Digital Re-print - May | June 2011
Synthesis of animal feed formulation techniques: Linear and Non-Linear model
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sustainable and provides nutrient and energy two nutrient requirements using two the nutrient requirements of the animal. But
requirements of a given species for a given different feed ingredients. in practice, it is really not possible to use it
response. A two-by-two matrix is set and a series of always, as it is a time and money consuming
The reliability of knowledge on the quality equations are established to find the solution method.
of ingredients and the constraints; both have of the problem. Square method is relatively Linear programming method is widely
an impact on the quality of diet formulation. easy and simple to work on. It is used with used for animal diet formulation.
Reliable and updated database on chemical only two nutrient ingredients. To use this It is a method to determine the least
composition, physical characteristics and bio- method, level of nutrient being computed cost combination of ingredients
availability information on feed ingredients is should be intermediate between the nutrient using a series of mathemati-
essential for diet formulation. concentrations of the two feed ingredients cal equations. This method
Synthesis of animal feed formulation techniques: Including all the information diet is for-
mulated to achieve the objective of least
This method is used to satisfy only one
provides a number of pos-
sible solutions to each series
Linear and Non-Linear model cost with adequate nutrients. There are
three important aspects while considering
the diet formulation, cost, nutrient level and
nutrient requirement. This method has lim-
ited use as it is based on certain limitations.
Simultaneous equation method is also
has limited use, because it is used for two
of equations, but when the factor of cost
is applied, there can only be one least cost
This method is in practice for a long
by Dr Pratiksha, Assistant Professor, School of Applied Sciences, Gautam Buddha • Different kinds of conventional methods nutrient ingredient combination diet. It uses time to give solutions to the problem of
University, Greater Noida, India to formulate the diets are: simple algebraic method to solve these diet formulation considering the cost factor
• Trial-and-error method equations. associated with it. Before using this technique
• Two by two matrix method Trial and error method is generally used for ration formulation, certain information
t is well known fact that nutrition Levels of nutrients and micro nutrients (that is, two percent • Square method to formulate rations for swine and poultry. should be available about the important
is the most important factor A lot of work has been done in the area calcium or vitamin A deficient). • Simultaneous equation method This method tries different diets and manipu- nutrient ingredient to be included in diet.
for animal growth, reproduc- of finding different levels of nutrient ingredi- Two types of formulations are used in • Least cost formulation lates it until the nutrient requirements of the First, all available ingredients should be
tion and proper maintenance. ent in diet and formulation. On the basis of diets; fixed formulation and variable formula- • Linear programming method animal are met. This method makes possible listed with associated cost factor. Tables
percentage of nutrient level, components are tion. Fixed formulations are used for the • Two-by-two matrix method solves the formulation of a ration that meets all representing the nutrient composition of
Dietary information is essential for con- included in animal diet. diets where the ingredient composition is
ducting research and performing experi- No one feed ingredient can supply all of known and is not altered. It decreases the
ments. The diet should supply all the essen- the nutrients and energy need for the best amount of variation in dietary constituents
tial nutrients and adequate amount of energy growth. Diet should contain a mixture of that could jeopardise experimental results or
to satisfy requirement for body growth, well feedstuffs, vitamin and mineral premixes that have a negative influence on the well being
health conditions and animal yields. provide the right essential nutrients as well of animals.
Another important aspect of diet is to as the energy necessary to use the nutrients. To assure nutrient specifications, ingredi-
maintain environmental and flesh quality. The amount of each feed ingredient ent standards for nutrient concentrations are
A number of feeding standards have been depends on several factors, including nutrient established prior to the procurement of the
defined and practiced for a long time. requirements, ingredient cost, availability of ingredients. Dietary contaminants are con-
Conventional and non-conventional feed each ingredient, and processing character- trolled by procuring ingredients according to
resources are used to formulate the diet for istics. strict contaminant standards and by testing
ruminant livestock in developing countries. For formulating diets for experimental ingredients for contaminants of concern.
