Decision Analysis

Overview

Decision Analysis focuses on the decision making process under a variety of situations. At its simplest, decision making can be characterized as the process comprising the following steps:

  1. Define the problem.
  2. Specify an objective measure.
  3. Generate alternative solutions.
  4. Select the optimum alternative.
  5. Implement the solution.

QMS focuses on the selection of the optimum alternative, and assumes that you have defined the problem, the objective, and the alternatives, and are prepared to implement the solution.

One of the classic divisions of decision problem classes is based on the amount of information available to the decision maker. Problems are divided into decisions under certainty (outcomes are known in advance), risk (probabilities of outcomes can be defined), and uncertainty (probabilities unknown). QMS solves problems under uncertainty using the maximax, maximin, Hurwicz, Savage, and LaPlace (with expected value) criteria, and under risk using the “optimize expected value” and “minimize expected regret” criteria.

Outputs include the following:

Under uncertainty
Under risk
Bayesian analysis

Creating/Editing a Decision Analysis Problem

All of the decision models use the same input format and data. You must first specify the number of actions (alternatives) and the number of events (outcomes). Once you have entered the desired number of rows and columns you must press Resize in order to properly dimension the input matrix.

The optimization type of Maximize or Minimize must be selected. You may name the outcomes, or use the default (e.g. “Event1,” “Event2,” etc.). You may also name the alternatives as you enter the data into the table (default is “Action1,” “Action2,” etc.). Input the payoff values which result from each choice/chance combination. Finally, enter the probabilities for each of the outcomes (if known); the default is equal probability for each. If probabilities are entered, they must sum to 1.0.

Indicate whether you wish to input the Bayes' Contingency Table; you will be prompted to enter the conditional probabilities for the imperfect predictor of the outcomes. Each row must sum to 1.0. Also indicate your preference for display decisions under uncertainty, under conditions of risk, or both. Finally, indicate the Hurwicz's Alpha Value; it must be a decimal value between 0.0 and 1.0 (the default is 0.5).

Solve is used to generate and display the solution.

Key Concepts

Choice
Evaluation of alternatives to select the one(s) that can be shown to be “best” by some criterion.
Chance
An outcome controlled not by the decision maker but by outside forces, nature, or other people.
Consequence
The payoff or value of some measure that results from the combination of a choice and a chance.
Certainty
The outcomes of the chance events are known to the decision maker at the time of the decision.
Uncertainty
The decision maker cannot even assign the probabilities of the outcomes of chance events.
Risk
The decision maker is able to assign probabilities to the outcomes of chance events.
Criterion of optimism (maximax)
Selection of the alternative with the best best outcome. Called the minimin if payoff is cost or regret.
Criterion of pessimism (maximin or minimax)
Selection of an alternative with the best worst outcome. Also called the Wald criterion.
Hurwicz criterion
Selection of the alternative with the highest H value for the given level of optimism, where H = (α)best + (1 - α)worst.
Coefficient of optimism (α)
A value between zero and one that expresses the degree of optimism of the decision maker. If α = 0, the Hurwicz criterion becomes the Wald criterion; if α = 1, it becomes the maximax or minimin.
Savage criterion
Minimax regret, where regret is the difference between the payoff of the optimum alternative and the one in question. Regret is sometimes called “conditional opportunity loss.”
LaPlace principle
The principle of insufficient reason. A method of moving from decision making under uncertainty to decision making under risk by assigning equal probabilities to all outcomes.
Risk avoider
One who will accept a sure payment of less than the epected value of a chance payoff.
Risk seeker
The optimist, or gambler, who will pay more than the expected value of a chance payoff.
Risk neutral
The “economic man” who neither seeks nor avoids risk but makes decisions based on expected values.
Decision tree
A graphical representation of a decision, using chance points and choice points.
Choice point
In a decision tree, a choice point that represents a decision among alternative courses of action. (◻)
Chance point
A representation of an event the outcomes of which are not under control of the decision maker. (○)
Expected net gain from sampling (ENGS)
The difference between the value of sample information and the cost of obtaining it (ENGS = EVSI − SC).
Bayes' rule
A method of revising prior probabilities in light of added information.
P(B|A) = P(B) · P(A|B)
P(A)
Contingency table
A simple tabular method of obtaining revised probabilities.
Expected value of imperfect information (EVII)
The reduction in expected regret or improvement in expected payoff achieved by using imperfect indicators.
Expected value of sample information (EVSI)
The same as EVII, except that the imperfect information is obtained by sampling.
Efficiency of imperfect information
The percentage of the uncertainty (expected regret) removed by an imperfect indicator.
EVII
EVPI
Sampling cost (SC)
The expenses required in obtaining sample information.
Expected value of perfect information (EVPI)
The difference between the expected payoff under prior information and the expected payoff under perfect information (certainty). Equal to the expected regret under prior information.
Optimum sample size (N*)
The sample size for which ENGS is greatest.
Maximum feasible sample size (NMAX)
The sample size for which the value of the sample information equals the cost of sampling and ENGS equals zero.