36
1.
Introduction
Young et al, [1969] and Orlob [1970] looked at the policy of the sequencing of reservoir construction to meet increasing water demands over time.
They took as the physical system the configuration of dams in East Texas
required for annual transportation of 12 million acre-ft of water in Texas,
as specified by the Texas Water Plan [Texas Water Development Board,
1968]. They examined a prespecified ultimate network configuration and
assumed a deterministic hydrology. There were two reservoir capacities at
each site, either zero or the design capacity; that is, a reservoir was either
not built or it was built. For each combination of dam sizes a simulation
(similar to network analysis) gave the return from operating the system to
minimize pumping and maintenance costs.
The method of analysis was similar to Hufschmidt's and can be summarized as follows.
1. Preliminary sizes of elements of the system and operating rules for
the reservoir were determined by a formal optimization procedure.
2. An initial screening was carried out by simulation of the given hydrology, element sizes, and operating rules for a large number of alternative
development schedules selected by random sampling of the cost response
surface. The range of variables was reduced by random sampling over the
independent variables.
3. A gradient search was used to further reduce the range of variables
to be searched. (The surface of the objective function used contained many
crevices and was not concave.)
4. The most attractive schedules were improved by a method of successive perturbations.
5. Element sizes were further refined by a second simulation procedure,
which constrained the flows in some of the expensive canals.
6. A second screening was carried out via a formal optimization of the
most attractive systems and development schedules.
7. Finally, a pattern search [Hooke and Jeeves, 1961] was used to reach
the optimum in the vicinity of the crevices.
Woolsey [1969] looked at the problem of competing public and private
investments in water resources, a problem first formulated quantitatively
by Steiner [1959], as applied to an actual problem in the Delaware River
Basin. Because the problem was formulated as an integer programming
problem, the method of solution used was the partial enumeration algorithm of Balas [1965], as modified by Glover [Glover and Zionts, 1965],
and coded by Peterson [1967]. The model of the river basin allowed for
(1) a choice of alternative dam sizes at each site, and (2) a way to satisfy
the energy and irrigation demands by operating several dams in concert.
1.
Introduction
Young et al, [1969] and Orlob [1970] looked at the policy of the sequencing of reservoir construction to meet increasing water demands over time.
They took as the physical system the configuration of dams in East Texas
required for annual transportation of 12 million acre-ft of water in Texas,
as specified by the Texas Water Plan [Texas Water Development Board,
1968]. They examined a prespecified ultimate network configuration and
assumed a deterministic hydrology. There were two reservoir capacities at
each site, either zero or the design capacity; that is, a reservoir was either
not built or it was built. For each combination of dam sizes a simulation
(similar to network analysis) gave the return from operating the system to
minimize pumping and maintenance costs.
The method of analysis was similar to Hufschmidt's and can be summarized as follows.
1. Preliminary sizes of elements of the system and operating rules for
the reservoir were determined by a formal optimization procedure.
2. An initial screening was carried out by simulation of the given hydrology, element sizes, and operating rules for a large number of alternative
development schedules selected by random sampling of the cost response
surface. The range of variables was reduced by random sampling over the
independent variables.
3. A gradient search was used to further reduce the range of variables
to be searched. (The surface of the objective function used contained many
crevices and was not concave.)
4. The most attractive schedules were improved by a method of successive perturbations.
5. Element sizes were further refined by a second simulation procedure,
which constrained the flows in some of the expensive canals.
6. A second screening was carried out via a formal optimization of the
most attractive systems and development schedules.
7. Finally, a pattern search [Hooke and Jeeves, 1961] was used to reach
the optimum in the vicinity of the crevices.
Woolsey [1969] looked at the problem of competing public and private
investments in water resources, a problem first formulated quantitatively
by Steiner [1959], as applied to an actual problem in the Delaware River
Basin. Because the problem was formulated as an integer programming
problem, the method of solution used was the partial enumeration algorithm of Balas [1965], as modified by Glover [Glover and Zionts, 1965],
and coded by Peterson [1967]. The model of the river basin allowed for
(1) a choice of alternative dam sizes at each site, and (2) a way to satisfy
the energy and irrigation demands by operating several dams in concert.