Agriculture Reference
In-Depth Information
at a certain level greatly reduces the model flexi-
bility in finding combinations of feeds that meet
animal nutrient requirements at a minimum
cost. Also, in a linear programming diet optimi-
zation model, feed intake is the sum of the ele-
ments in the solution vector, and it is usually
not known before the diet is formulated. But if
the intake is not fixed at a determined level, the
model feed composition matrix changes for dis-
tinct solution vectors and so does the nutrient
supply, because nutrient availability is depend-
ent on the intake level. In order to circumvent
this problem, an iterative algorithm can be
structured in which an initial feed composition
matrix can be created with the use of an initial
estimate of the dry matter intake and the model
can then be solved. The feed composition matrix
can be updated through the calculation of the
composition of feeds with the model solution
intake. The model can then be re-solved with
the use of the updated feed composition matrix
(Moraes
et al
., 2012). Through the iterative
updating of the model feed composition matrix
and solving of the model, differences in the feed
composition matrix can be made as small as
desired by increasing the number of iterations.
Therefore, a system with nutrient fractions
divided according to digestibility can be used in
a linear programming framework, and diet for-
mulation can be specific to the model deter-
mined level of intake.
Finally, from a feed management perspec-
tive, probably the most important aspect with
respect to mineral excretion is the availability of
mineral sources for diet formulation, especially
the separation of mineral sources. It is conceptu-
ally easy to understand that increasing the
number of feeds available for diet formulation
increases the model's flexibility in finding a
minimum cost diet. This concept has a direct
application for supplying minerals to livestock.
Traditionally, one mineral premix composed of
the nutritionally required minerals is added to
the diet in a quantity determined by the most
limiting mineral. Besides the most limiting min-
eral, all other minerals were fed in surplus and
the excessive amounts were excreted in the urine
or faeces because most mineral intake above the
requirement level is excreted in faeces and/or
urine. This concept is being used to formulate
diets for dairy cows in the California Central
Valley. In order to reduce salt excretion by dairy
cows, the sodium chloride, or the choice of
sodium source, is now available separately from
the mineral premix and the amount of salt fed is
determined by the sodium requirement, thus
reducing sodium excretion. The concept can be
applied to any mineral, or more generally, to any
nutrient source that is competitively priced or
environmentally regulated.
Feed management practices are key ele-
ments in a livestock production unit operation.
A better understanding of feed nutrient compo-
sition and animal nutrient requirements can
lead to a more precise diet formulation, reducing
dietary costs and excessive animal mineral and
nitrogen excretion. Precision feeding concepts
can be used in systems in which the imple-
mentation of these techniques is economically
and practically feasible. Variability of nutrient
requirements for a population of animals can be
examined and feeding strategies can be exam-
ined from a probabilistic perspective. Feed nutri-
ent composition can be characterized according
to nutrient availability at different levels of ani-
mal productivity and intake. And, finally, the
feeds selected for diet optimization, for example
mineral sources, can have a great impact on the
amounts of nutrients fed and excreted.
Optimization Techniques Applied
to Diet Formulation
Modelling optimization techniques have been
extensively used in agriculture since the early
1960s (Dent, 1964; Black and Hlubik, 1980;
Kennedy, 1986). Dynamic programming and
linear programming are the most frequently
used techniques in agricultural systems man-
agement. The objective of this section is the pro-
vision of a mathematical description of these
techniques and applications to diet formulation
and to the minimization of environmental
impacts from livestock. Dynamic programming
is introduced, and linear programming and
extensions of the simplex algorithm, such as sto-
chastic programming and multi-criteria pro-
gramming, are examined. The last part of this
section describes strategies for implementing
regulatory policies in the diet formulation model
and introduces an example of model-driven
methane mitigation strategies in a dairy herd.
