoff of each alternative. α = 0.45. Question 1 What is the value of regret? -$100,000 $70,000 $73,333 $200,000 Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 | O4 | O5 | O6 Best | 399 | 372 | 380 | 288 | 142 | 395What is the value computed for the Hurwicz (also called realism) method with a .45 parameter? 140.75 131.26 121.30 138.55 Suppose that you are given the following payoff matrix: Payoffs | O1 | O2 | O3 | O4 | O5 | O6 Best | 261 | 216 | 236 | 380 | 368 | 366Your boss has asked you to identify the best strategy for maximax, maximin, and minimax regret. Which of the following strategies are these? 6, 4, 3 1, 1, 6 3, 4, 4 1, 4, 1 Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 C1 | 300 | 100 | -200 C2 | 200 | 200 | -50 C3 | 0 | 0 | 0What is the smallest value that the payoff for choice 1 and outcome 1 must exceed to have the method of equally likely outcomes recommending choice 1? 300 333.33 450 250 Which statement is true regarding maximax? Maximizes the minimum payoff over all alternatives Coefficient of realism < 0.50="" /> Maximizes the maximum payoff over all alternatives Pessimistic What is the function of the decision alternative that maximax criterion selects? Maximizes the minimum payoff over all alternatives Minimizes the minimum payoff over all alternatives Maximizes the maximum payoff over all alternatives Minimizes the maximum payoff over all alternatives Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 | O4 | O5 | O6 C1 | -111 | 161 | -90 | -168 | -223 | -250 C2 | 342 | 115 | -84 | -108 | 268 | 389 C3 | 150 | -95 | 314 | 222 | 341 | -94 C4 | 135 | 234 | -125 | 188 | -44 | 312 C5 | 201 | 297 | 204 | -136 | -220 | 118 C6 | 229 | 127 | -70 | 142 | -123 | 243Which of the following is the choice given by the principle of minimax regret? C2 C3 C1 C4 A company has outcomes for four different decision-making options they have. The following table shows the payoff of each alternative. α = 0.45. Question 4 What is the value of Hurwicz? $35,000 $73,333 -$100,000 $200,000 A company has outcomes for four different decision-making options they have. The following table shows the payoff of each alternative. α = 0.45. Question 5 What is the value of regret? $73,333 $70,000 -$100,000 $200,000 Decision making under uncertainty works with a payoff table that looks something like the following: Payoffs | Outcome O_1 | O_2 | ... | O_m Choice | C_1 | P_1,1 | P_1,2 | P_1,m C_2 | P_2,1 | P_2,2 | P_2,m ... C_n | P_n,1 | P_n,2 | P_n,mThe payoffs can be any real numbers. Suppose that you add the same constant to each payoff. What happens to the results under any of the decision strategies? There is no change. As long as the signs of the payoffs are not changed, the results will be the same. All but minimax regret will be left unchanged. Maximax and maximin strategies will be unchanged, but the results for realism, equally likely, and minimax regret can change A company has outcomes for four different decision-making options they have. The following table shows the payoff of each alternative. α = 0.45. Question 7 What $70,000 -$100,000 $200,000 $73,333 Which one of the following criterions identifies the alternative that has the highest average payoff? Equally likely Minimax regret Criterion of realism Maximax Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 C1 | 300 | 100 | -200 C2 | 200 | 200 | -50 C3 | 0 | 0 | 0What value of the parameter makes choice 1 preferred under the Hurwicz (Realism) method? .49 92 .45 .59 hich statement is true regarding maximax? Coefficient of realism < 0.50="" /> Maximizes the minimum payoff over all alternatives Coefficient of realism > 0.50 Pessimistic What does a value of 0 for the coefficient of realism indicate about a decision maker? Totally pessimistic about the future Somewhat pessimistic Somewhat optimistic Totally optimistic about the future Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 C1 | 300 | 100 | -200 C2 | 200 | 200 | -50 C3 | 0 | 0 | 0Suppose that you want to explore the sensitivity of the method of minimax regret. Which of the following increases (or decreases) to the payoffs of choice 1 will result in it being chosen under this method? The changes will be shown as 3 numbers, so 2, 3, 4 would mean increasing the payoff of choice 1, outcome 1 to 302; the payoff of choice 1, outcome 2 to 103; and the payoff of choice 1, outcome 3 to -196. Ties are not acceptable. 