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3. The Hierarchy of Criteria
3.1. The Structure of the Hierarchy
The hierarchical structure of the analysis is critical because it shows the topological priorities of the various elements and the paths, the weighted scores will follow as they are propagated up to the top Node and the final scores of the alternatives.
Figure 1. Hierarchy Example.
It should be noted that the success or failure of a comparative analysis project is directly proportional to the effort and detail that is put into the creation of the hierarchical chart. It is the spine of priorities. What is correctly deemed as important is critical to the success of an analysis.
Definitions of the two elements of a Hierarchy must be defined here before we go any further. They are the “Endpoint” and the “Node”.
An Endpoint is the basic element of the Hierarchy and is an individual criteria.
A Node is the grouping element of the Hierarchy and consists of as little as two Criteria or any combination of Nodes and individual Criteria.
3.2. Hierarchical Importances of the Criteria
Importance is applied in two ways: Topologically and by Weights of Importance
3.2.A. The first application of importance is produced by the topology or structure of the Hierarchy.
For Example, a Hierarchy begins with a top Node and explodes into a descending set of Nodes and Endpoints.
Each hierarchical level in descending order defines the order of priority.
The following five figures show the Hierarchy of the first case history, " A Comparison of Vacation Home Prospects" as a descending Outline, first showing only the first level, then the second, ... down to the fifth level.
Level 1. Hierarchy Example.
Level 2. Hierarchy Example.
Level 3. Hierarchy Example.
Level 4. Hierarchy Example.
Level 5. Hierarchy Example.
Each Node and Endpoint represents a specific percentage of contribution to the hierarchy’s total score for each of the Rivals. We define that percentage to be the Absolute Percent of Contribution.
Likewise, each Node and Endpoint represent a specific percentage of contribution to their parent Node's score. Let that percentage be defined, the Relative Percent of Contribution.
The Hierarchy is built using SV(ct) and the absolute and relative percent of contribution are calculated for every Node and Endpoint. The hierarchy and its percentages are then presented for approval to those people, who will be involved in the weighting, scoring and decision process of the project.
The Hierarchy is the blueprint of the project
and as such it is quite obvious that there will be several renditions of it before all the parties involved in the decision process are satisfied with the levels of priority and their percentages of contribution.
3.2.B The second application of importance is produced by the Weights of Importance of the Criteria subcomponents of each Node
As such, Weights of importance are assigned to every Endpoint and to every Node but the top Node.
Each Node's score for each Rival and Benchmark is determined from the Criteria scores of its subcomponents, be they Nodes or EndPoint Criteria.
If each of the subcomponents is assigned the same weight of importance then the node's score is the simple average of the scores of the subcomponents. But if the subcomponents are not evenly weighted then the node's score is determined by the weighted average of the scores of the subcomponents.
Herein lies the major significance of a comparative analysis. The weighting of each of a Node's subcomponents causes the Node to behave like a mixing valve amplifying some subcomponents while filtering the others.
3.2.C Examples of Percent of Contribution
The following example shows how the percent of contribution is determined for the Node whose name is "Rooms". It is a Node with six subcomponents consisting of four Nodes and two EndPoints.
Before the Weights of Importance are assigned to the six subcomponentss, their unweighted percent of contribution toward the score of their Parent Node will all be the same, namely, 1/6 or 16.%.
After the nodes have been weighted, the sum of the 6 wgts, 5,5,3,4,4,3 will be 24.
The % of Contributions for the Subcomponents of the "Rooms" Node
Contrib Calculations Data.
Thus the weights of the Nodes, "Bed Rooms" and "Number of Baths" caused them to gain 4.17% to become 20.83%; while "Porches/Decks" lost 4.77% to slip to 12.5%; "Kitchen" and "Living Room" remained the same at 16.67% and "Extra Room" with a loss of 4.17% slipped to 12.5%.
"Bed Rooms" and "Number of Baths" with a contribution of 20.83% will clearly play a much stronger role in determining the score of their Parent "Rooms". "Porches/Decks" and "Extra Room" both surrended 4.17% to each be at 12.5% while "Kitchen" and "Living Room" remained at the same percentages of 16.67%.
The following figure shows the Home Case History's Hierarchical Outline with the Percentages of Contribution of each Node and Endpoint (the Endpoint rows have a blank background), their Relative Percent of Contribution to their Parent Node, and their assigned Weights of Importance and finally their effective real weights. (Notice that the total of each Node's set of real weights is equal to the number of Criteria in that Node.).
The Absolute Contributions %'s indicate what percentage of that entity's score will be applied to the top score of each of the Alternatives.
Home Outline with Percentages and Wgts
The Project Outline is the spine of the project's spreadsheet and the easiest to edit and modify. Once the changes are made the outline is recompiled and both versions of the hierarchy are reconstructed and the percentages of contribution are recalculated.
The following figure is a two dimensional chart generated by V(ma) by producing
a separate column of outlines for each 2nd level Node in the Hierarchy and drawing a box about each entity.
In the past we have drawn more conventional hierarchical charts using various drawing programs. However, as attractive as they were, we have found this technique much more comfortable because it is merely another worksheet in the V(ma) Excel Workbook and can be zoomed, scrolled and commented on using Excel's standard drawing tools.
Home 2D Block Outline
Each case in the Case Histories section will have both a Project Outline and a 2D Block Outline as part of their file.
A 2D Block Outline of a much more complex Case History, called "Office Systems" is the next figure as a Pdf file. The reader must utilize the Pdf zooming tools to more comfortably read the small print.
Sheets with that much detail can be printed using a drafting sheet printer. CVA has done this several times to produce wall size hierarchical charts for meetings.
02_Office Systems_2D_Block_Diagram as a Pdf file.
At this point it is worthwhile to step back and ask why is a hierarchy necessary.
The answer is very simple. It is by the establishment of a hierarchical set of Criteria, that the Criteria Endpoints are determined.
In almost every comparative analysis it is almost impossible to determine the Criteria Endpoints from scratch. It is during the decision process of choosing the priority levels, which Nodes should be created, where they should be, calculating the contribution percentages, checking for imbalances that we build the Hierarchy and when we are through those entities that have no subcomponents become the Criteria Endpoints. It is they that are scored manually by the expert teams and put into the Voting Matrix. The Computer and the V(ma)software then score the Nodes, build the Workbook, the Vectorgram data base, the working spreadsheets and the final Criter_Smry_Sheet.
In summary, the Topology of the Hierarchy defines the priority levels of importance but the weighting of each of the Nodes' components changes the Hierarchy into a complex logical circuit by causing filtering and amplifications at every junction.
Thus, when managers are faced with an analytical comparative report to review for approval, it is imperative that they examine the hierarchical structure and the assigned weights of importance before they start reviewing the performance of the Alternatives.
V(ma) has provided three graphical aids to help. They are:
1.The 2D Block Diagram and Project Outline descriptions of the Hierarchy;
Scanning these will give one a sense of the order and levels of importance for the various Criteria.
2. The VectorStrings in the Vectorgrams:
The next section deals with the characteristics of the Vectors representing the various Criteria. Their size and angles will show how their Alternatives performed for each Criteria. And the overall shapes of the VectorStrings, "Posing as Alternatives", will show by their length and position at the "Finish Line" how well they performed.
3. The Criteria Smry Sheet:
The Smry sheet, utilizing the Four Quadrants of Importance and the Vertical Alternative Histograms, to perform its own examination and determine, "Who Won and Why".
Go to the Next Topic: 4. Voting Matrix
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