While formulating the diet, tendency is to purposes, it is necessary that all ingredients Variable formulations may allow for
reject the poor quality feeds that are avail- are controlled for all essential nutrients. changes in ingredient composition or con-
able in vast quantities. But, under practical conditions, such a centration. These changes in formulations
The objective is to use locally available control is difficult to set forth and mostly could lead to the incorporation of lower
feed resources effectively by applying basic restricted to rapid proximate composition quality, less costly ingredients, where unde-
nutrition principles to optimise animal yield, analyses. Specific attention should however sirable, non-assayed components, such phy-
health and weight. The alternative approach be given to obtain guarantees for absence of toestrogens, may be introduced.
is to use feeding standards that would ensure anti-nutritional factors. Variable formulated diet makes neces-
that the production system matches the Diet given to laboratory animal may be sary adjustments according to raw material
of two types: Natural Ingredients macronutrient variability, which could cause
Example 1: Example to formulate a linear or Purified Ingredients. Natural significant variation in the finished product.
programming model for the diet formulation. ingredient diets support reproduc- The largest volume of laboratory animal diet
Nutrient A B C D tion, growth, and maintenance of produced is comprised of agricultural com-
laboratory animals. Purified diets modities like corn, wheat, plant by-products,
are made of refined ingredients to soybean meal, oats, alfalfa meal, and animal
Gram 70 30 20 4 minimise nutrient variation, certain derived ingredients such as fish meal and
environmental contaminants and meat and bone meal.
available resources. the presence of active compounds naturally
The diets should be formulated so as it occurring in plants. There are different methods to
contain all essential nutrients in adequate Generally, purified diets are used for diet formulate animal diet
quantities. The diet should be supplied in a formulation as they can be manipulated to Diet formulation includes balance mix-
form, which is easily accepted by the cultivat- contain very high or low levels of specific mac- ture of ingredients which are economically
ed animal and should have little adverse envi- ro-nutri-
ronmental impact. The strategy of choosing ents (that
the feed ingredients is based on locally is, 60 per- Example 2: The ingredients have the following nutrient values and cost -
available feed resources and it requires the cent of A B C D Cost/Kg.
understanding of the relative roles and nutri- kcal from
ent needs of the two-compartment system fat or six
represented by the microorganisms in the percent Ingredient 1 (gram/kg) 140 90 40 ---- 50
rumen and the host animal. protein) Ingredient 2(gram/kg) 200 120 20 30 60
10 | may - June 2011 Grain &feed millinG technoloGy Grain &feed millinG technoloGy may - June 2011 | 11
R-Biopharm Rhône Ltd.
feed ingredients should be analysed properly. A nutrition program was developed for The application of non-linear program-
Nutrient levels are estimated from a variety high producing dairy herds to attain efficient ming to the field of animal nutrition is R-Biopharm – an integrated
of sources including published commodity and profitable levels of milk production growing day-by-day. The main goal in making
compendium data, wet chemistry testing of
approach to quality
[Sklan, D. and Dariel, I., 1993]. feedstuffs is to increase profits of animal
raw materials and finished product testing. A model was developed to represent the production by increasing the nutritional value mycotoxin analysis
Nutrient losses due to heat treatment and efficiency of nutrient use and its relationship to of the feedstuff or a mixture of feedstuffs.
mechanical processes during manufacturing, profitability on dairy farms [Tedeschi, L. O, 2004]. Feedstuffs containing 20 percent crude
or post-production effects of irradiation A cost analysis spreadsheet and validation of protein or more are considered protein
or autoclaving are not routinely taken into that spreadsheet on milking and custom heifer supplements. Protein supplements may be
consideration in these estimates. operations was developed [Guevara V.R., 2004]. classified as animal or plant proteins. Animal
After this nutrient requirement for the Lead factors are used in computerised ration proteins are generally considered to be AFLAPREP® EASI-EXTRACT® Zearalenone
particular species and ingredient limitation formulation programs developed at Virginia higher quality than plant proteins. EASI-EXTRACT® Aflatoxin FUMONIPREP®
AFLAPREP M® DONPREP®
should be given proper consideration. After Tech to increase milk production above a herd The main plant protein sources used AFLAOCHRA PREP® DZT MS-PREP®
collecting all the necessary information, a or group average for which total mixed rations in catfish feeds are oilseed meals, such as OCHRAPREP® EASI-EXTRACT® T-2 & HT-2
are formulated soybean meal, cottonseed meal, and peanut
for group feed- meal. Some other oilseed meals could be Enzyme Immunoassays
Table 1: Crude protein (CP) RIDASCREEN®FAST Aflatoxin M1 RIDASCREEN®FAST Zearalenon SC
ing [Stallings, C. used but are not generally available on a RIDASCREEN®FAST Aflatoxin RIDASCREEN®FAST DON
CP level Ingredients RIDASCREEN®FAST Aflatoxin SC RIDASCREEN®FAST DON SC
C; Mcgilliard, M. timely basis and at an economical cost per RIDASCREEN®FAST Ochratoxin A RIDASCREEN®FAST T-2 Toxin
L]. Chance con- unit of protein. Table 1 represents levels of RIDASCREEN®FAST Citrinin RIDASCREEN®FAST Fumonisin
<25% Whole cereals, pulses, oil seeds strained program- crude protein in different meals.
