Logistics Decision Analysis Methods

Analytic Hierarchy ProcessExpertChoice 2000

Presented by Tsan-hwan Lin

E-mail: percy@ccms.nkfust.edu.tw

Running AHP Process Create a new file Construct the hierarchy Set priorities

Examine and improve consistency

Synthesis Sensitivity analysis

Q & A

Creating a File and Goal Description

To create a new file Select File, New. Type a file name for your model. Select a drive/path

designation, if necessary. Then press Enter. Type the goal description and press Enter.

An alternative way to create a new file is to click on the new file icon .

Note: Expert Choice creates a model with only one node (the goal) and displays it in the ModelView's TreeView.

Adding the Objectives and Sub-objectives - 1 To add an objective

Select the Goal node. Select Edit, Insert Child of Current Node. Type a descriptive objective and press Enter. When the new node appears, type the next objective and press

Enter; or press Esc to stop inserting. An alternative way to add objective: right-click on the Goal node and

continue as described above. Tip: Try to keep the number of nodes under each parent under nine. Note: When you add objectives below the goal, the circle next to the

goal will change from black to yellow indicating that other elements are below it. If a red dot appears in either colored circle this means judgments must be made.

Adding the Objectives and Sub-objectives - 2 To add sub-objectives below an Objective

Select an objective that will have sub-objectives entered beneath it.

Select Edit, Insert Child of Current Node and continue as described above.

To add an objective to an existing model Select a node (an objective). To enter a node on the same level, select Edit, Insert

Sibling of the Current Node, or To enter a node beneath the selected node, Edit, Insert

Child of Current Node.

Adding Alternatives

Alternatives can be added to the model from the ModelView using the Alternatives pane.

Select Edit, Alternative, and then select Insert. Alternatively right-click in the Alternative pane and then select

Insert or just simply click the Alternative button.

Type an alternative. Note: Alternatives added from the ModelView are

known as active alternatives.

ModelView Overview When you start Expert Choice the first window that appears is

a blank ModelView. The ModelView is divided into three major sections or panes.

The TreeView (the left pane) displays the hierarchy. By default, nodes with children (objectives) are displayed next to yellow circles ,

and nodes with no children (covering objectives) are displayed next to black circles . If a node has children that have not been assessed, a red dot will appear in the center of the circle . When all objectives in the TreeView have been assessed, the circles are replaced by squares that graphically display the priority of each factor.

The Alternatives pane (top-right) shows the active alternatives. The lower-right pane displays the Information Document for the

current (selected) node. Note: The appearance of the ModelView can be altered; to do

this use the View menu commands.

Making Paired Comparisons - 1 Pairwise comparisons are made from the ModelView in one

of the following ways: From the ModelView, select Assessment, Pairwise. One of the three

pairwise comparison windows (Numerical , Verbal , or Graphical) will be displayed (Verbal is the default).

To select another window, click one of the tabs: Numerical , Verbal , or Graphical .

Note: If some comparisons have been previously made then the Assessment tabs will be displayed in the ModelView.

The comparison matrix is displayed in the lower pane. The numerical representations of the verbal judgments are displayed here as numbers from 1 to 9. If the row element (on the left) is preferred, then the judgment is displayed in black. If the column element is preferred, then the judgment is "inverted" and displayed in red. When enough judgments have been made to calculate priorities, they will also be displayed as bar graphs (also, the tab )that overlay the row elements.

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3:1

Direct Entry of Priorities You can directly assign priorities without having to make

paired comparisons. This method is not recommended because it is not as accurate or

justifiable. To directly assign weights

Click on any of the three pairwise comparison tabs. Select Assessment, Direct. Enter a value between zero and one for each objective, or drag a bar

using the column to the right of “Value”. When done press Esc. When asked to Record Judgments, select Yes. Tip: Assume the length of the bars represent a factor's importance

relative to the others. For example, if the bar for Price is twice as long as the bar for Quality, then Price is considered twice as important. If the lengths of the bars are equal, then the factors are of equal importance.

Examining Inconsistency The Inconsistency menu, available from any of the pairwise

assessment windows, provides a convenient way to locate any inconsistencies among a set of pairwise judgments.

The Inconsistency Ratio is located in the lowest left-hand cell of the first column of the matrix.

A ratio of 0.10 or less is considered acceptable. To view the most inconsistent judgment

From any comparison mode, select the Inconsistency From the pull-down list, select 1st

Selecting 1st moves the cursor to the most inconsistent judgment in the set of judgments being compared; selecting 2nd moves to the second most inconsistent judgment and so on.

