Operations Research Models and Methods / Computation / Decision Analysis

Model Dialog

Constructing the Model

 

To begin the model construction process, select New Problem from the OR_MM menu. The dialog shown below is presented to accept the data for the model. In the following we describe the components of the dialog.

Some of the options on the dialog can be changed with the Change Structure button that will be described later.

 

Control Buttons

The buttons at the upper right open and close the dialog and provide default values for the settings. When the model is complete, press the OK button to build the model worksheet. The Cancel button closes the dialog without effect. The Default button fills the fields and sets the buttons for a 20 node model

Name

 

The name should be representative of the situation under consideration. It should be a single word with no punctuation and start with a letter. A number of named ranges are created on the worksheet, so the name must obey the range naming restrictions of Excel. The program automatically creates names with the prefix DEC. The automatic name can be changed.

Objective

The objective of the decision process is to maximize or minimize the expected value of some criterion represented by the values on the decision tree. The option is set with these buttons.

Tree

 

 

This checkbox indicates whether the decision network is a tree or a more general network structure. The computational procedures assume that the decision process describes a directed network with no cycles, but it does not require that process take the form of a tree. It is often true that the size of the model can be considerably reduced by using a non-tree structure. An example is presented later.

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.

Random

When this box is checked, the program builds the model with randomly generated data. The random generation procedure produces valid decision tree models with at most two arcs leaving each node. This option is useful to create large sample models without data entry.

Numbers of Nodes and Arcs

These are the size parameters of the tree. They can be easily changed as the model is constructed. For the example, we enter the known values for the Repair model.

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.

Value Measure
The model will maximize or minimize some quantitative measure, perhaps to maximize profit or minimize cost. It is useful to enter the name of the measure here. The text is used as part of the names of some of the columns on the worksheet display.
Model Options

These checkboxes determine which columns are included in the arc and node displays of the worksheet. Since the example has test costs that are conveniently represented on the arcs we have checked the Arc Values box. The terminal nodes also have costs, so we have checked the Node Values box. With this option, all nodes can be assigned costs, however, when the button labeled Values only on Terminal Nodes is checked, the solution process only considers the values on the terminal nodes.

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.

Utility Functions

Decision makers sometimes do not make decisions strictly on the basis of the expected value of outcomes governed by probability. Rather risk plays a role in judging alternatives. Decision analysis handles this by using utility functions to transform an objective measure so that it represents the risk in a situation. The program allows several standard utility function. We discuss this in a later section.

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.

Solver Options

The model is solved by a process that begins at the terminal nodes and works backwards until all chance and decision nodes have been evaluated. The solution specifies the optimum decision at each decision node. The program allows two procedures for performing the solution process: functions and algorithm.

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.

Graphic Options

The model structure and data are held in lists of nodes and arcs that are placed on a worksheet. It is often useful, however, to see a graphical representation of the model. A button is placed on the data worksheet that when clicked builds a graphical representation on a second worksheet. The material placed on the graph depends on the buttons checked in the model dialog. The graph for the example is shown below.

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.

 


Data Worksheet


Updated 5/30/2001
Operations Research Models and Methods

by Paul A. Jensen and Jon Bard, University of Texas, Copyright by the Authors