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Decision Analysis

Dr. Richard Jerz

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Goals

• Understand how businesses make decisions• To model business decisions using decision

trees• Understand sensitivity analysis• Learn to use Excel for decision analysis using

decision trees

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Business Decisions

• Businesses are driven by business decisions• Decisions under certainty• Tomorrow will occur• One customer offers a higher bid than another

• Decisions under uncertainty• Product and service configuration• Product pricing• Staffing• Location planning• Facility sizing• How much customer support• Investment decisions

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Causes of Uncertainty

• People’s behavior• Equipment failures• The weather• Politics

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Characteristics of These Decisions

• A set of possible future conditions that will have a bearing on the results of the decision

• A list of alternatives from which to choose• A known payoff for each alternative under

each possible future condition

• Solution: Choose the alternative with the highest “expected value” (EV), or sometimes referred to as “expected monetary value” (EMV)

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Making Good Decisions

• Models• Quantitative approaches• Analysis of trade-offs• Establish priorities

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Models

• A model is an abstraction of reality• Physical• Schematic• Mathematical

• Modeling trade-offs• Cost• Information• Understanding• Flexibility

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“Decision Tree” Models

• Decision trees are a structured tool to help make sequential decisions in the face of uncertainty

• Visual advantage and a calculated results advantage

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Key Characteristics of Decision Trees

• Composed of “nodes”• Decision (square nodes)• Event (circular nodes)

• And branches• Alternatives – branches leaving square nodes• Chance outcomes – branches leaving circular nodes

• “collectively exhaustive” (probabilities add to 1)• “mutually exclusive”

• Each final branch has a numerical value (cost, revenue, etc.)

• Time represented from left to right• Analyze from right to left• Choose the alternative that has the highest EV

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A manager must decide on the size of a video arcade to construct. The manager has narrowed the choices to two: large or small. Information has been collected on payoffs, and a decision tree has been constructed. Analyze the decision tree and determine which initial alternative (build small or build large) should be chosen in order to maximize expected monetary value.

Example – Decision Tree

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Constructing Decision TreesDefine the problem!Based upon logical (sequential) order of events 1. Add decision nodes (start with one)2. Add branches for alternative decisions

and/or event nodes3. Add event nodes4. Add chance outcomes5. Repeat steps 1-4 for all alternatives6. At the end of terminating branches, show

ending values7. Add probabilities to branches emanating

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Solving a Decision Tree

• Start with final branches and evaluate each event node and each decision node• For an event node, compute EV as the weighted

average. Write this EV above the event node• For a decision node, pick the branch with the

highest EV. Write this number above the decision node. Cross out (“prune”) branches not selected

• The decision tree is solved when all nodes have been evaluated

• The EV of the optimal decision is the EV of the starting node of the tree

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Detailed Analysis of Example

• Bill Sampras’ Summer Job Decision

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Decision Node

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Event Node

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More Decision Nodes

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“Recruiting” Event

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Decision Tree Model Complete

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Final Decision Tree Solution

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Sensitivity Analysis

• “What-if” analysis• Determine the range of values for which an

alternative has the best expected payoff• As much an “art” as it is a “science”

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Limitations of Models

• Quantitative information may be emphasized over qualitative

• Models may be incorrectly applied and results misinterpreted

• Nonqualified users may not comprehend the rules on how to use the model

• Use of models does not guarantee good decisions

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