4.7.
Summary
129
the algorithm felt at any time that the running time for the program was
becoming excessive, he could set a computation time limit and still obtain
a feasible solution—one that was close to the optimum.
4.7. Summary
In this chapter, w
r e have used the expansion of the water resources system of a hypothetical river basin (called the MD river basin) to illustrate
the efficacy of the decomposition algorithm proposed in Chapter 3. The
objectives of the proposed expansion were limited to two disparate facets
of a water resources system: (1) withdrawal consumptive use (irrigation)
and (2) withdrawal nonconsumptive use (generation of hydroelectric
energy). Other common purposes of water resources development, namely,
municipal, industrial, and recreational use, were incorporated implicitly in
the river basin model by specifying respectively minimum flows in the
relevant river reaches and minimum seasonal water levels in the reservoirs.
The model incorporated realistic economic and hydrological parameters.
The OKA solved the operating policy problem in a straightforward
fashion. Reservoir operating rules were not prespecified except for constanthead hydroelectric reservoirs. In this case identical high and low limits
were prespecified in the relevant arcs to maintain a constant head in the
reservoirs. No special problems w
r ere encountered with Little's BBA.
The detailed results found are listed in Appendix B. The objective functions used and an example of a bound calculation are exhibited in Sections
4.3 and 4.4. Highlights from the output data are tabulated, illustrated,
and discussed in Section 4.5. Of special interest is the role of the γ*, dual
variables in spotlighting those parts of the river basin where the water
supply does not meet all the demands. The sensitivity of decisions to
parameter changes and the use of penalty functions is discussed in Chapter
5.
The efficacy of the solution procedure was demonstrated by the fact
that the return from the first feasible solution was within 3.3% of the final
optimum. In Section 4.6 a heuristic method is explained for calculating
the computer execution time to reach a feasible solution of any similar
problem.
Summary
129
the algorithm felt at any time that the running time for the program was
becoming excessive, he could set a computation time limit and still obtain
a feasible solution—one that was close to the optimum.
4.7. Summary
In this chapter, w
r e have used the expansion of the water resources system of a hypothetical river basin (called the MD river basin) to illustrate
the efficacy of the decomposition algorithm proposed in Chapter 3. The
objectives of the proposed expansion were limited to two disparate facets
of a water resources system: (1) withdrawal consumptive use (irrigation)
and (2) withdrawal nonconsumptive use (generation of hydroelectric
energy). Other common purposes of water resources development, namely,
municipal, industrial, and recreational use, were incorporated implicitly in
the river basin model by specifying respectively minimum flows in the
relevant river reaches and minimum seasonal water levels in the reservoirs.
The model incorporated realistic economic and hydrological parameters.
The OKA solved the operating policy problem in a straightforward
fashion. Reservoir operating rules were not prespecified except for constanthead hydroelectric reservoirs. In this case identical high and low limits
were prespecified in the relevant arcs to maintain a constant head in the
reservoirs. No special problems w
r ere encountered with Little's BBA.
The detailed results found are listed in Appendix B. The objective functions used and an example of a bound calculation are exhibited in Sections
4.3 and 4.4. Highlights from the output data are tabulated, illustrated,
and discussed in Section 4.5. Of special interest is the role of the γ*, dual
variables in spotlighting those parts of the river basin where the water
supply does not meet all the demands. The sensitivity of decisions to
parameter changes and the use of penalty functions is discussed in Chapter
5.
The efficacy of the solution procedure was demonstrated by the fact
that the return from the first feasible solution was within 3.3% of the final
optimum. In Section 4.6 a heuristic method is explained for calculating
the computer execution time to reach a feasible solution of any similar
problem.