116
4. Application
of the Optimization
Algorithm
4.3. Solving the Operational Policy Problem
In this section we discuss how the OKA optimizes the flow variables of
the original system network whose configuration is detailed in Tables B.3
and B.4. The listing in Appendix Β includes the source and sink nodes,
and the values of the cost and the upper and lower flow limits corresponding
to each of the 131 arcs of the network. Twelve network arcs had (negative)
nonzero costs (called NZC arcs); data on the NZC arcs are detailed in
Table 4.5a.
The objective function used had the form
Minimize
%t
=
— (&7,β/7,6 +
&9,1θ/9,10 +
· · · +
653,62/53,52)
Zero initial values were assumed for all the node (π») numbers and a feasible nonoptimal flow circulation was imposed on the network. The solution
procedure followed was identical to that described in Sections 3.3.1-3.3.7
and utilized in Section 3.3.8. However, the complexity of the problem precludes the listing of intermediate results. The optimal solution is listed in
Tables B.8-B.10; a summary of the NZC arcs is in Table 4.5a and 4.5b.
Note that the node numbers in the optimal solution remain unchanged
(consult Table B.10). Consequently, for the arcs with zero costs (called
ZC arcs), the optimal
values are zero; thus any feasible flow in the ZC
arcs may be the optimal solution. On the other hand, the values of q„ for
the NZC arcs remain negative, and the optimal flows in these arcs must
equal their respective upper bounds. It is explicitly assumed that imported
water can be brought to all the dams of the system. If perchance there are
some dams to which imported water cannot be brought, a value of
can
be used for the appropriate canal cost.
The only information that was prescribed for reservoir operating rules
pertained to the hydroelectric reservoirs. Constant-head hydroelectric
generators were used in the model, and to ensure a constant head, an initial
condition was forced for each reservoir generating electrical energy for each
period. For example, referring to Fig. 4.1, reservoir 4 is used for generating
electric power through arc (5-7). Prescribing similar values for the high
and low limits in the arcs listed in the following tabulation ensured that
there was always exactly this amount of water in the reservoir, so that the
constant-head turbines could be operated. Excluding the restrictions of the
constant head, the reservoir operating rules are determined by the OKA.
4. Application
of the Optimization
Algorithm
4.3. Solving the Operational Policy Problem
In this section we discuss how the OKA optimizes the flow variables of
the original system network whose configuration is detailed in Tables B.3
and B.4. The listing in Appendix Β includes the source and sink nodes,
and the values of the cost and the upper and lower flow limits corresponding
to each of the 131 arcs of the network. Twelve network arcs had (negative)
nonzero costs (called NZC arcs); data on the NZC arcs are detailed in
Table 4.5a.
The objective function used had the form
Minimize
%t
=
— (&7,β/7,6 +
&9,1θ/9,10 +
· · · +
653,62/53,52)
Zero initial values were assumed for all the node (π») numbers and a feasible nonoptimal flow circulation was imposed on the network. The solution
procedure followed was identical to that described in Sections 3.3.1-3.3.7
and utilized in Section 3.3.8. However, the complexity of the problem precludes the listing of intermediate results. The optimal solution is listed in
Tables B.8-B.10; a summary of the NZC arcs is in Table 4.5a and 4.5b.
Note that the node numbers in the optimal solution remain unchanged
(consult Table B.10). Consequently, for the arcs with zero costs (called
ZC arcs), the optimal
values are zero; thus any feasible flow in the ZC
arcs may be the optimal solution. On the other hand, the values of q„ for
the NZC arcs remain negative, and the optimal flows in these arcs must
equal their respective upper bounds. It is explicitly assumed that imported
water can be brought to all the dams of the system. If perchance there are
some dams to which imported water cannot be brought, a value of
can
be used for the appropriate canal cost.
The only information that was prescribed for reservoir operating rules
pertained to the hydroelectric reservoirs. Constant-head hydroelectric
generators were used in the model, and to ensure a constant head, an initial
condition was forced for each reservoir generating electrical energy for each
period. For example, referring to Fig. 4.1, reservoir 4 is used for generating
electric power through arc (5-7). Prescribing similar values for the high
and low limits in the arcs listed in the following tabulation ensured that
there was always exactly this amount of water in the reservoir, so that the
constant-head turbines could be operated. Excluding the restrictions of the
constant head, the reservoir operating rules are determined by the OKA.