Least Cost Dairy Cattle Ration Formulation Model Based on the Degradable Protein System

L e a s t C o s t Dairy Cattle R a t i o n F o r m u l a t i o n M o d e l B a s e d o n t h e D e g r a d a b l e Protein S y s t e m J. D. O'CONNOR,1 C. J. SNIFFEN,1 D. G. FOX,1 and R. A. MILLIGAN2 Gornell University Ithaca, N¥ 14853

AI~TR&G'T Protein requirement equations for lactating dairy cattle based on 1985 NRC recommendations were incorporated into a linear programming model for computerized least cost dairy ration formulation. To incorporate the 1985 NRC protein system into a linear programming model for dairy cattle diet formulation, transfer activities were used in the model to represent variables in the protein system and accounting constraints were used to represent the biological relationships that define the protein requirements. Example dairy ration formulations based on the 1985 NRC protein system are presented for three milk yields. INTRODUCTION

Computerized diet formulations for cattle are typically based on NRC recommendations and are usually aimed at maximizing production. The 1978 NRC protein requirements for dairy cattle included only amounts of total CP to be fed (11). No attempt was made to establish standards for different types of protein required in diets. The 1985 and 1988 NRC protein systems recommend optimum mixtures of types of proteins, rumen degraded and escaped, in diets needed to improve N utilization and to maximize the productive efficiency of ruminants. The 1985 NRC committee integrated current data and concepts in ruminant N metabolism and proposed a systematic and quantitative approach for balancing diets for ruminants (12). The system takes into account factors affecting N metabolism such as feed protein composition and distribution, ruminal protein digestion

Received August 2, 1988.

AcceptedApril28, 1989. 1Departmentof AnimalScience. 2Departmentof AgriculturalEconomics. 1989 J Dairy Sci 72:2733--2745

rates, feed tureen passage rates, feed intake, TDN, rumen bacterial production, bacterial composition, efficiency of protein uptake by bacteria, digestibility of feed and bacterial protein, and recycled nitrogen. Incorporation of the 1978 NRC crude protein standard into computerized diet formulation models was managed by a single equation (constrain0. The 1985 NRC (12) and the 1988 NRC (13) publications list equations for quantifying protein requirements but do not give information on how to incorporate these equations into linear programs (LP) for computerized ration formulation. A system of equations must be used in a LP model to represent the 1985 and 1988 NRC protein standards. The purpose of this report is to illustrate how to structure least cost ration models that incorporate the 1985 NRC protein system for dairy cattle. The same structure applies to the 1988 NRC protein system; however, changes in coefficients are required to implement the 1988 NRC protein system, Example least cost ration formuiafions, costs, and protein requirements for three milk yield levels are presented based on the 1985 NRC protein system. MATERIALS AND METHODS

Table 1 lists the system of equations necessary to determine absorbed, rumen degraded, undegraded, and dietary CP requirements according to the 1985 NRC protein system (12). Requirements are linear and factorial in nature with respect to a single day and thus appear easily amenable to a LP framework. The 1985 and 1988 NRC protein requirements, however, are dependent on diet and rumen quantities that are not known until the diet has been formulated (e.g., ration DM, TDN consumed, indigestible DM, and bacterial quantifies). To incorporate the 1985 or 1988 NRC protein standards in a LP model, a system of equations defining dry DM, TDN, and protein balance equations must be included in the model.

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O'CONNOR El" AL.

TABLE 1. Equations describing the 1985 NRC protein system for dairy cattle. 1,2 Requirement equation

RPA

= (.2 x W ' 6 ) , ~ N M P A = (2.75 x W - ~ ) / M P N M P A (GAIN x (268 - 29.4 x ((I-IF x (.0783 x ((.891 x (FS x W)) "75) x ((.956 x GAIN)I'll9)))/ = (.956 x GAIN3))))/RPNRPA

YPA LPA

= =

SPA UPA

YBW x ( E X P (8.5357 - 13.1201 x EXP(-.00262T) - .002621" ) ) / Y P N Y P A I000 x P P x .01 x M I L K / L P N L P A

IF DBW <0 THEN DPA = 256 x DBW IF 12~,W >0 THEN DPA = 400 x DBW DM

= ~ l.O x F D j j=l j=l j=l D M - .92 TDN FPAIDM x IDM 6.25 (-.03186 + .02612) TDN BTPBCP x BCP BCP/BCPRAP DBPBTP x BTP SPA + UPA + FPA + RPA + YPA + LPA - DPA AP - DBP DUP/DUPUIP

IDM FPA B(~ BTP RAP DBP AP DUP UIP

= = = = = = = = =

IP RIP DIP

= (RAP + UIP)/(I + RIPIP) = RIPIP x CP = RAP RIP -

1When forage DM in the diet in greater than 40%. 2See Table 2 for definition of terms.

