Logistics Decision Analysis Methods

1
Logistics Decision Analysis Methods

• Analytic Hierarchy Process
• ExpertChoice 2000
• Presented by Tsan-hwan Lin
• E-mail percy_at_ccms.nkfust.edu.tw

2
Running AHP Process

• Create a new file
• Construct the hierarchy
• Set priorities
• Examine and improve consistency
• Synthesis
• Sensitivity analysis

3
Q A
4
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.

5
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.

6
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.

7
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.

8
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.

9
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.

10
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.

11
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.

12
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 cells 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.

13
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.

14
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.

15
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.

16
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.

17
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.

18
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.

19
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.

20
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.

21
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.

22
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.

23
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.

24
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.

25
Editing Nodes - 2

• Display the nodes in alphabetical order
• Select the parent of the cluster and then select
  Edit, Sort Cluster.

26
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.