2.3.
Constraints
51
where
= energy generation function for reservoir j
= minimum acceptable energy demand for the total river basin
(which will increase over the years)
= 1 if flow in link m enters reservoir j
= — 1 if the flow in link m leaves reservoir j
= 0 otherwise
Qimt = flow in link m during month i of year t
For the example problem in Chapter 4, the specific function used is listed
in Section 3.4.
Future demands for irrigation, recreation, and municipal and industrial
use of water can be met only by reservoirs in the locality adjacent to each
municipality, industry, or irrigation area. Consequently, the river basin is
divided into a number of subsections for these purposes, and the irrigation,
municipal, industrial, and recreation demands for each subsection may be
met only by dams in that subsection. The demands will show an increasing
value over the years.
Constraints (2.11) and (2.12) are inequalities that deal with municipal,
industrial, and irrigation demands of an arbitrary subsection. It is assumed
that four reservoirs already exist in the chosen subsection and three new
dams (N + l,iV + 2, ΛΓ + 3) may be added. The same constraints apply
to every subsection except that summation is over different reservoirs:
4
.MV+3
Z^it+ Σ Fut > Fu
for all i and t
(2.11)
where Fa is the minimum municipal and industrial demand for a subsection
of the river basin, and F ijt is the water supplied for municipal and industrial
use from reservoir j in month i of year t. Also
4
JV+3
Σ D ijt + Σ Dm >
for all i and t
(2.12)
where Gu is the minimum irrigation need for a subsection of the river basin.
2.3*6. Physical
Constraints
Typical physical constraints that must be introduced into the model of
the river basin are (1) bounds on river (canal) flows, and (2) mass balances
on each reservoir. These physical constraints limit the flow of water through
the system so as to satisfy the conservation of mass balances on the quan-