DTree analyzes decision trees and determines the optimal set of decisions based on expected values.A decision tree consists of a set of (a) decision nodes with decision branches or arcs, (b) chance event nodes with event branches, and (c) payoffs to be received from a series of decisions and events.
Example. An engineering manager must decide whether to build a one- or two-story facility. The payoff from each choice depends on whether demand is high or low, and the P(high) = .8 and P(low) = .2. The tree can be depicted as follows, with the decision nodes and arcs/branches in blue, the event nodes and arcs in red, and the payoffs in green.
![dtree1 dtree1](../assets/images/autogen/a_dtree1.gif)
By adding nodes for each payoff and numbering the nodes, starting with 1, the decision tree input to DTree is as follows.
![dtree2 dtree2](../assets/images/autogen/a_dtree2.gif)
Model Input Requirements
DTree input consists of a list of arcs from this expanded tree, one arc or branch per line, plus one line for each payoff, as follows:
Decision branch or arc: D fromnode tonode arcid description Event branch or arc: E fromnode tonode probability arcid description Payoff: P node payoff
where
- fromnode: number of node where arc begins
- tonode: number of node where arc ends (arrowhead points to)
- arcid: 4-character identifier for this arc
- description: (optional) longer description of the branch or arc
- probability: likelihood of this event happening
- payoff: payoff received if this node is reached
Limits: program is limited to 99 nodes (decision nodes, chance event nodes, payoffs) and 98 arcs.
DTree Output
DTree analyzes the problem and gives the following:
- Branch report, listing each decision or event arc and its characteristics
- Decision tree diagram, showing decision nodes in square brackets, chance event nodes in parentheses, and payoff nodes in curly brackets. Non-optimal decision branches are indicated with an x.
- Node Summary Report, for the evaluated and optimized tree, each node and its payoff or expected payoff value if the optimal strategy is followed
- Optimal strategy: the decision(s) to follow to maximize expected payoff.
DTree input data for above example:
D 1 2 Bld1 Build one-story D 1 3 Bld2 Build two-story E 2 4 .5 HiDm High demand E 2 5 .5 LoDm Low demand E 3 6 .5 HiDm High demand E 3 7 .5 LoDm Low demand P 4 100 P 5 10 P 6 300 P 7 -50
Other example problem data:
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