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This is to certify that the
thesis entitled

INCORPORATING ENVIRONMENTALLY COMPLIANT
EXCESS NUTRIENT DISPOSAL COSTS INTO LEAST COST
DAIRY RATION FORMULATION

presented by

JOLEEN CHRISTINE HADRICH

has been accepted towards fulfillment
of the requirements for the

MS. degree in AGRICULTURAL
ECONOMICS

 

 

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Date

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6/07 p'ICIRC/DateDueindd-pt

 

INCORPORATING ENVIRONMENTALLY COMPLIANT EXCESS NUTRIENT
DISPOSAL COSTS INTO LEAST COST DAIRY RATION FORMULATION

By

Joleen Christine Hadrich

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Agricultural Economics

2007

ABSTRACT

INCORPORATING ENVIRONMENTALLY COMPLIANT EXCESS NUTRIENT
DISPOSAL COSTS INTO LEAST COST DAIRY RATION FORMULATION

By

Joleen C. Hadrich

Livestock ration formulation minimizes feed cost subject to animal nutrient
requirements for a target performance level. This method ignores the cost of disposing
nutrients in excess of nutritional requirements, which are disposed of in animal waste. To
address these issues this research evaluates incorporating the potentially substantial cost
of disposing nutrients in excess of nutritional requirements. Nutrient disposal costs are
estimated using an economic engineering approach and incorporated into a modified least
cost ration formulation using separable programming. Including disposal cost allows for
an assessment of the trade off between lower input cost feed ingredients and higher
disposal costs with nutrient excretion to evaluate a joint decision which minimizes feed
and nutrient disposal costs.

To illustrate the method and its importance this study evaluates disposal costs and
its implications on ration formulation for two representative Michigan dairy farms.
Results for Farm 1 and 2 demonstrate that ration formulation does change when
phosphorus disposal costs are included in the feeding decision. Land availability and
proximity, animal density, crop rotation, and initial phosphorus content are shown to be
important to determining phosphorus disposal cost. The results imply that it is quite
simple to modify ration formulation to account for nutrient disposal costs in addition to

feed input costs.

T0 Dean, Daryl, Joelle, and Joylynn, thanks for everything

iii

ACKNOWLEDGEMENTS

I would like to thank my committee, composed of Dr. Christopher Wolf, Dr. J.
Roy Black, Dr. Stephen Harsh, and Dr. Michael Vandehaar for their guidance throughout
the thesis research process. In particular, I would like to thank Dr. Wolf for being my
research advisor and major professor. His advice and encouragement during the
development of the thesis was greatly appreciated.

I would also like to thank Nicole Olynk for her knowledge in dairy nutrition and
her answers to my constant questions about the rations formulated for my model. Special
thanks go out to Megan McGlinchy and Crystal Jones for their added input during the
research process. Finally, I am extremely grateful to my brothers and sisters for taking

care of everything at home.

iv

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES .......................................................................................................... vii
Chapter 1: Introduction ....................................................................................................... 1
Chapter 2: Liteature Review ............................................................................................... 5
2.1 Animal Science Literature .................................................................................. 5
2.2 Ration Formulation Literature ............................................................................ 8
Chapter 3: Nutrient Disposal Cost Function ..................................................................... 11
3.1 Manure Production ........................................................................................... 12
3.2 Cropping Program ............................................................................................ 15
3.3 Manure Application Rate ................................................................................. 16
3.4 Manure Disposal Cost ...................................................................................... 17
3.5 Phosphorus Disposal Cost ............................................................................... 19
Chapter 4: Ration Formulation ......................................................................................... 21
4.1 Ration Formulation with Disposal Costs ......................................................... 21
4.2 Relationships between Parameter Constraints and Feed Ingredients .............. 25
Chapter 5: Application to Representative Dairy Farms .................................................... 28
5.1 400 Acre Farm with Lactating Cows ................................................................ 28
5.1.1 Farm Characteristics ..................................................................... ' ............ 28
5.1.2 Ration Formulation Specification ............................................................. 32
5.1.3 Results ....................................................................................................... 34
5.1.3 Sensitivity Analysis .................................................................................. 38

