1.3. Techniques for the Optimization
of a Water Resources
System
17
2. Numerical methods that generate solutions to the optimization
problem by means of iterative procedures. Numerical methods can be used
to solve problems that cannot be solved analytically. Because water resources problems prove tractable to numerical techniques, numerical
methods are the ones to be considered here.
We will briefly summarize a few of the more important numerical optimization tools in this section in order to bring out the significant role that
the model and objective function play in the optimization of a water resources system. The factors that can be included in a model of a water
resources system and the form in which they must be included are dictated
by the optimization methods that can be used. It is because of such restrictions that simulation has been used as an alternative to optimization,
for simulation can accommodate almost any type of model.
1.3.1. Linear and Nonlinear
Programming
One approach to optimization ignores the structure of the problem and
on each iteration manipulates all the variables simultaneously in the quest
for an optimum. This approach may be referred to as the simultaneous
optimization technique, and is typified by linear and nonlinear programming. Linear programming [Beveridge and Schechter, 1970, pp. 287-324]
has been used to solve such diverse problems as:
1. analysis of water resource decisions in international river basins
[Rogers, 1969]
2. allocation of capital for water resources development [Marglin,
1962; Masso and Gibrat, 1957; Masso, 1962]
3. finding reservoir operating rules [Loucks, 1969; Manne, 1960;
Thomas and Revelle, 1966]
4. treatment of polluted water [Lynn et al, 1962; Revelle et al. } 1968;
Sobel, 1965; Thomann and Sobel, 1964]
A linear programming problem is one in which a linear function is the
criterion to be minimized or maximized, a criterion subject to constraints
that are also linear functions. A combination of scalars or vectors denoted
in general by A\ is said to be linear if the scalars or vectors can be assembled in the form
CiXi
+ C2X2 +
· · · +
CnXn
where the c's are constants. For example, the function
4*i + 3a: 2 + 5*3 + 2
of a Water Resources
System
17
2. Numerical methods that generate solutions to the optimization
problem by means of iterative procedures. Numerical methods can be used
to solve problems that cannot be solved analytically. Because water resources problems prove tractable to numerical techniques, numerical
methods are the ones to be considered here.
We will briefly summarize a few of the more important numerical optimization tools in this section in order to bring out the significant role that
the model and objective function play in the optimization of a water resources system. The factors that can be included in a model of a water
resources system and the form in which they must be included are dictated
by the optimization methods that can be used. It is because of such restrictions that simulation has been used as an alternative to optimization,
for simulation can accommodate almost any type of model.
1.3.1. Linear and Nonlinear
Programming
One approach to optimization ignores the structure of the problem and
on each iteration manipulates all the variables simultaneously in the quest
for an optimum. This approach may be referred to as the simultaneous
optimization technique, and is typified by linear and nonlinear programming. Linear programming [Beveridge and Schechter, 1970, pp. 287-324]
has been used to solve such diverse problems as:
1. analysis of water resource decisions in international river basins
[Rogers, 1969]
2. allocation of capital for water resources development [Marglin,
1962; Masso and Gibrat, 1957; Masso, 1962]
3. finding reservoir operating rules [Loucks, 1969; Manne, 1960;
Thomas and Revelle, 1966]
4. treatment of polluted water [Lynn et al, 1962; Revelle et al. } 1968;
Sobel, 1965; Thomann and Sobel, 1964]
A linear programming problem is one in which a linear function is the
criterion to be minimized or maximized, a criterion subject to constraints
that are also linear functions. A combination of scalars or vectors denoted
in general by A\ is said to be linear if the scalars or vectors can be assembled in the form
CiXi
+ C2X2 +
· · · +
CnXn
where the c's are constants. For example, the function
4*i + 3a: 2 + 5*3 + 2