1. Decision Analysis Your Logo Here Jane Hagstrom University of Illinois Jane Hagstrom University of Illinois

2. 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.

3. 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

4. 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

5. 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.

6. Organizing Our Thinking about Hard Decisions 1. Problem context 2. Fundamental and means objectives (How will we evaluate our decision?) 3. Alternatives 4. Problem structure 5. Assessments of chance, utilities/values 6. Decision analysis algorithm gives “optimal” policy 7. Sensitivity analysis produces requisite model

7. 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

8. 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.

9. 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

10. 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?

11. 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

12. 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

13. 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

14. Creating a Good Problem Structure Identifying objectives Determining how low-level fundamental objectives should be measured Identifying alternatives Influence diagram Time sequence of events

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

16. 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.

17. Sensitivity Analysis Any approach should be used iteratively Try different values Tornado diagram Rainbow diagram Risk profiles

18. 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

19. 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

20. 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.

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

22. 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.

23. 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

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

25. Or … Go forth and make good decisions! …Congratulations to all our graduates!