assigning the incidences corresponding to i3 a much higher weight than

the incidences corresponding to either i-i or i1+i. The resulting IDM,

for a blocking factor of 6, would then appear something like the one in

Fig. 4-3 a) (for minimization of the sum of the output weights). The

outputs could then be as in Fig. 4-3 b) or c). The assignment of

weights is a subjective matter, but it is one area where engineering

intuition can be employed to guide the selection of the solution

procedure.


4.3 Function-Variable Output Set Assignment

 The assignment of variable type outputs is made by treating the

FVIM as an incidence matrix and using the same algorithm as was used

for the index outputs. The aim is to employ the maximum output product

criterion developed by Edie (1970). The maximum product criterion is

used in an attempt to enhance the convergence properties of the system

of equations. It states that the outputs should be assigned in such a

way as to maximize the product of the sensitivities of the functions to

their chosen outputs. Then sensitivities become weights for the inci-

dence matrix elements. The maximum product of the output weights can

be achieved by minimizing the negative of the logarithms of the output

weights. The real problem is to assign meaningful weights to the

elements in the FVIM. What is actually desired is to assign outputs .to

the expanded problem, each element having a weight proportional to its

corresponding element in the Jacobian. If this were done the restric-

tions on FVIM output set assignments would most likely be violated.

 The procedure adopted for calculating the FVIM weights is the

following. The Jacobian is calculated for the expanded set of