Decision Analysis

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Jane HagstromUniversity of Illinois

Jane HagstromUniversity of Illinois

What is Decision Analysis? In the broadest sense, an organized

approach to solving a decision problem.

In the narrow sense, a method of formulating a decision problem in terms of decision trees.

Where Is Decision Analysis Used? Cost/benefit/risk analysis of capital

investments Cost/benefit/risk analysis of new

product introduction Cost/benefit/risk analysis of power

plant operation Cost/benefit/risk analysis of medical

procedures

When Should We Use Decision Analysis? When we’re not sure of our objective When we’re not sure what factors

should influence our decision When we’re uncertain about the

values of factors affecting our objective

When method of determining a good decision is not obvious

Why Should We Use Decision Analysis? Organizes our thinking about hard

decisions Allows us to model major factors that

might affect our decision Output gives us a good

(optimal/reasonable) decision policy Allows us to perform sensitivity analysis

on all components of our model.

Organizing Our Thinking about Hard Decisions1. Problem context2. Fundamental and means objectives (How

will we evaluate our decision?)3. Alternatives4. Problem structure5. Assessments of chance, utilities/values6. Decision analysis algorithm gives

“optimal” policy7. Sensitivity analysis produces requisite

model

Modeling Factors that Affect Our Decision Low-level fundamental objectives provide

value objectives for an influence diagram Means objectives and problem context

suggest decisions that should be made Problem context and objectives suggest

values (risky and known) that will affect objective values

Sensitivity analysis allows us to arrive at a requisite model

Optimal Policy Mathematical formulation allows the

computation of an optimal policy. A requisite model with good numerical

quantities produces a truly optimal policy. In the absence of good numerical

quantities, the computation of an “optimal” policy either provides a good policy or provokes us to think about what aspects of our model are not satisfactory.

•Sensitivity Analysis Helps Us Understand the Problem Context Allows us to start with a simple model and

then helps us develop a requisite model Identifies values which might vary enough

to affect the goodness of our decision Allows a decision-maker to identify the

important factors to consider in making the decision

Sensitivity Analysis Tells Us What Information Is Important Should we consider the possibility of

deciding to change the value of a controllable quantity?

Should we gather more information about uncontrollable quantities?

Should we assess probabilities for the values of uncontrollable quantities?

Should we assess utility for the objective?

Sensitivity Analysis Helps Us Choose Our Analysis Method Simple requisite model allows use of

decision analysis Need for many chance events suggests

use of Monte Carlo simulation or special computations of queuing model values

Advantage in having large number of decision events suggests use of linear, nonlinear, or integer optimization

Limitations in Using Decision Analysis Methodology

Difficult to create large model Only handles small number of alternatives

for one decision event Only handles small number of states for

one chance event Computation time requirements grow

large as the number of events grow large Even utility may not completely model

decision-maker’s attitude toward risk

Important Skills in Decision Analysis Creating a Good Problem Structure Associating Values and Probabilities

with Events Interpreting a Policy Tree Interpreting Sensitivity Analysis Creating a Requisite Model Computing Value of Information

Creating a Good Problem Structure Identifying objectives Determining how low-level

fundamental objectives should be measured

Identifying alternatives Influence diagram Time sequence of events

Associating Values and Probabilities with Events Gathering information Assessing probabilities Assessing utilities

Interpreting a Policy Tree Intermediate values and probabilities are

conditioned on the events higher up/to the left in the tree.

Policy recommendation is based on maximizing expected utility/monetary value/..

Optimal policy may include recommendation as to what to do based on which outcome of some chance event occurs.

Sensitivity Analysis Any approach should be used

iteratively Try different values Tornado diagram Rainbow diagram Risk profiles

Tornado Diagram Shows a comparison of how the

policy and objective value varies when each of several input values in the model is changed

Is used to identify the most important events affecting the decision policy and objective value

Rainbow Diagram Shows how the policy and objective

value vary as a single input value is varied.

Identifies importance of gathering more information and/or suggests an appropriate approach to modeling the value using a chance or decision event

Risk Profiles Give a more accurate picture of how

risky a policy is Allow comparison of the riskiness of

different policies Allow elimination of a policy from

consideration when it is stochastically dominated by some other policy.

Creating a Requisite Model Start with a simple model Use sensitivity analysis to refine it

If You’re Going to Be a Decision-Maker ... Keep the Clemen book and the software Use the early chapters in Clemen to help

you organize your thinking about the decision

Unless the decision policy is obvious, use the software to do a rough analysis

Either continue to use the software until you feel you can make a good decision, or at some point switch to some other method of analysis.

If You’re Going to Assist in Making a Decision … Same as if you’re the decision-maker,

plus Create a good prototype model and solve

it Be prepared with sensitivity reports as

well as a policy recommendation If more decision analysis seems

appropriate, keep improving the model Use all of Clemen to help you assess

probabilities and utilities

What next? Simulation Utility Theory Algebraic Methods of Optimization Bayesian Statistics Stochastic Models Group Decision-Making

Or … Go forth and make good decisions!

…Congratulations to all our graduates!