The equations in Table 1 that describe the 1985 NRC protein system are not directly usable in a LP diet model and must be rearranged and rewritten to conform to a LP framework. Variable and parameter names used in the model are explained in Tables 2 and 3, respectively, using 1985 NRC parameter and variable naming conventions (12). Table 4 lists the DM, TDN, and protein material balance equations expressed after the quantity (variable) from the left side of equation is subtracted from the expression on the right side and then the right side of the equation is set equal to zero. The resulting equations form a series of DM, TDN, and protein material balance equations. Once these relationships have been expressed in this manner, incorporating the 1985 NRC protein system in an LP model is accomplished by including a transfer activity for each variable in the protein system and an accounting constraint for each equation in Table 4. To obtain the proper diet and rumen information within an LP model, transfer activities representing variaJournal of Dairy Science Vol. 72, No. 10, 1989

bles in the system and accounting constraints defining the equations must be added to the model. Transfer activities, which store values for variables in the protein system, include feed intake, TDN intake, indigestible DM intake, bacteria, and protein required. Accounting rows of constraints define the equations that describe the biological relationships between the variables. The general least cost ration model for the 1985 NRC protein system can be stated algebraically as: Minimize Z= Subject to AX >, =, or < B X>O

C'X

COMPUTERIT~D DAIRY DEGRADABLE PROTEIN MODEL

2735

TABLE 2. Variable names used in least cost ration model based on the NRC (1985) protein system. Name Diet A C CP DIB DM ~4

Unit

Description

g/d g/d g/d g/d kg/d kg/d kg/d kg/d g/d

Protein in diet that is rapidly degraded in mmen Bound protein in diet Crude promin in diet True protein in diet that is degraded in rumen Dry matter in diet Amount of feedstuff j, DM basis Indigestible DM intake Total digestible nutrients intake True protein in diet that is not degraded in tureen

TDN ins Animal DBW kg/d GAIN kgJd MILK kg/d T d W kg Y'BW kg Protein tcqnitcmcnts AP g/d DIP g/d DNP g/d DPA g/d DUP g/d FPA g/d IP g/d LPA g/d MPA ! Ud NCP g/d trip g/d UPA g/d RPA g/d SPA g/d YPA g/d Rumen BCP2 g/d BTP2 g/d RAP2 g/d DBP2 g/d mr g/d

Body reserve change (fat) Rate of growth (protein) Milk yield Days pregnant Animal live weight Expected calf birth weight Absorbed protein Degraded intake (crude protein) Digestible nucleic acid (crude) protein Difference protein (absorbed) Digestible undegraded (crude) protein Metabolic fecal protein (absorbed) Intake (crude) protein Lactation protein (absorbed) Absorbed protein less lactation and metabolic fecal Nucleic acid (crude) protein Undegraded intake (crude) protein Urinary protein (absorbed) Retained protein (almorbed) Surface protein (absort~) Conceptus protein (almort~) Bacterial crude protein Bacterial true protein Rumen available protein Digestible bacterial true protein Rumen influx (crude protein)

1Differs from NRC definition. 21ncludes protozoal contributions.

where: Z= C=

least cost ration (S/d), n x 1 vector o f objective function coefficients (e.g., feed prices) ($/kg/ d), A = m x n matrix of technical coefficients (e.g., TDN, CP, and protein degradability content of feeds), B = m x 1 vector o f nutrient or other restrictions (e.g., protein required), and

X = n x 1 vector of activities (e.g., feedstuffs, nutrient intake, bacterial CP, and protein required). The basic least cost ration model that describes the 1985 N R C protein system accounts for animal, economic, feed, and rumen factors. The model contains variables for the intake o f DM, TDN, and indigestible DM. In addition, the model contains variables for rumen bacterial protein quantities such as CP and true protein production, digestible bacterial protein, Journal of Dairy Science Voi. 72, No. 10, 1989

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TABLE 3. Parameter names used in least cost ration model based on the 1985 NRC protein system. Name Diet AIj A2j A3j A4j ASj AA~) _Agj ~. kdj Ankp~al

