Supplement to Chapter 5 – Decision Theory

LEARNING OBJECTIVES
After completing this supplement, you should be able to:
1. Describe the different environments under which operations decisions are made.
2. Describe and use techniques that apply to decisions making under uncertainty.
3. Describe and use the expected-value approach.
4. Construct a decisions tree and use it to analyze problem.
5. Compute the expected value of perfect information.
6. Conduct sensitivity analysis on a simple decisions problem.

SUPPLEMENT OUTLINE
Introduction
Causes of Poor Decisions
Decisions Environments
Decisions Making under Certainty
Decisions Making under Uncertainty
Decisions Making under Risk
Decisions Trees
Expected Value of Perfect Information (EVPI)
Sensitivity Analysis
Summary
Key Terms
Solved Problems
Discussion and Review Questions
Problems
Selected Bibliography and Further Reading

INTRODUCTION

Decision Theory represents a general approach to decisions making. It is suitable for a wide range of operations management decisions. Among of them are capacity planning, product and service design, equipment selection, and localization planning. Decisions that lend themselves to a decision theory approach tend to be characterized by these elements:

1. A set of possible future conditions that will have a bearing on the result of the decision.
2. A list of alternatives for the manager to choose from.
3. A known payoff for each alternative under each possible future condition.

To use this approach, a decision maker would employ this process:
1. Identify the possible future conditions (e.g., demand will be low, or high; the competitor will or will not introduce a new product). These are called states of nature.
2. Develop a list of possible alternatives, one of which may be to do nothing.
3. Determine or estimate the payoff associated with each alternative for every possible future condition.
4. If possible, estimate the likelihood of each possible future condition.
5. Evaluate alternatives according to some decision criterion (e.g., maximize expected profit), and select the best alternative.

The information for a decisions is often summarized in a payoff table, which shows the expected payoffs for each alternative under the various possible states of nature. These table are helpful in choosing among alternatives because they facilitate comparison of alternatives. Consider the following payoff table, which illustrates a capacity planning problem.

POSSIBLE FUTURE DEMAND

Alternatives                      Low     Medium   High
Small facility                     $10*    $10          $10
Medium facility                   7          12            12
Large facility                     (4)           2            16
*Present value with millions

The payoffs are shown in the body of the table. In this instance, the payoffs are in terms of present values, which represent equivalent current dollar values of expected future income less costs. This is a convenient measure because it places all alternatives on a comparable basis. If a small facility is built, the payoff will be the same for all three possibles states of nature. For a medium facility, low demand will have a present value of $70 million, where seas both moderate and high demand will have present values of a $12 million. A large facility will have a loss $4 million if demand is low, a present value of $12 million if demand is moderate, and a present value of $16 million if demand is high.

The problem for the decisions maker is to select one of the alternatives, taking the present value into account.
Evaluation of the alternatives differs according to the degree of certainty associated with the possible future conditions.

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