1. For the set of consumers whose constraints are violated, find the pipe segments that they all share
in common. Identify those pipe segment within this group that are shared with no other consumers.
In the event that there are no pipe segments shared with no other consumers, choose those pipe
segments shared with the minimum number of other consumers.
2. Increase the pipe segment diameters within this set enough so that the consumer whose constraint
from eq 4-2 was closest to satisfaction in the original solution now has his constraint satisfied. The
first pipe segment to have its diameter increased should be the one that this consumer shares with
the largest number of other consumers within the set of consumers with violated constraints.
3. Now remove this consumer whose constraint is satisfied from the set and find the new set of
common pipe segments for the remaining set of consumers with violated constraints, again including
the minimum number of other consumers in this set.
4. Again increase the pipe segment diameters within the remaining set enough so that the consumer
whose constraint was closest to satisfaction in the new set now has his constraint satisfied. The choice
of the pipe segment diameter to increase first is done in the same way as in step 2 above.
5. Repeat the above steps until all consumers have their constraints satisfied.
Figure 9. Method A.
violations that result. In the process we will consider the other consumers whose
constraints have also been violated.
Starting from an infeasible point, which is at the lowest possible cost for any
design, we want to move in the direction that will satisfy all of the constraints that
are violated by this solution. Since the critical consumer is the consumer whose
constraint has been violated by the greatest amount, we will have to travel the
"furthest" from our infeasible point to the boundary of his constraint. Thus, it would
seem tempting to try to resolve this constraint first and then look and see what other
violated constraints remain. However, it's possible that we can plot a course that will
take us straight to a point that will resolve all constraints rather than handling them
one at a time. To do so we might consider the algorithm given in Figure 9.
Note that the last consumer to have his constraint satisfied is the consumer who
was identified as the critical consumer in the original solution. Now, however, all of
the consumers whose pressure constraints were violated in the original solution are
"critical" consumers as well, having pressure levels just meeting the constraints,
within the tolerance achievable with the discrete pipe diameters available.
As an alternate to the above methodology, we could proceed by adjusting
diameters of the critical consumer first, but only enough to bring his piping pressure
loss to the level of the next highest consumer, i.e., using the method in Figure 10.
Since in many cases consumers will share more than one pipe segment, we still
may be left with a number of alternatives that must be evaluated at each of the steps
above. If in each case we choose the alternative that produces the minimum amount
of increase in cost over the previous design, we should be able to move to an ultimate
solution that satisfies all the constraints while reducing the cost as much as practical.
Because we may be faced with many possible alternatives when a number of pipe
segments are shared by two or more consumers, we may decide to stop the process
after finding an alternative whose cost is within some reasonable tolerance of the