Sensitivity in SuperDecisions

Contents(to make hyperlinks active use slide show mode)

• 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.

The Car Hierarchy model

Car Hierarchy Sensitivity1. 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

Car Hierarchy Sensitivity (cont’d)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

Car Hierarchy Sensitivity (cont’d)4. The dotted line for the priority of the “what-if” node is initially set to 50%, orat x = .5. When x = 0, its priority is 0, at x = 1, its priority is 1. As you changeIts priority the priorities of the other criteria change proportionately.The Avalon is the cheap car, theBabylon the mid-price and the Carryon the luxury expensive car. The verticalline here is at the priority Price has inthe model: about 49 %. At this priorityfor Price the Avalon gets 31% of the priority, the Babylon about 26% andthe Carryon about 43%. Grab the cursorwith your mouse and move it to the right on the x-axis to see that after about70% the Avalon becomes best choice. Sensitivity can also be done for the othercriteria in the model: Prestige, etc.

Car Hierarchy Sensitivity (cont’d)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 nodes2. Priorities of the Control Criteria nodes3. 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 getto the Sensitivity Input selectordialogue 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

Sensitivity for Costs node (cont’d)• 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, Network 0, Costs, Done

Fig. 2 – Click Update for graph

Sensitivity for Costs node (cont’d)• 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.

Sensitivity for Costs node (cont’d)

• 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.

Sensitivity for Costs node (cont’d)

Input Value Priority: Costs1 Pre-emptive Attack

on Iraq2 Attack Iraq only with Allied

Help

3 Work with UN to ensure Weapons 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

Table of values leading to the graph on previous page. Selecting more steps on the edit parameter dialogue box will give more data points.