4.5. Results of the
Optimisation
123
best feasible solution would not be examined, in view of their having lower
bounds than the best feasible solution. As a result, the total computation
time would be reduced significantly. In Chapter 5 the efficacy of using a
penalty function is discussed in greater detail.
4.5. 1. Comparison
of Operating
Policies for
Initial
and Final
Configurations
The differences in operating policies for different system configurations
were elucidated by studying the NZC arcs. Tables 4.5a, 4.5b, 4.6a, and
4.6b show the effects of the operating policies on the flows and dual variables associated with each NZC arc for the configuration that existed
initially and the final optimal configuration.!
For the initial configuration (i.e., before any new dams are added) all
flows in the NZC arcs equaled their corresponding upper-limit constraints.
Furthermore, the values of the dual γ# variables corresponded to the absolute value of the cost coefficient for each respective arc and thereby indicated that the resources of the initial configuration were being stretched to
the limit. For example, the flows in arcs 42, 45, 49 through 54, 96, and 99
equaled the upper limit for each respective arc, so that the installed electrical and irrigation facilities (including pumps, canals, and so on) were
being used constantly at maximum capacity.
The final network configuration differs from the original configuration
in a number of respects:
1. The upper bounds of arcs 47 and 101 were raised from 0 to 30, indicating that hydroelectric facilities were added.
2. The flows in both arcs 47 and 101 increased from 0 to 30 and the
flows in arcs 52 and 54 increased from 15 to 27 and 35 to 55, respectively;
the overall supply of hydroelectric energy and irrigation water was
augmented.
3. Four of the
variables were not equal to the absolute value of the
corresponding cost coefficient. The 7*7 variables of arcs 52 and 54 were
equal to zero because the flows in these arcs are less than their respective
upper bounds. No revenue improvement would result from raising the
upper bounds on flows for these arcs.
Arcs 51 and 53 had values of 7^ less than the absolute value of the corresponding cost coefficient. Examination of the configuration around arc
J The dual problem associated with the operational policy problem and the dual
variables are discussed and defined in Section 3.3.
Optimisation
123
best feasible solution would not be examined, in view of their having lower
bounds than the best feasible solution. As a result, the total computation
time would be reduced significantly. In Chapter 5 the efficacy of using a
penalty function is discussed in greater detail.
4.5. 1. Comparison
of Operating
Policies for
Initial
and Final
Configurations
The differences in operating policies for different system configurations
were elucidated by studying the NZC arcs. Tables 4.5a, 4.5b, 4.6a, and
4.6b show the effects of the operating policies on the flows and dual variables associated with each NZC arc for the configuration that existed
initially and the final optimal configuration.!
For the initial configuration (i.e., before any new dams are added) all
flows in the NZC arcs equaled their corresponding upper-limit constraints.
Furthermore, the values of the dual γ# variables corresponded to the absolute value of the cost coefficient for each respective arc and thereby indicated that the resources of the initial configuration were being stretched to
the limit. For example, the flows in arcs 42, 45, 49 through 54, 96, and 99
equaled the upper limit for each respective arc, so that the installed electrical and irrigation facilities (including pumps, canals, and so on) were
being used constantly at maximum capacity.
The final network configuration differs from the original configuration
in a number of respects:
1. The upper bounds of arcs 47 and 101 were raised from 0 to 30, indicating that hydroelectric facilities were added.
2. The flows in both arcs 47 and 101 increased from 0 to 30 and the
flows in arcs 52 and 54 increased from 15 to 27 and 35 to 55, respectively;
the overall supply of hydroelectric energy and irrigation water was
augmented.
3. Four of the
variables were not equal to the absolute value of the
corresponding cost coefficient. The 7*7 variables of arcs 52 and 54 were
equal to zero because the flows in these arcs are less than their respective
upper bounds. No revenue improvement would result from raising the
upper bounds on flows for these arcs.
Arcs 51 and 53 had values of 7^ less than the absolute value of the corresponding cost coefficient. Examination of the configuration around arc
J The dual problem associated with the operational policy problem and the dual
variables are discussed and defined in Section 3.3.