5.2 750 Acre Farm with Lactating Cows, Dry Cows, and Heifers ......................... 42
5.2.1 Farm Characteristics ................................................................................. 42
5.2.2 Ration Formulation Specifications ........................................................... 45
5.2.3 Results ....................................................................................................... 48
Chapter 6: Conclusion ....................................................................................................... 53
References ......................................................................................................................... 55

LIST OF TABLES

Table 1: Dairy manure and nutrient production levels ..................................................... 12
Table 2: Nutrient removal rate for Michigan field crops .................................................. 16
Table 3: Nutrient requirement parameters ........................................................................ 24
Table 4: Nutrient content of feedstuffs ............................................................................. 25

Table 5: Manure application rates and costs for varying levels of phosphorus in the

lacataing cow dairy ration ......................................................................................... 30
Table 6: Nutrient constraints for lactating cows ............................................................... 32
Table 7: Modified LP tableua for lactating cows .............................................................. 33
Table 8: Lacatating cow LP ration comparisons ............................................................... 34
Table 9: Lactating cow ration formulation under varying fat inclusion levels ................. 39
Table 10: Lactating cow ration formulation under price changes .................................... 41

Table 11: Manure application rates and costs for varying levels of phosphorus in the total

farm ration ................................................................................................................. 44
Table 12: Nutrient constraints for lactating cows, dry cows, and heifers .............. '. .......... 46
Table 13: Modified stacked LP tableau for total farm ...................................................... 47
Table 14: Total farm LP ration comparisons .................................................................... 49

vi

LIST OF FIGURES

Figure 1: Lacatating cow excess phospohrus disposal costs as determined by incremental
increases in lactating cow phosphorus intake .......................................................... 37

Figure 2: Total farm excess phosphorus disposal costs as determined by incremental
increases in total farm phosphorus intake ................................................................. 51

vii

Chapter 1: Introduction

Livestock ration formulation minimizes feed cost subject to animal nutrient
requirements for a target performance level. This approach allows the farm manager to
make livestock feeding decisions based on the relative prices and nutrient content of
available products. For example, dairy cows are fed to minimize cost subject to
achieving a specified level of milk production, which, in turn, dictates protein, energy,
mineral and vitamin levels. However, focusing solely on input costs ignores the cost of
over-feeding specific nutrients, such as phosphorus, which may accompany the lowest
cost protein and energy sources. Over-feeding nutrients leads to nutrient excretion
disposed of in manure. This research reconsiders livestock ration formulation to evaluate
a joint decision which minimizes feed and nutrient disposal costs.

Manure and wastewater can contribute to excess phosphorus and nitrogen levels
in soil and water leading to the need for nutrient loading limit levels to prevent pollution.
With increasingly rigorous enforcement of the Clean Water Act and Clean Air Act
farmers are now facing environmental compliance costs manifested through nutrient
management. Most states have defined generally acceptable management practices to
prevent further pollution (Bosch, Zhu, and Kornegay 1997). In many states these
practices are related to a “Right to Farm” law protection making the standards quite
important for farms to avoid nuisance lawsuits. Actual compliance costs pertaining to
phosphorus removal are individual to the farm situation and depend on various factors
such as, animal density, waste management methods, and feeding practices, among others
(Keplinger and Hauck 2006; Boland, Preckel, and Foster 1998). The cost of handling

excess phosphorus is farm-specific; therefore what one farm might find cost prohibitive

another may not. However, it is clear that environmental compliance costs are significant
on many farms and the livestock diet formulation decision is a major source of nutrient
import onto the farm.

The importance of nutrient disposal cost considerations in diet formulation is
especially timely now as a large amount of by-products are generated as biofuel
production increases. By-products of the ethanol industry, such as distillers dried grains
with solubles (DDGS), are low cost sources of protein and energy which permit
substitution for corn grain and soybean meal in livestock diets, but also supply
phosphorus in excess of nutritional requirements. I The dairy industry has been feeding
DDGS to dairy cattle for over a century, but with new technologies DDGS contain
considerably higher quantities of protein, energy, and phosphorus than in earlier years
(Schingoethe 2004). Furthermore, many times homegrown forages included in the ration
formulation provide sufficient phosphorus nutrients for the dairy cow, therefore the
phosphorus in the DDGS leads to excess nutrients in the ration (Cerosaletti, Fox, and
Chase 2004). Due to the direct link between the phosphorus intake and phosphorus
excretion in dairy cattle (Morse 1992; Myers 2003; Knowlton et a1. 2004) feeding
management is a critical control point for phosphorus management on dairy farms to
prevent nutrient loading (Rotz et a1. 2002; Wu, Satter, and Sojo 2000; Spears, Young,
Kohn 2003; Dou et a1. 2003; Cerosaletti, Fox, and Chase 2004; Toor, Sims, and Dou
2005). This potential tradeoff between low-cost feedstuffs and higher nutrient disposal