Unit

Description

kg DM/kg g/kg D M kg/kg CP kg/kg CP kg/kg CP kg/kg DM mcai/kg DM kg/kg DM kg/kg DM $/kg DM $/kg MILK %/h

Dry matter content of foodstuff j Crude protein content of foodstuff j, DM basis "A" fraction protein content of foedstuff j, DM basis "B" fraction protein content of fccdstuff j, DM basis "C" fraction protein content of foodstuff j, DM basis Total digestible nutrient content of fceMstuffj, DM basis (lx) Net energy for lactation content of fccdstuff j, DM basis (3x) NDF content of fcedstuff j, DM basis Forage content of feedstuff j, DM basis Cost of the feed.m~ j, D M basis Price received for milk Rate of ~ degradation of the "B" protein fractionof the feedstuffj Rate of ruminal passage of the fee&tuff j

%/h

BF % FS g/g HF g/g PP % Protein requirements LPNLPA g/g MPNMPA g/g RPNRPA g/g YPNYPA g/g Rumen BO'RAP g/g BTPBCP g/g DBPBTP g/g DNPNCP g/g DUPUIP g/g FPAIDM g/g Pal,tP g/g

Milk fat perr.emage Frame size adjustment factor Hormonal adjuvant adjustment factor Milk protein percentage Efficiency of protein use Efficiency of protein use Efficiency of protein use Efficiency of protein use

for for for for

lactation maintenance gain gestation

Bacterial CP trapped from mmen available protein Bacterial true protein per bacterial crude protein Digestible bacterial protein per bacterial true protein Digestible nucleic acid protein per nucleic protein Digestible undcgradcd protcin per undegradcd intake protein Metabolic fecal protein required per indigestible dry matter in diet Rumcn influx (CP) protein required as a percentage of intake CP

and rumen available protein. Finally, variables are included that determine the dietary, rumen degraded, and undegraded CP requirements based on the aforementioned variables. It is these structural features that separate least cost ration models for the 1985 NRC protein system from more traditional least cost diet models for cattle ration formulation.

Anlnml-Depenclent Factors The model requires information about animal weight and estimates of productive status. Information about daily milk yield, daily body reserve change during lactation, and milk fat or milk protein percentage is required to determine lactation protein requirements. Either a milk true protein percentage or an estimate of protein percentage based on milk fat percentage can be used (11). Information about expected Journal of Dairy Science Vol. 72, No. I0, 1989

calf birth weight and days pregnant is necessary if gestation requirements are to be included in the model. The 1985 NRC assumes an expected calf birth weight of approximately 34 kg (12). Information about animal frame size, rate of gain, and whether or not the animals have been implanted with hormonal adjuvants is also required if the diet is to be formulated for growing cattle. Metabolic efficiencies of protein utilization recommended by the 1985 NRC system for maintenance, lactation, gestation, and growth are: 67, 65, 50, and 50%, respectively (12). Table 5 lists animal-dependent factors: 1985 N R C assumed factors (12) and variables used in example formulations.

FeecJ-DepenclentFactors Protein in the digestive systems can be represented in terms of three major fractions: A, B,

COMPUTERIZED DAIRY DEGRADABLE PROTEIN MODEL TABLE 4. Dry matter, TDN, indigestible dry m a t t e r , a n d l~otcin material balance equations r e p r e s e ~ the 1985 N R C protein system. Material balance equation

~ 1.0xFDj-DM=0. j..t

j-i DM - .92 TDN - IDM = 0. FPAIDM x IDM - F P A = 0. 6.25 (.02612) TDN - BCP = 6.25 (.03186) BTPBCP x BCP - BTP = 0. BCP/BCPRAP - RAP = 0. DBPBTP x BTP - D B P = 0. MILK

=

MILK

(1000 C01) PP/LPNLPA MILK - LPA = 0. MPA = SPA + UPA + RPA + YPA - DPA FPA + LPA + MPA - AP = 0. A P - DBP- DUP = 0. DUP/DUPUIP - UIP = 0. RIPIP x CP - RIP = 0. RAP

+ U I P - R I P - IP = 0.

