Agriculture Reference
In-Depth Information
policies regulating methane emissions are
appropriate in dairy production systems.
(as expected) and the subjectivity in assigning
the weights overpowered the possibility of opti-
mizing multiple objectives. The model is deter-
ministic, i.e. there is no uncertainty in feed costs,
in animal nutrient requirements, or in feed com-
position. A deterministic linear programming
model was used because the shadow prices for a
methane mitigation constraint were an impor-
tant part of the model output; therefore, the
model's linearity ensured that interpretation of
results would be straightforward.
The model examined the effects of enforc-
ing two categories of environmental policies on
methane emissions from dairy cattle, thus forc-
ing a reduction of methane emissions by two
distinct strategies. The first policy strategy (the
TAXM model) involved the taxation of methane
emissions by using carbon dioxide equivalent
prices in the carbon market. The model forced a
reduction in methane emissions by changing
the dietary composition according to a methane
prediction equation. The tax on methane emis-
sions is included through the objective function,
and the reduction in methane emissions is,
conceptually, achieved through the formulation
of a new diet, at a higher cost, which has a lower
proportion of fibre. The second strategy to
reduce methane emissions through a regulatory
policy (the REDM model) involved the reduction
of emissions by predetermined amounts. The
reduction was forced through a methane con-
straint which restricted emissions based on a
baseline model (the BASEM model). The reduc-
tion in methane was also achieved through a
higher cost diet, which usually had an increased
proportion of protein and energy content and a
decreased proportion of fibre. Nitrogen and min-
eral excretions were calculated through mass
balance and were used to assess the sensitivity of
excretions to reductions in methane emissions
achieved through dietary manipulation. The
formulation of TAXM can be described mathe-
matically as:
Minimizing Diet Costs
and Environmental Impacts
in a Dairy Herd
Several optimization modelling techniques have
been presented up to this point. A brief mathe-
matical description and selected examples have
also been provided. However, applications of
these techniques in minimizing the environmen-
tal impacts of livestock production were briefly
introduced, and the results of specific modelling
strategies were briefly discussed. This section
provides a comprehensive examination of a diet
optimization model (Moraes
et al
., 2012) imple-
mented to minimize diet costs and methane
emissions simultaneously from a dairy cattle
herd. A mathematical description of the model is
provided, and key results are discussed to dem-
onstrate the role of the model structure in mini-
mizing methane emissions from dairy cattle and
examining the effects of regulatory policies in
the milk production system.
A linear programming model was devel-
oped (Moraes
et al
., 2012) to minimize methane
emissions from a hypothetical dairy herd
through the inclusion of environmental policies
in the least-cost diet model framework. The
hypothetical dairy cattle herd was composed of
animals in seven categories: three categories of
heifers, dry cows, primiparous and multiparous
cows at early lactation and mid- to late lactation.
Feed composition and animal nutrient require-
ments were calculated using the NRC (2001).
The main idea behind model development was
the construction of a mathematical tool to assist
producers in meeting demands set by environ-
mental policies and, at the same time, develop a
model that could jointly minimize diet costs and
the environmental impacts of dairy cattle. A lin-
ear programming model was the method of
choice because it would provide a flexible frame-
work for including the effects of environmental
policies either in the model constraints or in the
objective function. Multi-criteria programming,
especially goal programming, was not the
method of choice because, for different goal
weights, a different solution was reached
7
19
7
∑
∑
∑
min
xc
+
ep
ja
j
a
a
=
1
j
=
1
a
=
1
(6.10)
Subject to
x
∈
S
where
x
ja
is the amount of feed
j
for animal cate-
gory
a, c
j
is the cost of feed
j, e
a
is the amount of
methane emitted by animal category
a, p
is the