costs can be used to arrive at economically desirable management decisions.

 

' Distillers grains with solubles are processed in two forms: dried distillers and wet distillers. For the
purposes of this paper dried distillers grains with solubles will be considered.

Environmental consequences and increased access to by-product feeds indicate
that phosphorus based nutrient plans must be implemented at the operational level to
prevent future environmental costs and/or fines. This indicates that nutrient disposal may
introduce additional costs through feed bills, exporting manure off farm, and cost of
purchased commercial nitrogen (when manure is applied at phosphorus removal rates).
Growing concerns about environmental pollution, worker health, and the welfare of
animals from intensified livestock production systems require re-evaluation of livestock
diet formulation to account for nutrient disposal costs of phosphorus on farmland.

Incorporating nutrient disposal costs in ration formulation allows the producer to
evaluate a joint decision which minimizes the total ration cost which includes feeding and
disposal costs. Thus, a tool to be used at an operational level can assist producers and
nutritionists in designing true least cost rations. The objectives of this thesis are to: (a)
develop a nutrient disposal cost function which accounts for animal density, land
availability, crop selection, hauling distance, soil nutrient stocks, manure disposal
technology, and environmental regulations, (b) estimate a ration formulation model that
recognizes nutrient disposal costs, and (c) demonstrate the methods and present results
and implications for feeding decisions for two representative dairy farms.

An economic engineering approach was used to build a farm nutrient disposal
cost function. The nutrient disposal cost was implemented in a modified linear
programming model using separable programming. Ration formulations were formulated
for two representative farms. Farm 1 was a 400 acre farm with 200 lactating cows. Farm
2 was a 750 acre farm with 200 lactating cows, 40 dry cows, and 200 replacement

heifers. The results from both representative farms demonstrated that including the

nutrient disposal cost in ration formulation reallocated feed ingredients to achieve lower
levels of phosphorus fed in the ration.

The thesis proceeds in the following manner: Chapter 2 reviews the literature
describing relationships between animal nutrition and nutrient excretion as well as
methods utilized to Optimize multiple objectives; Chapter 3 derives the cost of nutrient
disposal with environmental regulation constraints and requirements; Chapter 4 builds the
nutrient disposal cost into a least cost ration formulation; Chapter 5 illustrates the optimal

joint decision for the representative farms; Chapter 6 summarizes and concludes.

Chapter 2: Literature Review

The literature review provides information regarding dairy nutrition and the
methods used for determining ration formulation. It is divided into two main sections:
dairy nutrition and ration formulation methods literature. The dairy nutrition literature
explains the role and nutritional requirements of phosphorus for the dairy animal.
Additionally, the dairy nutrition literature reviews sources of nutrient loading on dairy
farms as well as methods of prevention. The ration formulation methods literature
summarizes previous methods used to solve ration formulation decisions with more than
one objective.
2.1 Dairy Nutrition Literature

Numerous studies, particularly dairy science research literature, have identified
the increased amount of nutrient loading in agricultural systems and the need for
prevention of this environmental concern. Studies have evaluated animal management
(Rotz, et. al, 2002), nutrient precision feeding (Rotz et al. 2002; Wu, Satter, and Sojo
2000; Spears, Young, and Kohn 2003; Dou et al. 2003; Cerosaletti, Fox, and Chase 2004;
Toor, Sims, and Dou 2005), crop and soil management (Rotz et al. 2002), as well as
whole farm nutrient balance (Wang et al. 2000; Spears, Young, and Kohn 2003) to
determine the critical control point for nutrient loading. The main conclusion from each
of these studies is phosphorus management is best controlled through ration formulation.