RAP - RIP - DIP = O.

and C (12). The A fraction, rapidly degraded intake protein fraction, contains most NPN, free amino acids, small peptides, and other protein that is rapidly converted to ammonia. This fraction can be measured by solubility in a buffer solution or by using the rate of ruminally degraded protein in 1 to 2 h as determined by in situ methods (12). Rapidly degraded protein content of feeds used in example formulations were obtained from Erdman et al. (5). The C fraction, bound protein, contains protein that is unavailable to the animal (i.e., n o t used by rumen bacteria or digested in the intestines). Protein in this fraction is assumed to pass from the rumen unaltered by bacterial intervention. This fraction can be measured using acid detergent insoluble nitrogen or by the pepsin insoluble nitrogen method (12). Estimates of unavailable protein content o f feeds used in example formulations were obtained from Erdman et al. (5).

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The B fraction protein can be found by difference once the A and C fractions are known. Rates of ruminal protein degradation of the B fraction for various feed ingredients can be obtained from Erdman et al. (5) or Nocek and Russell (14). Rates of rumen passage for feedstuffs are required to determine optimum mixtures of rumen degraded and escaped protein in dairy cattle. Rates of rumen passage can be obtained from Harmell and Satter (5), Colucci et al. (2), Synder et al. (16), Eliman and Orskov (4, 5), and Erdman et al. (5). Many protein supplements and most feedstuffs have a ruminal passage rate within the range of .03 to .07 h -1 (13). Rates of ruminal passage were obtained from Erdman et al. (5). The model also requires information about DM, NEI, TDN, NDF, and CP content of feeds. The TDN content of feeds at maintenance should be used for both lactating and growing animals. Dry matter, NE1, TDN, and CP contents of feeds were obtained from the 1978 NRC publication (11). The NDF composition of ingredients was obtained from the 1988 N R C publication (13); NDF content of brewer's and distillers grains was discounted to 12% according to Mertens (10). Table 6 lists feeddependent factors used in the example formulations. Rumen and Bacterlal-Oependant Factors The 1985 N R C rumen and bacterial parameter names, descriptions, units, and estimates are listed in Table 7. Economic Factors Feed costs ($/1000 kg) are the only economic factors considered and were representative of feed costs for feedstuffs, June 1988. Costs assigned to feedstuffs are listed in Table 6. Objective Funotion In formulating least cost diets, the objective is to find the combination of feedstuffs that minimizes the cost of the diet while satisfying the imposed constraints. Feed costs per kilogram of DM are the only nonzero objective function coefficients in the model. Journal of Dairy Science Vol. 72, No. I0, 1989

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TABLE 5. Animal-dependent factors used in least cost ration model based on the 1985 NRC protein system. Name

Variable/parameter

Unit

High

Milk production Medium Low

Live weight Frame size factor Milk yieM Milk fat percentage Milk protein percentage Body reserve change Days pregnant Expected calf weight Rate of growth Hormonal adjuvant factor Maximum D M intake

kg kg/kg kg/d % % kgtd d kg kg/d kg/kg kgld

600 1 26.30 3.5 3.0 0 0 34 0 1.0 22

600 1 27.22 3.7 3.3 0 90 34 0 1.0 20

Maintenance Lactation Pregnancy Gain

g g g g

Requirement

g FPA/kg IDM 90

Productive variables/ parameters:

W FS MILK BF

PP DBW

T YBW GAIN HF DMImax Metabolic

600 1 18.14 4.0 3.5 0 150 34 0 1.0 18

parameters:

MPNMPA LPNLPA YPNYPA RPNRPA .50 Metabolic fecal nitrogen: FPAIDM

MPN/g MPA LPN/g LPA YPN/g YPA RPN/g RPA

Conl~rilnbl The least cost ration model that incorporates the 1985 NRC protein system includes nutrient accounting conswaints and nutrient constraints. Nutrient Accounting Constraints As stated, NRC 1985 protein requirements are determined in part by dietary and ruminal quantifies that are not known until the ration has been formulated. To obtain the necessary information within a LP model for determining protein requirements, accounting constraints for DM, nutrient, and bacterial quantities need to be included. The equations in Table 4 describe the accounting constraints used in the model. Once the above accounting constraints have been incorporated in a LP model, nutrient constraints can be included to formulate diets. Nutrient Conltmln~ In a diet model, nutrient constraints compare the available nutrients in the diet with nutrient requirements of an animal (8). Nutrients conJotrnal of Dairy Science Vol. 72, No. 10, 1989

