64
2. Formulating
the
Problem
2.5.6. Evaporation
Losses
Evaporation losses from the surface of a reservoir can be up to 10% of
the total inflow, so that these losses have been included in the mathematical
model [variable Ei jt in Eq. (2.13)]. The procedure used to calculate the
evaporation losses has been described in Section 2.3.6.
2.5.7. Other
Constants
(a)
DISCOUNT FACTOR
The discount factor [variable a in the objective function (2.1) and in
inequality (2.2) ] depends on the discount rate r
a = [1/(1+r)]'
In the United States this rate is determined by the Water Resources Council, and in 1970 was 4.625%.
(b)
BOUNDS ON ARC PLOWS
The capacity of an arc [C m in constraint (2.16)] is the maximum
amount of water that can flow through the arc (a reach of river or a canal) without flooding. The lower bound on arc flow (L m ) is usually zero,
but many have a nonzero value when water quality standards or navigation requirements demand a definite flow of water in that arc. In the
example discussed in Chapter 4, all of the values of C m and L m are assumed.
(c)
INITIAL RESERVOIR CONDITIONS
The initial condition for each reservoir [Ο,Ό in equation (2.15)] have
been assumed.
(d)
OTHER CONSTANTS
Values for the number of reservoirs initially present in the system (N in
the objective function and in various summations), the maximum possible
number of reservoirs in the systems (M in the objective function and in
various summations), the total number of links in the system [M\ in constraint (2.13)], and the length of the time horizon (!T ma x in the objective
function) are assumed in the example problem.