Past research identified a possible positive relationship between phosphorus
intake and reproductive performance. Numerous studies have evaluated this relationship;
however Nutrient Requirements of Dairy Cattle (NRC) identified evidence from past

research that feeding phosphorus in excess of nutritional requirements does not increase

reproductive performance. In particular, NRC reviewed seven studies which evaluated
dietary phosphorus inclusion rates ranging from 0.24% to 0.62% of dietary dry matter
intake (DM1) and effects on reproductive performance (2001). The results from the
studies demonstrated that the reproductive performance of dairy cows was not improved
with greater phosphorus inclusion levels in rations fed. Therefore, NRC reduced the
phosphorus inclusion rate of 0.48% DMI from the 1989 level to a 2001 recommended
inclusion range of 032-03 8% DMI. This range was chosen rather than a set level, since
phosphorus inclusion is dependent on feed quality of the ration mix and target milk
production levels (NRC 2001).

Phosphorus loading may develop on farms from more than one source. For
example, dairy producers may feed phosphorus in excess of nutrient requirements due to
variation in phosphorus content of homegrown and purchased feed, inconsistencies
between NRC recommendations and advice from nutritionists, among other factors.

Dou et a1. (2003) evaluated phosphorus levels fed on dairy farms in New York,
Pennsylvania, Delaware, Maryland, and Virginia to determine the critical control point
for phosphorus loading. The results indicated that even though farmers relied on
professional nutritionists and veterinarians to develop their ration formulations
phosphorus was still fed 34% above the 2001 NRC recommended levels (Dou et al.
2003). Dou et al. concluded that nutrient levels of feedstuffs were not accurately
portrayed in the feeding decision, such as homegrown forages were not tested for nutrient
content levels; therefore, causing phosphorus to be fed in excess of nutritional

requirements.

Cerosaletti, Fox, and Chase (2004) conducted a survey in the Cannonsville
Reservoir Basin in Delaware County, New York to evaluate dietary strategies on herd
sizes ranging from 45-100 cows. A whole farm mass balance was used to determine
nutrient imports, exports, and recycling on farm with home grown forages. Homegrown
forages fed in ration formulation represented an on farm recycling of phosphorus whereas
milk production represented the opportunity to export phosphorus off farm. The amount
of phosphorus that was not exported off farm was excreted in dairy manure, which was
applied to crops as fertilizer, and then utilized by the crops, which were later harvested
and fed to the cows, hence completing the phosphorus cycle. Therefore, a whole farm
mass phosphorus balance was used to determine the nutrient levels on farm. The
responses from the survey concluded that phosphorus intake levels exceeded phosphorus
nutritional requirements by 32% across all herds studied. Two phosphorus limited diets
were implemented. Results concluded that after reducing the phosphorus in the ration
formulations, phosphorus intake levels were still in excess of requirements due to high
levels of phosphorus in the forages.

Rotz et al. (2002) used DAFOSYM to evaluate the long term effects of changing
crop production, feed use, and return of manure nutrients back to the land over various
weather scenarios. Results concluded that eliminating the use of phosphorus fertilizer
and phosphorus feed supplementation reduced the accumulation of phosphorus in the
soil. However, a change in the cropping program minimally reduced the soil phosphorus
content. Decreasing the amount of phosphorus fed allowed for a cost savings in
purchased minerals and decreased the amount of phosphorus excreted. Rotz et al.

concluded that the most easily implemented change was reducing the amount of

phosphorus fed to the animal such that it coincided with the 2001 NRC recommendations
while considering the whole farm phosphorus balance.

Based on the abundance of research in the nutrient/precision feeding area, feeding
management is the key area in reducing nutrient loading by balancing phosphorus supply
and intake against cow nutritional requirements and target performance levels. Reducing
phosphorus is a highly integrated problem which is influenced by animal density, waste
management methods, and feeding practices, among other factors. In addition, recycling
phosphorus with the use of homegrown forages also represents and additional component
of this problem since it has been stated that a dairy ration will have adequate phosphorus
levels for nutritional requirements with just the forages of the diet. Therefore, any
supplementation, which is typically needed for protein sources, will undoubtedly increase
phosphorus levels fed (Beede, 2003).