.67 .50 .65

straints included minimum NEI, minimum NDF, maximum NDF, exact UIP, and exact DIP. A constraint for NE 1 based on the 1978 NRC energy requirement (11) was included so that the diets formulated contained the minimum amount of energy needed for production. The 1978 N R C (11) gives the NE 1 requirement (exclusive of energy required for pregnancy, gain, and weight change during lactation) as: NEI = .08 .75 + (.35 + .1 BF) MILK. Because milk is a decision variable in the model, the NE 1 constraint must be written as: n

X

A7j x F D j - (.35 + .1 BF) MILK

j=l

> .08 W 75 A minimum NDF constraint was included in the model to ensure that diets contained adequate fiber for rumen function. The minimum requirement for N D F was assumed to be 1.1%

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COMPUTERIZED DAIRY DEGRADABLE PROTEIN MODEL TABLE 6. Feed-dependent factors used in least cost ration model. Hay crop Soybean Ground silage meal 44% corn

Item

Iutemational feed number: Analysis: Forage, % DM DM, % NE1, Mcal/kg TDN, % DM NDF, % DM CP, % DM A, % CP B, % CP C, % CP Calculated degradability: kd, %/h kp, %/h DIP, % CP UIP, % CP Costs: $/kg NRC (1985) degradability: DIP, % CP UIP, % CP

Corn silage

Urea

Brewers grain

Distillers grain

5.04-604

4-21-018 3-02-823 5-05-070 5.02-141 5-02-843

100 40 1.30 59 50 17.2 64.4 31.2 4.8

0 89 1.86 81 14 49.6 17.0 83.0 0

0 89 2.03 88 9 10 24.1 75.9 0

50 35 1.59 70 51 8 65.2 20.7 14.1

0 99 0 0 0 281 100 0 0

0 92 1.50 66 12 26 25.5 62.5 12

0 92 2.03 88 12 29.8 50.1 41.1 8.8

1.6 4.5 72.5 27.5

7.8 4.8 68.4 31.6

4.4 4.4 62.0 38.0

3.4 4.6 74.0 26.0

0 0 100 0

5.2 4.7 58.3 41.7

5.8 4.6 73.0 27.0

.0385 80 20

.330 72 28

.110 35 65

o f body weight (10): I1

% x F Dj _> 1.1 W.

.033 73 27

.301 100 0

(10).

.231 38 62

47

53

more slowly degraded B fraction. The conswaint for meeting the degraded intake protein requirement exactly is: A + DIB-

A maximum N D F constraint was included in the model to ensure that diets did not exceed rumen capacity. The maximum limit o f N D F intake was assumed to be 1.2% o f body weight

.209

DIP =

O.

Using these accounting and nutrient constraints, diets can be formulated to provide optimum mixtures o f rumen degraded and undegraded protein, NDF, and NE 1 for lactating dairy cattle.

n

ASj x F Dj <- 1.2 W. j=l F o r optimum efficiency o f ruminants, the undegraded intake protein supplied b y the diet must meet or exceed the a n i m a l ' s need for undegraded intake protein. The constraint for providing the exact amount o f undegraded intake protein in the diet to meet the undegraded intake protein requirement is written as:

Forage Constraints Since the model is valid for situations where the roughage content o f the diet exceeds 40%

TABLE 7. Rttmen had bacterial-dependent parameter names, estimates, md units used by the 1985 NRC protein system. Parameter

UIB + C - UIP = O. The 1985 N R C protein system assumes that degraded intake protein in the diet is the sum o f rapidly degraded protein, A fraction, and the

name

Estimate

Unit

BTPBCP DBPBTP BCPRAP DNPNCP RIPIP

.80 .80 .90 1.0 .15

g g g g g

BTP/g BCP DBP/g BTP BCP/g RAP DNP/g NCP RIP/g IP

Journal of Dairy Science Vol. 72, No. 10, 1989

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O'CONNOR ET AL.

TABLE 8. Objective function and nutrient accounting constraints in least cost ration model for lactating dairy cattle based on the 1985 NRC protein system.

mmiz~:

J~ cj × F Dj

Subject to

Nutrient accounting consl~aints: [01]

~ 1 ×FDj-DM=O. j=~

[02]

~ A2j × F D j - C P = 0 . j-i

[031

j=l

[04}

):~

[05]

j=~

[061

j=l ASj x A2j x F Dj - C = 0.

[071

j=l A'6j × F Dj - TDN = 0.

