7.2 Examples

 The variables f, A, B, a, b, c, d and hf are declared to be

 decision variables. This leaves the two-index variables v, ,, x and y

 and the one-index variables L, V, H, h and T to be solved in the two-

 index functions VF, M, LM and XY and the one-index functions LT, Q, LE,

 E and VE. The system of function types and variable types can be seen

 to be square. The FVIM and IDM's appear in Fig. 7-1.

 In addition to the variable type decisions, index decisions are

 declared as 0 and Ui +1, where Ui is the range upper limit for il, the

 stage number index. This reduces the total number of variables in the

 problem to the same as the total number of functions. All decision

 variable values are shown in Table 7-1. For the first problem there is

 an added decision that a liquid side stream consisting of 301 of the

 total flow is withdrawn from the liquid stream leaving the firs: stage.

 The first step is the application of the decoupling algorithm.

The index li is not eligible to be a decoupling index since j2 will not

fully precedence order for decrementing (index decision 0 prevents

this), while j3 will not fully precedence order for incria'm nting (ifde;.

decision U. prevents this). The index i0 is not eligible to be a

decoupling index because j5 has range limits offset f:.i both L.. and
 12
U.. Because of this, the problem will exhibit no decoupling at all.

 The next step is to assign the index outputs. For i1 there is no

choice at all. The index outputs for ji, j2 and j3 must all be offset

from it by zero. Similarly the index output for j4 mus; be offset From

iA by zero. The index output for J5 is chosen to he offset from iq by

zero. The blocking factors for both indices are set to 3, as is indi-

cated by the IDM's.