2.2 Ration Formulation Methods Literature

Ration formulation is often determined using linear programming which
minimizes feed cost subject to animal performance and nutritional requirements for a
target performance level. Past literature has recognized that the current ration
formulation cost minimization is limiting in its ability to optimize a dairy ration and
minimize costs subject to nutritional and environmental requirements due to the non-
linear nature of environmental constraints. With increased emphasis on environmental
concerns a modified linear programming model can be developed which incorporates
these factors.

Many multiple objective programming methods have been explored and applied

to solve this problem: multi-goal programming, compromise programming, goal

programming with penalty functions, and weighted goal programming (Romero and
Rehman 2003). Multi-goal programming in an applied dairy setting was evaluated by
Lara and Romero (1992) who argued that producers were more interested in the optimal
ration which achieves a compromise amongst several objectives versus the least cost
ration. Therefore, utility functions were incorporated in the model to account for the
individual farmer preferences (Lara and Romero 1992). This method works well in
theory but in practice the difficulties of defining utility functions make application
difficult.

Stokes and Tozer (2002) evaluated multiple objective programming using
distance functions in a compromise goal setting to minimize the ration cost as well as
excess nutrient excretion (phosphorus and nitrogen) for dairy cows. Subjectivity was
introduced into this model with the use of distance functions to minimize the distance
from the ideal and anti-ideal values in compromise goal programming. Additionally, the
lack of information regarding the appropriate metric and weights to use in the
compromise programming makes this model difficult to apply in a real-world setting.

Jean dit Bailleul et al. (2001) modified the traditional least cost ration formulation
algorithm for swine diets by including a cost associated with excess nitrogen excretion
levels. This nutrient cost was determined exogenously and included in the objective
function of the ration formulation in a stepwise form. Pomar et al. (2006) applied the
same technique to reduce the amount of phosphorus concentration in pig diets by
accounting for disposal and feed input costs simultaneously. The cost included in this
application pertained to the excess and unavailable phosphorus in the swine diets. In the

research by Jean 'dit Bailleul et a1. (2001) and Pomar et al. (2006) the environmental costs

entered exogenously which failed to recognize that a joint decision would be optimal to
minimize the total feeding and disposal cost.

The appropriate farm decision can be accurately incorporated in a useable model
by determining the excess nutrient costs endogenously from manure disposal costs and
marrying these results with the linear programs that livestock industries already utilize.
Including a nutrient disposal cost in the traditional linear program captures the tradeoff
between costs of feedstuffs included in the ration and more expensive manure disposal
costs due to phosphorus fed in excess of nutritional requirements. Our model allows the
farm decision-maker to assess trade-offs between higher costs for livestock diets and the

resulting environmental compliance costs.

10

Chapter 3: Nutrient Disposal Cost Function

Manure is a by-product of livestock production which is usually recycled on farm
as fertilizer. The nutrient composition of manure is a function of the ration fed and
animal species. Manure application rates are a function of manure nutrient content, (e. g.,
nitrogen and phosphorus application method, crop and soil content). Therefore, if the
dairy producer utilizes feedstuffs with high levels of certain nutrients, such as
phosphorus, it may increase the cost of nutrient disposal through manure application.
Current environmental laws monitor nutrient levels in soil in an effort to alleviate
detrimental environmental effects of nutrient loading. For example, soils tests are
performed on farms to determine the level of phosphorus in the soil. High levels of
excess phosphorus entering the surface and groundwater can lead to algal blooms and
eutrophication; therefore manure application rates are monitored to prevent such
occurrences.

An economic engineering approach was used to build a farm nutrient disposal
cost function. This approach allows us to estimate manure application cost dependent on
various farm characteristics, practices, and technologies. Factors determining the cost
- function include: manure production, crop use of manure nutrients, manure application
rate, manure disposal technology, and feed ingredients in the ration. Manure application
is assumed to be the primary source of fertilizer which is supplemented with commercial
fertilizer as needed. This management strategy minimizes commercial fertilizer costs and
is the most efficient method to recycle manure on farm. Each of these factors is dealt

with in turn below.