[08] [09] [10]

DM - .92 TDN - IDM - 0. FPAIDM × IDM - FPA -- 0. 6.25 (,02612) TDN - BCP = 6.25 (.03186) BTPBCP x BCP - BTP - O. BCP/BCPRAP - RAP = O. DBPBTP x BTP - DBP = 0. MPA ~ SPA + UPA + RPA + YPA - DPA 1.0 MILK MILK (10 PP/LPNLPA) MILK - LPA = 0. FPA + LPA + MPA - AlP = 0. AP - DBP - DUP = 0. DUP/DUPUIP - UIP = 0. RIPIP x CP RIP 0. RAP + UIP - RIP - IP = 0. RAP - RIP - DIP = 0.

A3j x A2j x F D j - A = O . (kdj / (kdj + kpj )) x A4j x A2j × F Dj - DIB = 0.

~: <~pj/% + ~pj )> ×% × % × F ~ -

u.~-- o.

i

[11]

[121 [13] [14] [151

=

[16] [17] [18]

[19] [20] [21] [22]

-

=

o f the d i e t ' s D M (12), the f o l l o w i n g conslraint is needed: n

Z % × F Dj - 4 0

DM _, 0

j=l Computer Techniques

D e v e l o p m e n t o f the L P m o d e l s was greatly facilitated b y the use c o m m e r c i a l l y p a c k a g e d software. A Lotus 1-2-3 TM (9) w o r k s h e e t was

Journal of Dairy Science Vol. 72, No. I0, 1989

d e s i g n e d to set up the LP m o d e l formulation. T h e solution was d e t e r m i n e d using the Professional Linear P r o g r a m m i n g P a c k a g e TM by Sunset S o f t w a r e T e c h n o l o g y (15). T h e L P p a c k a g e reads the p r o b l e m formulation f r o m and writes the solution to the w o r k s h e e t file. T h i s software c o m b i n a t i o n s operates using the M S - D O S operating systems (version 2.0 or a m o r e recent version) and requires an I B M P C - c o m p a t i b l e m i c r o c o m p u t e r system with a m i n i m u m o f 512K RAM.

COMPUTERIZED DAIRY DEGRADABLEPROTEIN M O D E L

2741

TABLE 9. Nutrient and forage constraints in least cost ration model for lactating dairy cattle based on the 1985 NRC l~'Otein system. Nutrient constraints: [231

j-]

[241

j=l

[251

j=a

[26]

j=~

A7j x FDj - (.35 + .1 BF) MK,K _> .08 W"75 A + DIB-DIP=

[27] j=~l Forage constraints:

[281

UIB +

C-

0.

UIP = 0 .

A8jxFDj >- 1.1 W A8j x FDj < 1.2 W

g A9j x FDj -AO x DM > 0.

j=l

Lout Cost Lactating Dairy Cow Tableau

Tables 8 and 9 give the least cost LP model for dairy cattle using 1985 NRC-assumed factors. Table 10 depicts the least-cost tableau for implementing the 1985 NRC protein system for a mature, lactating cow yielding 36.3 kg milk/ d, 3.5% milk fat, and 3.0% milk protein. Example Lactating Dairy Formulations

Nutrient analyses and costs of feeds used in the sample formulations are listed in Table 6. For simplicity, it was assumed that no change in body reserves occurs during lactation. Diets were balanced exactly for rumen degraded and undegraded CP, minimum NEI, and maximum and minimum NDF. Example least cost ration formulations, ration costs, and protein requirements for three milk yields are presented in Table 11. RESULTS AND DISCUSSION

This paper describes how to incorporate the 1985 NRC (12) protein system into least cost ration models for computerized diet formulation for dairy cattle. The equations and tableau presented illustrate how to structure least cost ration models to calculate and balance diets for optimum mixtures of dietary, rumen degraded, and undegraded CP required according to the

1985 NRC system. The model takes into account DM intake, promin digestibility, feed composition, protein distribution (i.e., fractions A, B, and C), animal characteristics, economic factors, and rumen bacterial factors. Examples of least-cost dairy ration formulations, costs, and protein requirements for three milk yield levels are presented in Table 11. Diets were balanced for degraded and undegraded protein fractions and not for solubility. Solubility was not included as a constraint because the 1985 N R e protein system does not define a soluble protein requirement, and the purpose of this report was to illuswate how to structure a least cost model to include degraded and undegraded intake protein requirements and to illustrate the usage of the model. The diets shown in Table 11 are useful for illustrating the dynamics of the model. In this case, no bypass protein supplements were included in the formulated diets. The model suggests that the bacterial protein resulting from the intake of corn lower the undegraded protein requirement so that the bypass protein from the corn and haylage is sufficient to meet the undegraded protein requirement. In the case of the highest production, the model predicted that urea would be useful for meeting the degraded protein requirement. The model is very sensitive to protein fractions, rates of protein degradation, and rates of ruminal passage of feedstuffs. Under different Journal of Dairy Science Vol. 72, No. 10, 1989

o

m. ¢'D

TABLE 10, Least cost tableau for lactating dairy cow based on the 1985 NRC protein system. Unit

