Applied Decision Methods

Sample Solution

  Laplace Criterion The Laplace criterion is a decision-making rule that is used when the probabilities of the different states of nature are unknown or equal. The rule states that the optimal decision is the one that has the highest expected value, where the expected value is calculated by averaging the payoffs for each state of nature. Payoff Table The payoff table below shows the profits realized (in $000's) for each alternative under the different scenarios faced by the plant manager.

Full Answer Section

Laplace Weights The Laplace criterion assumes that the probabilities of the different states of nature are equal. In this case, there are two states of nature: the bid is accepted or the bid is rejected. Since the probabilities of these two states of nature are equal, the Laplace weights are both equal to 1/2. Expected Value The expected value for each alternative is calculated by averaging the payoffs for each state of nature, weighted by the Laplace weights. The expected value for each alternative is shown below. Optimal Decision The optimal decision is the one with the highest expected value. In this case, the optimal decision is to buy 3 machines, because it has the highest expected value of $21. Conclusion Based on the Laplace criterion, the optimal decision for the plant manager is to buy 3 machines. This is because the expected value of buying 3 machines is the highest, when the probabilities of the different states of nature are equal.