ming is used to Lateral Flow Tests North America
25-50% Oil seed meals
formulate com- Vitamins and minerals RIDA®QUICK DON RIDA®QUICK Aflatoxin
Animal by-products (meat meal, blood meal), plant mercial feeds for Vitamin and mineral premixes are gener- RIDA®QUICK Fumonisin
protein concentrates, isolates, extractives
animals [Britt, J. ally added to feeds. They provide more vita-
S; Thomas, R. C; mins and minerals than what is needed for
AFLACARD® Total AFLACARD® T20
mathematical model is derived with Linear Speer, N. C; Hall, M. B., 2003]. growth to make up for any losses that may AFLACARD® B1 OCHRACARD®
Programming specifications. Now method of A stochastic-linear program Excel work- occur during feed manufacture or storage.
LPP is used to solve it and it provides solu- book was developed that consisted of two They are made from high quality ingre- R-Biopharm Rhône Ltd.
Block 10 Todd Campus
tion for the feed mixture. worksheets illustrating linear and stochastic dients, using forms of vitamins and minerals West of Scotland Science Park
Acre Road, Glasgow, Scotland. G20 0XA
Let us consider an example to formulate program approaches. which animal can readily digest. www.r-biopharm.com
a linear programming model for the diet Both approaches used the Excel Solver The rate of growth and the efficiency email@example.com
formulation. Suppose 1 kg of feed mix must add-in. Excel spreadsheet was set up so that the with which the nutrients are utilized mainly
contain a minimum quantity of each of four calculated margin of safety (MOS) value, accord- depend on three factors, which may be used GFM05 Mog65th#2 Sizing 124x85:GFMT 132x90 01/02/2011 13:38 Page 1
nutrients as in Example 1: ing to the requested probability, was the same to maximize it8. Accounting all these facts,
Now objective is to find the amounts of for both the linear and stochastic programs. weight gain of an animal depends upon:
active ingredients and filler in one kg of feed A multiple-objective programming (MOP) Digestible crude protein MAKE SURE IT’S A…
mix. Now it is considered as one kg of feed model was applied to the feed formulation Total digestible nutrient
mix is made up of three parts - ingredient 1, process with the objectives of minimising Digestible dry matter
ingredient 2 and filler so let: nutrient variance and minimising rations cost. Metabolic weight is used as a base for For all your SIZING and other SEPARATORS
A study was conducted to introduce a whole of the calculations. Moir had earlier vibratory equipment needs –
dual model in an original linear program to reported that a level between 200 and 300K. whether you’re specifying,
x1 = amount (kg) of ingredient 1 in obtain the shadow prices of resources that Cal DE per Kg0.75 is generally encountered purchasing or installing –
one kg of feed mix take part in optimisation, in feed formulation. while studying the intake in growing animals. make sure it’s a MOGENSEN…
x2 = amount (kg) of ingredient 2 in The shadow prices of nutrients resourced A non-linear model is defined as:
one kg of feed mix
x3 = amount (kg) of filler in one kg of
showed degrees of influence of a diet's least
cost when increasing or decreasing expected
Our grain storage systems
feed mix diet nutrient ‘b’ values of a diet.
The higher the shadow prices of a nutri-
I=1,2,3,…………….m, j=1,2,3,……….l come with six continents
where x1 ≥ 0, x2 ≥ 0 and x3 ≥ 0 Where f(x), g(x) and h(x) are functions
ent resource, the more obvious its influence defined on, X is a subset of and x is a vector
on least cost. When the shadow price of a of n components. SPREADERS Westeel offers a full line of professionally engineered grain
Now the nutrient constraints are set up kind of resource equals to zero, it means that storage products and systems for international sale – all
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The LP model can be solved for a com- researchers in implementing decision oriented optimising the feed in terms of weight gain Lincolnshire NG31 7SF, UK
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The principal objective in the application While formulating a mathematical model yield and weight gain of an animal. It has already www.mogensen.co.uk COMPACTORS Manitoba, Canada R3C 2N5 Tel: (204) 233-7133
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tory results. constraints and objective function. practical utility in the field of animal nutrition.
Management Systems Registered to ISO 9001:2008. MF20484-0511
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