Equation

ALFHCS

CORNSIL

SBM44

GRNDCORN

.-d

BREWERS

DISTLLRS UREA DM

CP

A

DIB

UIB

C

TDN IDM

(kg/d) .3

7

9 kg/kg g/kg

Obj Fn DM CP

.096 1 172.0

.094 1 80.0

.371 1 496.0

.124 1 100.0

.227 1 260.0

.251 1 298.0

gag g/kg gag g/kg kg/kg kg/kg g/g g/g g/g g/g g/g g/g kgAg g/g

A DIB UIB C TDN IDM FPA BCP BTP RAP DBP MPA MILK LPA

110.77 13.90 39.08 8.26 .61

52.16 7.04 9,52 11.28 ,70

84.32 254.85 156,83 0 ,81

24.10 37.95 37.95 0 .88

66.30 85.35 77.15 31.20 .66

149.30 68.31 54.17 26.22 .88

gig

AP

g/g

DUP

g/g

on,

g/g

RIP

g/g

IP

g/g mcal/kg

DIP NEl

gag gag

DIP uip

kg/kg kg/kg kgAg

NDFmin NDFmax Forage DM

34 1 - 1 2810.0 2810.0 0 0 0 0 0

-1 O

-1 -1 -1 -1 -1 -.9 -1 9O 163

.15 1.30

1.59

1.86

.186

,150

2.03 1

.50 .50 1.0

.51 .51 .5

.14 .14 0

.09 .09 0

.12 .12 0

.12 .12 0

-.4

1

.~

.,.,e

..
Z!

il

Jl

II

II

II

if

II

II

II

li

"7

II

.7

II

7

II

~,.~l

II

,q.

il

li

7-

7 -

II

I

il

7 ¢'4

l|

li

il

"7

"7.7.7 -

gl

A

II

.7

V

,.ul ,,~1

IJ A

"7

A

~i~

COMPUTEBr'~-n DAIRY DEGRADABLE PROTEIN MODEL

II

7

Journal of D ~

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Vol. 72, No. 10, 1989

2744

O'CONNOR ~

AL.

