150
6. Water Quality and Pollution
Considerations
ogy available, (3) satisfying all physical constraints, and (4) meeting all
minimum quality standards. The problem will be formulated so that the
mathematical statements are directly analogous to those presented in
Chapter 2 and are compatible with them.
6.3.1. Additional
Terms for the Objective
Function
The objective in adding waste water treatment plants is to minimize
over the set of alternative projects the sum of the discounted present value
of the total costs (capital and operating); hence the following terms have
to be subtracted from the existing terms in the objective function (2.1) :
TWx
Μ*
ΤΤΟΛΧ
Μ*
12
/' = Σ
«
Σ
λ,Α. +
Σ
« Σ Λ. Σ*«ι
(β·
1 )
*-ι
ί-ι
i=»i
i-i
the capital cost of
the operating costs
the projects over
for all the treatthe planning period
ment plants
Water quality benefits, both direct and indirect, derived from higher prices
for municipal and industrial water, recreational use, tourism potential, and
scenic beauty, if they can be evaluated, can be added into expression (2.1)
or subtracted from (6.1). There has been and no doubt will be much discussion of the magnitude and reality of these benefits, but if it is decided
to include them in a planning model, they can be incorporated into the
model with little difficulty if they are made functions of the volume of
water flow and quality in the stream.
6.3.2. Additional
Budgetary
and Institutional
Constraints
The budgetary constraint is dependent upon congressional and/or state
water resources appropriations as in Section 2.3.1.
M*
α Σ *jtCit
(6.2)
y»JV *+l
Constraint (6.2) exists for new projects. The additional institutional constraints are
M*
Σ
λ Λ < 1
for all*
(6.3)
6. Water Quality and Pollution
Considerations
ogy available, (3) satisfying all physical constraints, and (4) meeting all
minimum quality standards. The problem will be formulated so that the
mathematical statements are directly analogous to those presented in
Chapter 2 and are compatible with them.
6.3.1. Additional
Terms for the Objective
Function
The objective in adding waste water treatment plants is to minimize
over the set of alternative projects the sum of the discounted present value
of the total costs (capital and operating); hence the following terms have
to be subtracted from the existing terms in the objective function (2.1) :
TWx
Μ*
ΤΤΟΛΧ
Μ*
12
/' = Σ
«
Σ
λ,Α. +
Σ
« Σ Λ. Σ*«ι
(β·
1 )
*-ι
ί-ι
i=»i
i-i
the capital cost of
the operating costs
the projects over
for all the treatthe planning period
ment plants
Water quality benefits, both direct and indirect, derived from higher prices
for municipal and industrial water, recreational use, tourism potential, and
scenic beauty, if they can be evaluated, can be added into expression (2.1)
or subtracted from (6.1). There has been and no doubt will be much discussion of the magnitude and reality of these benefits, but if it is decided
to include them in a planning model, they can be incorporated into the
model with little difficulty if they are made functions of the volume of
water flow and quality in the stream.
6.3.2. Additional
Budgetary
and Institutional
Constraints
The budgetary constraint is dependent upon congressional and/or state
water resources appropriations as in Section 2.3.1.
M*
α Σ *jtCit
(6.2)
y»JV *+l
Constraint (6.2) exists for new projects. The additional institutional constraints are
M*
Σ
λ Λ < 1
for all*
(6.3)