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Contents
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• Sensitivity in hierarchies
• Sensitivity in networks
• Sensitivity in BOCR complex models
– Sensitivity with respect to the BOCR priorities
– Sensitivity with respect to control criteria
– Sensitivity with respect to judgments

SENSITIVITY IN HIERARCHIES
• Sensitivity in hierarchies requires picking an
independent top node (for example, the goal), a
“with respect to” node in a level below it (for
example, a criterion), varying the values of that
node and seeing how it affects the best outcome
(for example, the alternatives).
• The following shows sensitivity with respect to
the Price criterion for the car hierarchy sample
model from SuperDecisions. Sample models
are under the Help command.

Car Hierarchy Sensitivity
1. Select Computations>Sensitivity to get into sensitivity analysis. Select
Edit to pick your independent variable.

Car Hierarchy Sensitivity (cont’d)
2. The first node in the model, alphabetically, will appear in the Input
Selector dialogue box. Change it to the goal node by selecting it and
pressing Edit to get into the Parameter Selector dialogue box

3. The Edit Parameter dialogue box appears, Fig. 1. Select parameter type 2
(SuperMatrix), Network 0, the wrt Node is the Independent Variable, the Goal, and
the 1st other node is the one we are interested in, Price. Six steps are adequate for
this linear type of sensitivity. Press Done to get back to the Sensitivity Input
selector, Fig. 2, to see your selections. They are correct here. Press Update to
see the graph, next page.

Fig. 1 Fig. 2

4. The dotted line for the priority of the
“what-if” node is initially set to 50%, or
at x = .5. When x = 0, its priority is 0,
at x = 1, its priority is 1. As you change
Its priority the priorities of the other criteria
change proportionately.
The Avalon is the cheap car, the
Babylon the mid-price and the Carryon
the luxury expensive car. The vertical
line here is at the priority Price has in
the model: about 49 %. At this priority
for Price the Avalon gets 31% of the
priority, the Babylon about 26% and
the Carryon about 43%. Grab the cursor
with your mouse and move it to the
right on the x-axis to see that after about
70% the Avalon becomes best choice.
Sensitivity can also be done for the other
criteria in the model: Prestige, etc.

To see the values used to plot the current graph select File>Save
in Sensitivity and save to a .txt file. Start Excel, select
File>Open and enter the name you gave the .txt file. The Data
Import Wizard will appear. Keep clicking Next to import the
data. Below are the values for the Price graph with 6 steps.
The more steps you have, the closer you can get to the Price
value that corresponds to the synthesized results.
Input Value Matrix: Goal 1Price Avalon Babylon Carryon

0 1.00E-04 2.14E-01 1.79E-01 6.07E-01

0.2 2.00E-01 2.53E-01 2.11E-01 5.36E-01

0.4 4.00E-01 2.91E-01 2.43E-01 4.66E-01

0.6 6.00E-01 3.30E-01 2.75E-01 3.95E-01

0.8 8.00E-01 3.68E-01 3.07E-01 3.25E-01

1 1.00E+00 4.07E-01 3.39E-01 2.54E-01

Sensitivity in a simple network
• This section is under construction….

Sensitivity in a Complex Model
By a complex model we mean a BOCR model that
has a top level network containing the BOCR
nodes, control criteria hierarchies in the
subnets attached to the BOCR and decision
subnets attached to the selected control
criteria. Sensitivity can be done 3 ways, with
respect to:
1. Priorities of the BOCR nodes
2. Priorities of the Control Criteria nodes
3. Judgments in the pairwise comparison matrices

Doing Sensitivity for BOCR nodes
• In a complex BOCR model, one can examine what effect
changing the priority of a merit node, for example,
Benefits, does to the ranks and synthesized priorities of
the alternatives. To see the priorities of the BOCR go to
Assess>Ratings and turn on the View>Priorities
command in Ratings. These are the b, o, c and r
priorities for Benefits, Opportunities, Costs and Risks,
used in the formula to combine the B, O, C, and R
synthesized vectors that are being passed up from the
control criteria subnets. The Raw values are passed up
to be used in the formula. The Additive (negative)
formula is bB + oO – cC – rR,
the Multiplicative formula is (bB × oO)/(cC × rR)

