1

0*

0

0

2

0

0

+

3

0

0

4

0

+

0

5

0

+

+

6

0

+

7

0

0

8

0

+

9

0

10

+

0

0

11

+

0

+

12

+

0

13

+

+

0

14

+

+

+

15

+

+

16

+

0

17

+

+

18

+

19

0

0

20

0

+

21

0

22

+

0

23

+

+

24

+

25

0

26

+

27

*0 = pipe size unchanged; + = pipe size increased; = pipe size

decreased.

increased by more than one discrete size. We will ignore this possibility for the

moment and return to it later, since it would result in many more combinations to

be checked, most of which would violate *h*1.

If we first look at all the possible combinations of increasing or decreasing the

three pipe sizes without regard to the constraints, we have 33 = 27 independent

possibilities; they are enumerated in Table 12. Combination number 1 is our design

as it now stands, the "do nothing" option. A number of these combinations are

known not to yield improvement in our design, however, and may be immediately

dismissed without further evaluation.

Specifically, any combination that increases any pipe sizes while decreasing none

will only result in additional pipe capital and heat loss costs and thus will be worse

than our design as is. Thus, the combinations 2, 4, 5, 10, 11, 13 and 14 can be

dismissed.

In addition, we know that any combination that increases the diameter of either

the final pipe servicing consumer 2 [(7,2)] or consumer 3 [(7,3)], while decreasing the

other and leaving pipe segment (6,7) unchanged, would be more costly than doing

the same yet not increasing the diameter of the one pipe; thus, we eliminate

combinations 6 and 8. As we proceed to explore the various combinations remain-

ing, we will discover that many other possible combinations will immediately be

shown to be infeasible by the infeasibility of related combinations.

In Table 13 we have listed the remaining combinations. Table 13 also gives the

68

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