1. Chapter 4R - Decision Analysis
ISDS 2001 - Matt Levy

2. Problem Formulation
Problem Formation is the first step in the Decision Analysis process.
It all starts with a verbal statement of the problem so we can identify
decision alternatives or chance events .
We also need to identify the consequences of each decision
alternative.
The possible outcomes for a chance event is referred to as the state of
nature.
The point of decision analysis is analyze a decision alternative so a
state of nature follows and a predicted consequence can occur.

3. Influence Diagrams
Graphical depiction that shows the relationships between the
decisions, chance events, and consequences for a decision problem.
Rectangles or Squares depict decision nodes.
Circles or Ovals depict chance nodes.
Diamonds depict consequence nodes.
The lines connecting the nodes are called arcs.

4. Influence Diagrams

5. Payoff Tables
Payoff - The decision resulting from a specific combination of a
decision alternative and a state of nature .
A payoff table show the combinations of decision alternatives and
states of nature.

6. Decision Trees
Provides a graphical representation of the decision making process.
Shows the natural or logical progression that will occur over time.
Squares are used to depict decision nodes.
Circles are used to depict chance nodes.
Branches connect the nodes.
Branches leaving each chance node correspond to states of nature.
Payoffs are shown at the end of states of nature branches.

7. Decision Trees

8. Decision Making without Probabilities
Meaning -- does not require the probabilities of the states of nature.
Appropriate when the decision maker has little confidence in the
ability to assess probabilities.
Or when a simple best-case or worst-case scenario is desired.
The decision maker needs to understand the approaches available and
make the most appropriate judgement call.
So how do we do this? There are 3 approaches: Optimistic,
Conservative, and Minmax Regret.

9. Optimistic Approach
Evaluates each alternative in terms of the best payoff.
For example, Maximum profit or if minimization is required it could
be the smallest.

10. Conservative Approach
Evaluates each decision alternative in terms of the worst payoff that
can occur.
The one with the worst payoff is what is recommended.
Basically, we are choosing "the maximum of the minimum"
The book uses an example where monetary profit is involved.
The conservative approach can also be found where the payoff may
be in terms of emissions.
One could read about carbon taxes and cap-and-trade to come up with
some real life examples.

11. Minimax Regret Approach
Neither purely optimistic nor conservative.
Meant to show the opportunity loss, or regret if we choose another alternative besides the one with
the maximum payoff.
In reality, there are many decision factors that may come into play that drive decision analysts
towards alternative decisions.
For example, using the scenario in the book -- selecting to build a large complex with the maximum
payoff may also require the largest up-front investment.
The Minimax-Regret Approach shows the difference between the best alternative and another less
optimal one.
Rij = | Vj - Vij |, where:
Rij = the regret associated with decision alternative di and state of nature sj.
Vj* = the payoff value corresponding to the best decision for the state of nature sj.
Vij = the payoff corresponding to the decision alternative di and state of nature sj.
Note the role of the absolute value. In minimization problems it will be the smallest entry in column j.

12. Decision Making with Probabilities
Many times we are able to obtain the probability assessments for each state of nature.
When they are available, we can use the expected value approach, let:
N = the number of states of nature.
P(sj) = the probability of state of nature sj.
Basically this is the sum of the weighted payoffs for the decision alternatives.
This can be combined with a decision tree to compute the EV at each chance node.

13. End of Chapter 4R
That's all for now!