The choice of decision variables has received comparatively less

attention although the problems of simplifying the resulting solution

procedure (Lee, Christensen, and Rudd, 1966) and avoiding singular

systems (Edie, 1970) have been treated.

 The problem of deciding in what order to solve the equations has

been solved (Sargent and Westerberg, 1964) to the extent that acyclic

(non-recycle) systems can be discovered and equations involved in

various recycle calculations can be identified.

 All of the algorithms developed thus far require an explicit

representation of each equation and variable before the analysis can

begin. For units described by a large number of equations (for example,

a 50 plate distillation column with three components, which results in

350 equations) the total number of equations becomes quite large, and

application of the above algorithms becomes time consuming and requires

large amounts of computer storage space. In chemical engineering design

and simulation the proliferation of equations and variables is quite

often dlia to staged processes, which are modeled with indexed equations

and variables, which are the same on every stage except for index value.

Great savings of time and computer storage are realized by analyzing

the set of indexed equations, each equation writtt.n enly once, rather

than having to expand the set of equations and write separate equations

for different index values. Unfortunately., existing algorithms are not

directly applicable to these indexed eqaLtioris. Another shortcoming of

existing algorithms is that the solution procedures derived for indexed

equations (written in expanded form) would not be valid for an arbitrary

range on index values.