Synthesis of animal feed formulation techniques: Linear and Non-Linear model

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Synthesis of animal feed formulation techniques: Linear and Non-Linear model

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     FEATURE                                                                                                                                                                                                                                                                               FEATURE

                                                                                                                                                       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
                                                                                                                                                                                                         being used.
                                                                                                                                                                                                             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
                                                                                                                                                       ingredients limit.
                                                                                                                                                                                                         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
                                                                                                                                                                                                    Immunoaffinity Columns
      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
                                                                                                                                                                                                    RIDASCREEN®FAST Zearalenon
                <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-
                                                                                                                                                                                                    Test Cards
                                                                                           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.               
  a linear programming model for the diet                      Both approaches used the Excel Solver                 The rate of growth and the efficiency      
                                                                                                                                                                                                                                                                                                                Asia                                                Europe
  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
                                                                                                                     To maximize
                                                                                                                     Subject to:
                                                                                                                                                                                                                                                                                               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
                                                                                                                                                                                                                                                                                               of experience.
       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
  according to given information as                       reaching this nutrient value does not have an          Optimising feed for weight gain                                                                                                                                               backed by Westeel’s superior service and product support.
      And the objective function is to minimise:. influence on a special diet least cost within                      Non-linear programming is used to max-                                             SIZERS                                                                                 ƒ Commercial Grain Storage Bins (up to 674,000
                                                                                                                                                                                                                                   CONVEYORS                                                     bushels/18,343 tonnes)
  It represents formulation of a complete a particular ‘b’ value. This paper also dis-                           imise the body weight of sheep under the
  linear diet model.                                      cusses the development of direction of feed            given experimental conditions and satisfying            The first name in                                                                                                     ƒ On-Farm Grain Storage Bins (starting from
                                                          formulation-optimizing techniques in China             NRC feeding standards (Pratiksha, 2006).                processing & recycling                                                                                                  2,390 bushels/65 tonnes)
  Well-balanced ration                                    [Xiong BenHai, Luo QingYao, Pang ZhiHong].                 To sum up, an effort has been made to               Mogensen                                                                                                              ƒ Aeration Systems
      A number of models have been derived                     The importance of Non-linear Programming          give a new dimension to the already existing                              A Division of                                                                                       ƒ Bin Unload and Grain Handling Systems
  for different objective of study and con- Applications is growing due to rapidly increas-                      multi-dimensional non-linear models and its                               Grantham Engineering Ltd                                                                            ƒ Systems Engineering and Design
  strains.                                                ing sophistication of managers and operation           use to formulate a real-world problem of                                  Harlaxton Road, Grantham,                               SCREENS

      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
  plicated set of nutrient requirements to give mathematical models, as well as to the growing                   of the animal and to solve it as well.                  Tel               +44 (0)1476 566301
  a relatively well-balanced ration [VandeHaar availability of computer routines capable of                          This objective supports the all over effect of      Fax               +44 (0)1476 590145
  and Black, M. J., 1991].                                solving large-scale nonlinear problems.                nutrient ingredients simultaneously on the animal       E-mail                                                                                  P.O. Box 792, 450 Desautels Street Winnipeg,
      The principal objective in the application               While formulating a mathematical model            yield and weight gain of an animal. It has already                                              COMPACTORS                                            Manitoba, Canada R3C 2N5 Tel: (204) 233-7133
                                                                                                                                                                                                                                                                                               Fax: (204) 235-0796
  of LP to feed formulation is the production related to real life problems, many different                      been accepted that non-linear programming has
  of least cost rations that will produce satisfac- situations lead to non-linear formulation of                 a great deal of future prospects as it has direct                                                                                                                   
  tory results.                                           constraints and objective function.                    practical utility in the field of animal nutrition.
                                                                                                                                                                                                                                                                                               Management Systems Registered to ISO 9001:2008. MF20484-0511

  12 | may - June 2011                                                                                                      Grain  &feed millinG technoloGy                  Grain    &feed millinG technoloGy                                                                                                                                    may - June 2011 | 13

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                        •    Conditioning
                                                                           •       Synthesis of
                             as part of the                                        animal feed
                             pelleting process
                                                                            Linear and Non-Linear

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Description: It is well known fact that nutrition is the most important factor for animal growth, reproduction and proper maintenance.