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A Thesis Presented to the Faculty of the College of Natural Science Michigan State University

In Partial Fulfillment of the Requirements for the Degree Master of Science


David Gordon Gossman

June 1979




In each of the last chapter the analysis has concluded with the production of a matrix. The first of these was the information and specialty needs matrix, the second was the philosophical matrix and the third was the vocabulary matrix. They shall henceforth be referred to as "IM", "PM", and "VM" consecutively. These matrices will now be used to produce the organizational matrix or "OM". The organizational matrix will be used to both represent the organizational structure and to help point out places where this structure will need to be changed in order to produce effective communication.

The first step in this computation is the element by element multiplication of IM with PM and then IM with VM. (This is neither the dot product nor the cross product; it is analogous to the method of adding matrices.) This is done in order to eliminate, for the present, those values in PM an VM which correspond to edges in the information and speciality needs topological graph which do not exist. These two matrices are then summed, but not before the (IM) times (VM) matrix is divided by the scaler quantity of two. This division by two effectively reduces the significance of vocabulary differences to half that of philosophical differences. This ratio is rather arbitrary and may need some future adjustments. Finally this summed matrix is added to IM to yield OM. The entire formula is as follows:

OM = IM + (IM) (PM) + ((IM) (VM))/ 2

The resulting matrix, OM, will have elements with values of zero or one through two points five. Zeros are an indication of no communication link. The other values indicate links with varying degrees of difficulty in communication. This communication difficulty will vary directly with calculated value in matrix. Quite roughly, and somewhat arbitrarily, values from one to one point five indicate that very few problems will exist in bridging communication differences. Links with values between one point five and one point nine will most likely experience moderate difficulty in communication. This range of difficulty, however, should not prove to be overpowering. Communication links with values of one point nine or higher will experience a great deal of difficulty in communication. Every effort should be made to either eliminate them or at least make sure they are not crucial to the information flow needed to solve the R&D organization's problem.

If these links are crucial and cannot be bypassed, as will occur occasionally, special care must be taken by the R&D manager. This care must be reflected in both the choice of the individuals to fill the specialist positions and in the careful monitoring of this portion of the organization for signs of communication difficulties.

At this point in the assessment of organizational needs it may be necessary to return to the original topological graph and make some changes. These changes should reflect the desire to eliminate those edges which correspond with values of high communicative difficulty and replace them with either additional links to management personnel or perhaps appropriate routing of information through specialists themselves. After any changes are made in the graph a new IM should be prepared and the procedure for calculating OM repeated using the IM.


Once a satisfactory organizational matrix has been determined, as in the prior step, there is only one more step which needs to be taken in order to determine the organizational structure. This step involves the determination of the complexity of the organization which surrounds each individual. This is done to insure that communication overload or underload does not occur.

These are two major factors which determine the organizational complexity surrounding an individual. The first factor (f1) is determined by summing all of the values in both the column and row of the organizational matrix corresponding with the particular individual. The second factor (f2) is the average number of edges that the directly adjacent nodes (with respect to the node for which the complexity is being measured) have with other directly adjacent nodes in the topological graph. Given the subgraph at (a) the node representing the individual position being analyzed, (b) all nodes directly connected to that particular node, and (c) all the edges connecting those nodes, where all nodes in the subgraph equal (n) and all edges equal (d) we have,

f2=(d-(n-1))/(n-1) = (d-n+1)/(n-1).

The organizational complexity (CI) for individual (I) is therefore equal to (f1) times (f2):

CI = (f1)(f2).

As CI increases so does organizational complexity and therefore the greater the likelihood of overloading the individual. Alternatively, the smaller CI, the greater the likelihood of underload. Individual tolerances for organizational complexity vary greatly from one individual to another. The R&D manager will therefore need to be selective in his choice of personnel in cases where the complexity goes to an extreme. Generally, although not always, values should not exceed 240 and should be no smaller than 100. Furthermore, from a hierarchical point of view, complexity values near the top of the hierarchy should be greater than those at the bottom and should vary in roughly a linear manner with respect to the hierarchial level.

It may be necessary at this point to return to the topological graph and again make adjustment in order to change the organizational complexity surrounding some individuals. Once this is completed the steps necessary for producing a new OM need to be repeated again. This final organizational matrix is now ready to be used as the model for the initial organization of the research group.

Continue to Chapter X