The Repair example does have a tree structure, so the box is checked. For the tree structure it is only necessary to specify the number of nodes. The number of arcs is always one less.

The minimum sized tree has three nodes and two arcs. It is often convenient to begin with this minimal tree and add related nodes and arcs in a sequential manner.

Node and arc costs are accumulated by the solution process when the process goes through the associated nodes and arcs. For example, the cost of test X is only expended if the decision is to do the test. Alternatively, the cost of replacing the motherboard associated with node 2 is expended if the test is not made. Any solution objective will include only one of these two values.

It is always possible to represent all objective values only on the terminal nodes. Every terminal node identifies a unique path through the decision tree, so all values along this path can be accumulated and assigned as the value for the terminal node. For example the cost for node 11 can be computed as the costs of tests X and Y plus the cost of repairing component A, a total of 220. If this is done, the Arc Values option should be left blank and the Values only on Terminal Nodes should be checked. This option usually requires a good deal of extra computation, so we have decided to specify arc values for the example.

The Arc Parameter and Node Parameter boxes are strictly for convenience. For some models, arc and node values and arc probabilities are computed with Excel functions that have parameters. When these boxes are checked, columns are provided to hold the parameters.

When utility functions are used, the model must be specified as a maximization and objective values are allowed only on the terminal nodes. The program associated with the dialog box enforces these restrictions.

The Function option uses Excel functions provided by the add-in to evaluate the decision nodes. The solution is determined automatically by the program. This is often useful for sensitivity analysis. A change is immediately reflected in objective values and decisions.

The Algorithm option is called by clicking a button on the worksheet. The solution is only obtained when the button is clicked. This option is usually better during the construction process of the model.

The graph identifies the three types of nodes by color, beige for decision, blue for chance and gray for terminal. Within the decision node, we see the name, node value, optimum value and optimum decision. Within the chance node we see the name, node value, and expected value. A terminal node only shows the name and node value. When the Include Titles button is checked, titles appear to the left of the numerical values. This makes the graphic larger, so we have not chosen this option for the example.

The arcs connecting the nodes are show on the figure with arrowheads indicating direction. The numbers above the lines are the arc values, while the numbers below the lines are arc probabilities. The optimum decisions are shown with the red arcs. For a tree network, all the arcs appear on the graphic, but for more general network structures, some arcs may crossover the nodes. In this case it may be better to leave the Show all links button unchecked.

With the Autoplace button checked, the program selects the relative locations of the nodes on the graphic. These are controlled by the Level and Depth columns of the node display. The Level of a node indicates the placement of the node from left to right. For example, node D1 is at level 0, while node A is at level 4. The Depth of a node indicates the placement of the node from top to bottom. For example D1 is at depth 0, while the node labeled A, B, E is at depth 5. The program does a pretty good job of placement, however, the user might want to control the placement manually by specifying the depth and level for each node.