taken to insure that the FVIM remains output set assignable. For the

example problem, had x or y been chosen as the decision variable type,

an output set assignment could not have been made. FVIM decisions may

not be chosen so that the restrictions on FVIM outputs must be violated

in assigning outputs.

 Consider the FVIM in Fig. 3-4 a). There are three function

types and four variable types. Choosing x as the decision variable

type results in the FVIM in Fig. 3-4 b) and choosing z results in

Fig. 3-4 c). The FVIM in b) is not output set assignable according to

the rules whereas the one in c) is. The decisions must be chosen so

that there are the same number of variable type as function types

with any given number of indices.

3.3.3 Index Outputs

 Index outputs are the outputs assigned in the Index Display

Matrices. They indicate which of the variables of the output variable

type will be the output for particular function index values. In

extending index outputs from the IDM to a general solution procedure

knowledge of the following properties is necessary.

Theorem 3-1: All Index Display Matrices, when treated as incidence

matrices are output set assignable provided they are not null.

Proof: The proof is by induction and is divided into two parts, one for

a list and one for a range.

List: There must be at least one list element, which is an offset from

the function index value. This is known from the definition of variable

index lists. Therefore, for one function index value there is an output

set assignment. Now suppose that there are output set assignments for

an IDM with k rows. Row k+l introduces a new function index value,


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