TABLE 11. Example least cost dairy ration formulations could be added to the model to improve sensifor three milk yield levels. tivity to feeds with differing Irue protein (B fraction) characteristics. The model could be Milk production, kg/d expanded to cover amino acid requirements 36.30 27.22 18.14 based on different protein fractions and animal Ration, kg DM/d: products. Models that adjust nutrient requireHay crop silage 11.06 11.62 8.97 ments of cattle for known variations (6) could Corn silage 3.28 be incorporated also. A dynamic energy utilizaSoybean meal Corn, ground 11.89 8.77 4.89 tion component based on carbohydrate fractions Brewers grain, dry could be integrated with the protein fractions. Distillers, dry To scale the model to prevent the accumulaUrea .09 tion of errors, it is suggested that feedstuff, Total 23.04 20.40 17.14 Economics. $ per cow/d: DM, TDN, and indigestible DM activities be Ration cost 2.57 2.21 1.78 expressed on a kilogram basis and protein acRequivmcats, g/d: tivities on a gram basis. Dietary crude 3360 2902 2294 The use of commercially available software, Rumea degraded 2386 2019 1616 such as Lotus 1-2-3 TM and the Professional Undegraded 974 883 678 Linear Programming Package TM by Sunset Software Technology, allowed for easy modifications to the problem formulation and greatly reduced model development time because input conditions (i.e., different protein fractions and and output routines and solution algorithms did rates) the model would have included different not have to be developed and debugged. ingredients. For example, the A fraction of the The approach described is based on limited protein in distiller's grains, listed in Table 6, seems to be high, and as a result, the degrad- data, and rations based on the approach should ability of distiller's grains appears to be over- be used with caution until further experimental work or observed results confirm their accuracy predicted relative to the degradability estimate or modify and improve them. The 1985 and given in the 1985 NRC manual. The degrad1988 NRC protein systems are more compliability of ground corn also appears to be high cated and more biologically based than prerelative to the 1985 NRC estimate. When the vious NRC protein systems. Thus, more comdistiller's protein A fraction is reduced to 22% plex least cost models that take into account and the rate of degradation of the B fraction is animal, economic, feed, and bacterial factors reduced to 3%/h the overall degradability of are needed to formulate diets accurately for distillers is closer to NRC estimates with the protein requirements of lactating dairy cattle. result that it is included in the high producing cow ration. ACKNOWLEDGMENTS These models are applicable to feeding situations where cattle are being fed diets that The authors gratefully acknowledge Hatch contain greater than 40% roughage DM in the Project 455 (NE-132 regional forage/dairy sysdiet. The bacterial yield equation proposed by tems analysis project) and Eli Lilly Co. for the 1985 NRC protein system is nonlinear for financial support and the IBM project EZRA at cases where the diet roughage DM concentra- Cornell University for computer support. tion is less then 40% (12). Thus, these described models are not applicable to high grain REFERENCES feeding situations. 1 Black,L R., and J. Hlublk. 1980.Basicsof computerizexl The described LP model could be modified ration formulation. J. Dairy Sci. 63:1366. in a number of ways. The basic structure of the 2 Colucci, P. E., L. E. Chase, and P. J. Van Socst. 1982. least cost model is appropriate for the 1988 Feed intake, apparent diet digestibility and rate of particulate passagein dairy cattle. J. Dairy Sci. 65:1445. NRC degraded and undegraded intake protein 3 Eliman,M. E., and E. R. Orskov. 1984.Factorsaffecting requirements for lactating dairy cattle. The only the outflow of protein supplementsfrom the rumen. 1. modifications needed to include 1988 NRC Feeding level. Anita Prod. 38:45. protein requirements are changes in coefficients 4 Eliman,M. E., and E. R. Orskov.1984.Factors affecting to the protein equations. Additional B fractions the outflow of protein supplementsfrom the rumen. 2. Journal of Dairy Science Vol. 72, No. 10, 1989

COMPUTERIZED DAIRY DEGRADABLE PROTEIN MODEL The composition and particle size of basal diet. Anita. Prod. 38:45. 5 Erdman, R. A., J. H. Vandersail, E. Russe,k-Cohen, and G. Switalski. 1987. Simultaneous measmcs of rates of ruminal digestion and passage of feeds for prediction of ruminal nitrogen and dry matter digestion in lactating dairy cows. J. Anita. Sci. 64:565. 6 Fox, D. G., C. J. Sniffen, and L D. O'Connor. 1988. Adjusting nutrient requirements of beef cattle for animal and environmental variations. J. Anita. Sci. 66:1475. 7 Hartnell, G. F., and L. S. Satter. 1979. Determination of rumen fdl, retention time and mminal turnover rates of ingesta at different s~ages of lactation in dairy cows. J. Anita. Sci. 48:381. 8 Hertzler, G., D. E. Wilson, D. D. Loy, and G. H. Rouse. 1988. Optimal beef cattle diets formulated by nonlinear programming. L /mira. Sci. 66:1115. 9 Lotus 1-2-3TM User's Manual. 1983. Lotus Corp., Cambridge, MA. 10 Mertens, D. R. 1987. Predicting intake and digestibility

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using mathematical models of ruminai function. ]. Anim. Sci. 64:1548. 11 National Research Council. 1978. Nutrient requirements of dairy cattle. 5th rev. ed. Natl. Acad. Sci., Washington, DC. 12 National Research Council. 1985. Ruminant nitrogen usage. Natl. Acad. Sci., Washington, DC. 13 National Research Council. 1988. Nutrient requirements of dairy cattle. 6th rev. ed. Natl. Aoad. Sci., Washington, DC. 14 Nocek, J., and J. B. Russell. 1988. Protein and energy as an integrated system. Relationship of ruminal protein and carbohydrate availability to microbial protein synthesis and milk production. J. Dairy S¢i. 71:2070. 15 Professional Linear Programming System User's Manual. Sunset Software Technol., San Marino, CA, 16 Synder, T. J., L. D. Muller, J. A. Rogers, and S. M. Abrams. 1984. Dige,sta passage measured by markers in dairy cows fed two ratios of corn silage:grain with 0 or 1.2% sodium bicarbonate, J. Dairy Sci. 67:1953.

Journal of Dairy Scicac¢ Vol. 72, No. I0, 1989