Improving Inconsistency To lower the Inconsistency Ratio for a set of judgments you can either:

(1) From the 1st most inconsistent judgment (and so on) you can change the judgment by making a new paired comparison, or

(2) Select Inconsistency and then select Best Fit. Alternatively, right-click on any cell in the matrix to see that cell’s best fit.

Best Fit (displayed above the first factor row in the matrix) shows the judgment for the current cell that would best improve your consistency. If the Best fit is displayed in red then the judgment suggested when entered must be inverted, making the column element preferred to the row element.

Note: If the comparison window is either Verbal or Graphical, then the Best Fit shown is a numerical representation of either the Verbal or Graphical judgment.

Tip: Do not enter the suggested Best Fit judgment unless you believe it to be true. Enter only a judgment that represents your best understanding and knowledge.

After changing a judgment the new Inconsistency Ratio will be displayed. There is one exception, if you deferred automatic calculation of the priorities by

using the Tools, Options, Calculations command, you must click the Calculate Icon or the new inconsistency will not be displayed.

Synthesis Overview Synthesis is the process of weighting and combining priorities throughout

the model after judgments are made to yield the final result. Global priorities are obtained for nodes throughout the model by applying

each node's local priority and its parent's global priority. The global priorities for each alternative are then summed to yield overall or synthesized priorities. The most preferred alternative is the one with the highest priority.

Your answer is presented in the form of a bar graph of the overall priorities of the alternatives. Your best choice is the alternative with the longest bar. See: Synthesize Menu Commands.

You can select either the Ideal or the Distributive mode to synthesize your model. This will not change the model in any way, and you can switch back and forth between the two nodes. In general, the priorities from either mode are within a few percentage points of each other.

After the synthesis is performed and you have your answer you may wish to do sensitivity analyses to determine how sensitive the results are to changes in the priorities of the objectives.

Synthesize How to synthesize

From the ModelView's TreeView, select either the Goal Node or an objective.

From the menu select Synthesize. There are two menus in Synthesize Window

File prints what is shown in the window. Edit has 2 commands:

Copy to clipboard - once the information is on the clipboard, you can paste the contents to Microsoft's Excel or Word. (If you use Word, use the tab function to align the columns.)

Create an Excel Pivot Table - this feature invokes Excel to view what was created.

There are two tabs in Synthesize Window The Summary tab shows bar graphs of the global priorities for the

alternatives. The Details tab shows the priorities for each alternative with respect to each

lowest level objective. The Details can be displayed with or without totals.

Local vs. Global Priorities The local priority represents the percentage of the parent node's

priority that is inherited by the child. The local priorities of the children of a node also sum to one.

The priority of each node relative to the Goal is called the global priority. The global priorities of a node represent the portion of the parent's priority inherited by the child. The global priorities of all the children equal the parent's global priority. The global priority of a child equals the local priority of the child times the global priority of the parent.

Ideal vs. Distributive Mode Use the Ideal mode when you are concerned with choosing

only one alternative (the best) and the other alternatives will no longer matter.

The Ideal mode assigns the full weight of each covering objective to the alternative that ranks highest under it. The other alternatives receive a weight in proportion to the highest alternative per covering objective. The weights/priorities for all the alternatives are summed to display the best alternative.

Use the Distributive mode when all alternatives matter. The Distributive mode distributes the weights of the objectives among

the alternatives; thereby dividing the full objectives' weights into proportions relative to the percentage of preference of each of the alternatives.

Sensitivity Analysis Overview The purpose of sensitivity analyses is to graphically see how

the alternatives change with respect to the importance of the objectives or sub-objectives.

Each sensitivity analysis can be performed from the Goal or from a selected objective or sub-objective.

In all cases, there must be at least two levels below the selected node. These levels can be comprised of at least one level of objectives and alternatives or two levels of only objectives.

Conduct Sensitivity Analysis How to conduct sensitivity analysis:

From the ModelView's TreeView, click on either the Goal node or an objective.

Select Sensitivity-Graphs. Select one of the options.

If you are at the Goal, you will see how sensitive the alternatives are to change with respect to the first level objectives.

If you are not at the Goal node, you will be asked: "Sensitivity with respect to Current Node or Goal?"

If you select Yes, then the priorities of the alternatives are with respect to the current node. It is as if the other portions of the model did not exist.

If you select No, then the priorities of the alternatives are with respect to the goal (the entire model). With this option, you see the variability of the alternatives with respect to the current node.

There are five types of analyses.

Sensitivity Analysis - Performance Performance sensitivity

The Performance graph displays how the alternatives perform with respect to all objectives as well as overall.

