Operations
Management
Decision Theory Course
Notes Operations
Management
Decision Theory
Charles E. Oyibo
Decision theory represent a general approach to decision making and is suitable for a wide range of operations management decisions including capacity planning, product and service design, equipment selection, and location planning. Decisions that lend themselves to decision theory approach tend to be characterized by these elements:
To use this approach, a decision maker would employ this process:
The information for a decision is often summarized in a payoff table, which shows the expected payoffs for each alternative under various possible states of nature.
POSSIBLE FUTURE DEMAND |
|||
|---|---|---|---|
| Alternatives | Low |
Moderate |
High |
| Small Facility | $10* |
$10 |
$10 |
| Medium Facility | 7 |
12 |
12 |
| Large Facility | (4) |
2 |
16 |
*Present Value in $ Millions
The payoffs are shown in the body of the table in terms of present values, which represent current dollar values of expected future income less costs.
Bounded Rationality: The limits imposed on decision making by costs, human abilities, time, technology, and the availability of information. Because of these limitations, mangers cannot always expect to reach decisions that are optimal in the sense of providing the best possible outcome (e.g. highest profit, least cost). Instead they must often resort to achieving a satisfactory satisfactory decision.
Suboptimization: The result of different departments each attempting to reach a solution that is optimum for that department. This is a limitation to making globally optimal decisions as what is optimal for one department may not be optimal for the organization as a whole.
Operation management decision environments are classified according to the degree of certainty present:
The importance of these different decision environments is that they required different analysis techniques.
When it is known which of the possible future conditions will actually happen, the decision is usually relatively straightfoward: Simply choose the alternative that has the best payoff under that state of nature.
At the opposite extreme is complete uncertainty: no information is available on how likely the various states of nature are. Under those conditions, four possible decision criteria are maximin, maximax, Laplace, and minimax regret.
Maximin--Determine the worst possible payoff for each alternative, and choose the alternative that has the "best worst." The maximin approach is essentially a pessimistic one because it takes into account only the worst possible outcome for each alternative. The actual outcome may not be as bad as that, but the approach establishes a "guaranteed minimum."
Maximax--Determine the best possible payoff, and choose the alternative with that payoff. The maximax approach is an optimistic, "go for it" strategy; it does not take into account any payoff other than the best.
Laplace--Determine the average payoff for each alternative, and choose the alternative with the best average. This approach treats each state of nature as equally likely.
Maximum regret--Determine the worst regret for each alternative, and choose the alternative with the "best worst." This approach seeks to minimize the difference between the payoff that is realized and the best payoff of each state of nature.
Between the two extremes of certainty and uncertainty lies the case of risk: the probability of occurrence for each state of nature is known.
Because the state are mutually exclusive and collectively exhaustive, these probabilities must ass to 1.00.
The EMV is the best expected value amonng the alternatives. The expected value is the sum of the payoffs for an alternative where each payoff is weighted by the probablity for the relevant state of nature. Hence, the approach is:
EMV criterion -- Determine the expected payoff of each alternative, and choose the alternative that has the best expected payoff of each alternative.
The EMV approach is most appropriate when the decision maker is "risk neutral" (i.e. neither risk averse nor risk seeking).
A decision tree is a schematic representation of the alternatives available to a decision maker and their possible consequences. Though tree diagrams can be used in place of payoff tables, they are particularly useful for analyzing situations that involve sequential decisions.
A decision tree is composed of a number of nodes and branches emanating from them. Square nodes denote decision points, and circular node denote chance events.
Decision trees are drawn from left to right, but analyzed from right to left: for the last decision that was made, choose the alternative that will yield the greatest return (or the lowest cost). If chance events follow a decision, choose the alternative that has the highest expected monetary value (or lowest expected cost).
EVPI is the difference between the expected payoff with perfect information and the expected payoff under risk.
There are two ways to determine EVPI:
Way 1: Compute the expected payoff under certaintyand subtract the expected payoff under risk:
EVPI = Expected payoff under certainty - Expected payoff under risk
To compute the expected payoff under certainty:
The EVPI indicates the upper limit on the amount the decision maker should be willing to spend to obtain perfect information.
Way 2: Use the regret table to compute EVPI. To do this, find the expected regret for each alternative. The minimum expected regret is equal to the EVPI.
Sensitivity Analysis provides a range of probability over which the choice of alternatives would remain the same. It involves determining the range of probability for which an alternative has the best expected payoff.
Page Last Updated: Sunday December 5, 2004 6:15 PM