Although the output choice was the maximum product, a closer

examination of the coefficient matrix reveals the source of the problem.

Some of the output products are the product of very large and very small

numbers. The small numbers represent undesirable output choices, but

these effects are cancelled out by the large numbers. Also, some of the

numbers representing ineligible outputs (either because of variable type

or index value) contribute to the large eigenvalues. These numbers are

not represented in the FVIM.

 The large eigenvalue indicates that a modification of the solution

procedure is necessary. A possible modification is to solve some of the

equations by Newton-Raphson rather than by Gauss-Seidel. For this

example, the modification chosen is to solve functions VT and VE

implicitly for the variables T and v. This results in all eigenvalues

of the convergence matrix being zero. The reason for this is that the

Gauss-Seidel partition fully precedence orders for this solution

procedure. Thus both the Gauss-Seidel and Newton-Raphson partitions

have eigenvalues equal to zero.

 The solution procedure, then, is to tear T and v, solve the Gauss-

Seidel equations for 1, L, x, h,, H, y and V, and calculate new values

for T and v by Newton-Raphson. The process is repeated until conver-

gence is achieved, i.e., until there are sufficiently small changes in

the torn variables from iteration to iteration.

 When implemented for computer solution, this solution procedure,

using the decision variable values in Table 7-4 and the tear variable

values in Table 7-6, reached a solution in six iterations, using 8.53

seconds of IBM 370/165 CPU time. The relatively large amount of CPU