It can be accessed from the ModelView's menu by selecting Sensitivity-Graphs and then selecting Performance.

Use the "left y-axis" to read each objective's priority. Use the "right y-axis" to read the alternative priorities with respect to each objective.

The Performance graph is also dynamic, so you can temporarily alter the relationship between the alternatives and their objectives by dragging the objective bars up or down.

Note: The lines connecting the alternatives from one objective to another have no meaning; they are included to help you find where a particular alternative lies as you move from one objective to another.

Sensitivity Analysis - Dynamic Dynamic Sensitivity analysis is used to dynamically change the

priorities of the objectives to determine how these changes affect the priorities of the alternative choices.

It can be accessed from the ModelView's menu by selecting Sensitivity-Graphs and then selecting Dynamic.

By dragging the objective's priorities back and forth in the left column, the priorities of the alternatives will change in the right column. If you think an objective might be more or less important than originally indicated, drag that objective's bar to the right or left to increase or decrease the objective's priority and see the impact on alternatives.

For example, as the priority of one objective increases (by dragging the bar to the right), the priorities of the remaining objectives decrease in proportion to their original priorities, and the priorities of the alternatives are recalculated.

Sensitivity Analysis - Gradient This graph shows the alternatives' priorities with respect to one

objective at a time. It can be accessed from the ModelView's menu by selecting

Sensitivity-Graphs and then selecting Gradient. The vertical red line represents the priority of the selected objective

and is read from the X-Axis intersection. The priorities for the alternatives are read from the Y-Axis; it is determined by the intersection of the alternative's line with the objective's (vertical) priority line.

To change an objective's priority, drag the red bar to either the left or right; then a blue bar showing the new objective's priority will be displayed.

The Gradient Sensitivity shows "key tradeoffs" when two or more alternatives intersect each other. This is even more important if the intersection is close to the objectives priority.

Sensitivity Analysis - Head to Head It shows how two alternatives compare to one another against the objectives

in a decision. It can be accessed from the ModelView's menu by selecting Sensitivity-Graphs

and then selecting Head to Head. One alternative is listed on the left side of the graph and the other is listed on

the right. The alternative on the left is fixed, while selecting a different tab on the graph can vary the alternative on the right. Down the middle of the graph are listed the objectives in the decision. If the left-hand alternative is preferred to the right-hand alternative with respect to an objective, a horizontal bar is displayed towards the left. If the right-hand alternative is better, the horizontal bar will be on the right. If the two choices are equal, no bar is displayed. The overall result is displayed at the bottom of the graph and shows the overall percentage that one alternative is better than the other; this is the composite difference. The overall priority can either be shown based on the objective weights (typical) or un-weighted.

Sensitivity Analysis – Two Dimensional This sensitivity graph shows how well the alternatives perform

with respect to any two objectives. It can be accessed from the ModelView's menu by selecting

Sensitivity-Graphs and then selecting 2-D. One objective is represented on the X Axis and another on the Y Axis.

The circles represent the alternatives. The area of the 2D plot is divided into quadrants. The most favorable alternatives as defined by the objectives and judgments in your model will be shown in the upper right quadrant (the closer to the upper right hand corner the better) while, conversely, the least favorable alternatives will be shown in the lower left quadrant. Alternatives located in the upper left and lower right quadrants indicate key tradeoffs where there is conflict between the two objectives.

Editing Nodes - 1 To rename nodes in the ModelView's TreeView

Select an objective in the TreeView to be renamed. Select Edit, Edit Node. Type the new name and press Enter.

To delete a node and all of its descendants in the TreeView Select the node in the TreeView to be deleted. Select Edit, Delete Node or press the Delete key.

To move a node Click and drag the node to be moved onto the destination node. The node

will become the first child under the destination node. To copy a node

Press the Shift key, then press and drag the node to the copy location, as you do this, a notepad will be displayed.

Editing Nodes - 2 Display the nodes in alphabetical order

Select the parent of the cluster and then select Edit, Sort Cluster.

Making a Factor Dormant from the Pairwise Comparison Matrix

When a factor (objective, sub-objective or alternative) is made dormant it is excluded from the pairwise comparison process.

From any pairwise comparison window: Press Ctrl and click a factor name (objective or alternative located in

the rows of the matrix). The factor row selected will be blocked. In addition, any comparison

made (or to be made) relating to that factor in the matrix will also be blocked.

By blocked we mean the paired comparison(s) to be made or previously made will not be included in the prioritization process.

To reactivate a factor Press Ctrl and click a factor name.