50, 80, 110 0, 10, 90 80, 100, 10 -80, -10, -10 Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 C1 | 300 | 100 | -200 C2 | 200 | 200 | -50 C3 | 0 | 0 | 0What value of the parameter makes choice 1 preferred under the Hurwicz (Realism) method? .55 .49 .45 .79 What is the numerical range for the coefficient of realism? A positive number greater than 1 0 ≤ coefficient of realism ≤ 1 A negative number -1 ≤ coefficient of realism ≤ 1 Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 | O4 | O5 | O6 Best | 399 | 372 | 380 | 288 | 142 | 395What is the value computed for the Hurwicz (also called realism) method with a .45 parameter? 140.75 156.63 138.55 146.27 Suppose that you have 4 different outcomes and 4 different choices with the following payoffs: Payoffs | O1 | O2 | O3 | O4 C1 | 66 | 18 | 41 | 24 the following methods gives choice 3 as optimal? Hurwicz Maximin Maximax Minimax regret Which statement is true regarding maximin? Maximizes the maximum payoff over all alternatives Optimistic Coefficient of realism > 0.50 Maximizes the minimum payoff over all alternatives Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 | O4 | O5 | O6 Best | 399 | 372 | 380 | 288 | 142 | 395What is the value computed for the equally likely method for choice C4? 143.94 144.00 154.25 150.81 Which of the following is correct regarding regret? Maximize the minimum opportunity loss within each alternative The difference between the maximum payoff and the minimum payoff The amount lost by not picking the best alternative The difference between the minimum payoff and the actual payoff Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 C1 | 300 | 100 | -200 C2 | 200 | 200 | -50 C3 | 0 | 0 | 0What value of the parameter makes choice 1 preferred under the Hurwicz (Realism) method? Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 C1 | 300 | 100 | -200 C2 | 200 | 200 | -50 C3 | 0 | 0 | 0Suppose that you want to explore the sensitivity of the method of minimax regret. Which of the following increases (or decreases) to the payoffs of choice 1 will result in it being chosen under this method? The changes will be shown as 3 numbers, so 2, 3, 4 would mean increasing the payoff of choice 1, outcome 1 to 302; the payoff of choice 1, outcome 2 to 103; and the payoff of choice 1, outcome 3 to -196. Ties are not acceptable. 0, 10, 90 20, 20, 120 80, -10. 10 -80, -10, -10 Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 C1 | 300 | 100 | -200 C2 | 200 | 200 | -50 C3 | 0 | 0 | 0Suppose that you want to explore the sensitivity of the method of minimax regret. Which of the following increases (or decreases) to the payoffs of choice 1 will result in it being chosen under this method? The changes will be shown as 3 numbers, so 2, 3, 4 would mean increasing the payoff of choice 1, outcome 1 to 302; the payoff of choice 1, outcome 2 to 103; and the payoff of choice 1, outcome 3 to -196. Ties are not acceptable. 80, 100, 10 20, 20, 120 -80, -10, -10 0, 10, 90 Which one of the following criterion requires use of the opportunity loss table? Maximax Maximin Minimax regret Criterion of realism A company has outcomes for four different decision-making options they have. The following table shows the payoff of each alternative. α = 0.45. Question 4 What is the value of maximax? $35,000 -$100,000 $200,000 $73,333 Suppose that the following payoffs are given: Payoffs | O1 | O2 | O3 | O4 | O5 | O6 C3 Which statement is true regarding maximin? Maximizes the maximum payoff over all alternatives Coefficient of realism > 0.50 Optimistic Pessimistic