Bush in Baghdad Model
• Load the NMD model for sensitivity.mod from the Sample models in SuperDecisions.
Select the Design>Standard Formula command which shows the selected formula is
Additive (negative). There are some issues with the numbers being displayed in the
Sensitivity module, but the general trend of the graph is correct. We are working on
these issues as of Sept. 2006 and hope to have them resolved soon.

Bush in Baghdad Model
• Synthesized results with Additive (probabilistic) formula shown in Fig. 1.
The priorities of Benefits, Opportunities, Costs and Risks are shown from
the Ratings spreadshee in Fig. 2 (select Assess>Ratings in the main model
to get into the Ratings Module and turn on View>Priorities to see Priorities.

Fig. 1. Synthesized Results

Fig. 2. B, O, C, and R Priorities

Sensitivity for Costs node
• Select Computations>Sensitivity
from the main menu in the top level
network. You must change the
Independent variable from the alphabet-
Ically first node, Economic, to the one you
want: Costs, when the Sensitivity
Analysis window opens. Select
Edit>Independent Variable to get
to the Sensitivity Input selector
dialogue box shown on the next slide.

Sensitivity for Costs node (cont’d)
The Sensitivity input selector dialogue box appears as shown in Fig. 1.
Click on the node that is initially shown there and select either
the New or Edit command which brings up the Edit Parameter dialogue
box shown in Fig. 2 where you can change the node to Benefits.

Fig. 1 Fig. 2

• Set up the parameters as shown in Fig. 1 with Parameter Type: 0 (for
Priorities); Network: 0 (for top-level network - click the empty space at the
bottom of drop-down list to make it 0 if it is not that way); Wrt Node: Costs
(select Costs from drop down list). The number of steps is okay at 6, but you
may make it more if you wish – say 10 or 20. Click the Done button to return to
the Input selector dialogue box as shown in Fig. 2. Click the Update button to
get the sensitivity graph for Costs shown on next slide.

Fig. 1 - Select parameter type 0, Fig. 2 – Click Update for graph
Network 0, Costs, Done

• The priorities of the
alternatives are read from the
projection on the y-axis of the
point at which the alternative
line intersects the vertical
dotted line. The priority for
Risks ranges from 0 to 1.0 on
the x-axis. Move the dotted
line by clicking on it and
dragging. The vertical line is
always shown initially at .5 on
the x-axis, or at 50% priority.

• The best option is Deploy
NMD for Risks between about
.19 and .04. Between 0.4 and
0.55 R&D is best.

• After Risks has a priority of
more than about 0.55 the
Terminate option is best.

• The same process can be repeated for
Benefits, Opportunities and Costs.
• Select Edit>Save and save the data points
that produced the graph to a .txt file.
Open it in Excel. Keep clicking Next in the
text import Wizard to get the values shown
on next slide.

Table of values leading to the graph on previous page.
Selecting more steps on the edit parameter dialogue box will
give more data points.
3 Work with UN to
ensure
1 Pre-emptive Attack 2 Attack Iraq only with Allied Weapons
Input Value Priority: Costs on Iraq Help Inspections

0 1.00E-04 2.39E-01 2.73E-01 3.65E-01

0.2 2.00E-01 1.77E-01 2.72E-01 3.67E-01

0.4 4.00E-01 1.24E-01 2.71E-01 3.68E-01

0.6 6.00E-01 7.70E-02 2.71E-01 3.69E-01

0.8 8.00E-01 3.62E-02 2.70E-01 3.70E-01

1 1.00E+00 1.70E-05 2.70E-01 3.71E-01

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