11

3.1 Manure Production

The amount of manure produced and the nutrient content of that manure, such as
nitrogen (N), phosphorus (P205), and potassium (K20), on farm varies with each animal
species and ration fed. When phosphorus is fed and secreted in milk it takes the form of
phosphorus (P). However, when it is in manure and fertilizer it takes the form of
phosphate (P205). Table 1 presents the manure, N, P205, and K20 production levels
compiled from the MWPS-18, SI for lactating cows, dry cows, and heifers (Midwest

Plan Services 2001).

Table 1. Dairy manure and nutrient production levels

 

 

 

 

 

 

 

 

 

 

Livestock Manure Manure N P205 K20
(lbs/day) (gal/day) (lbs/day) (lbs/day) (lbs/day)
150 pounds 12 1.44 0.06 0.01 0.05
250 pounds 20 2.41 0.11 0.02 0.09
750 pounds 45 5.42 0.23 0.08 0.23
1000 pounds 60 7.23 0.30 0.1 0.31
Lactating,
1000 pounds 111 13.37 0.72 0.37 0.40
Lactating,
1400 pounds 155 18.67 1.01 0.52 0.57
Dr” 1000 51 6.14 0.30 0.11 0.24
pounds
D”: 1400 71 8.55 0.42 0.15 0.33
pounds

 

 

 

 

 

 

 

Source: Midwest Plan Services 2001.

The underlying assumption of this thesis assumes inclusion levels of phosphorus
in dairy rations affect the P205 content of manure excreted by the animal. Published
results only report one value for P205 content of manure excreted and do not specify the
phosphorus levels in the rations used to compile the data. Therefore, calculated values of

phosphorus excretion for lactating cows were used rather than the P205 results from

12

published sources to better account for the varying levels of phosphorus inclusion in the
ration.

Past literature has demonstrated the most accurate way to account for phosphorus
excreted in manure for lactating cows is subtracting the amount of phosphorus in milk
produced from the amount of phosphorus in the ration (Myers, 2003). Phosphorus

excreted by lactating cows was calculated as:
PC =(PFED - PMILK )~2_3,

where the components of this equation were calculated as
PFED = PL *C*365,
PMILK = 0.0009 * MY.

PC is the total pounds of P205 excreted in lactating cow manure (all lactating cows for the
entire year); PFED is the total phosphorus fed in the lactating cow ration (lbs); PMILK is
yearly pounds of phosphorus secreted in milk; PL specifies pounds of phosphorus fed
(cow/day); C is the number of lactating cows in the herd; 365 represents days the ration
is fed, 0.09% specifies the average phosphorus content of secreted milk (NRC 2001); and
MY is defined as total farm milk yield production (lbs/year). The conversion of
phosphorus to P205 was calculated by multiplying phosphorus by 2.3 since there are 2.3
pounds of P205 per one pound of phosphorus (Michigan Department of Agriculture
2006).

Phosphorus excreted by dry cows and heifers was determined by subtracting the
amount of phosphorus retained for average daily growth from what was fed. Heifer and

dry cow manure phosphorus excretion levels were calculated as

Pi = (Pia) - Prim)“ 23,

13

where the components of this equation were calculated as
Pia) = PL" *N*365,

pi” = 0.007 * ADG
where i indicates heifer (H) or dry cow (D) group; P,- is P205 (lbs) excreted in the heifer

or dry cow manure (all animals for the entire year); P,,’;ED is total phosphorus fed in the
heifer or dry cow ration (lbs); Pg“. is yearly pounds of phosphorus retained by the dry

cow; PL' is pounds of phosphorus fed (animal/day); N is number of heifers or dry cows in

the herd; 0.7% represents the average phosphorus retained by the respective animal
which is dependent on ADG (Vandehaar and Kriegel 2005), and ADG is average daily
grth for the animal (lbs). The ADG for heifers and dry cows is dependent on age and
stage of pregnancy where applicable (Vandehaar and Kriegel 2005; NRC 2001).

The nutrient density of manure was calculated by dividing the total farm nutrient
content of the manure by the total farm gallons of manure produced. Total farm nutrients
for N, P205, and K20 were calculated as the summation of the specific manure nutrient
produced across all animal categories. Total farm gallons of manure were calculated as
the summation of gallons of manure produced across all animal categories. The nutrient

density (N, P205, and K20) of the manure was calculated as

 

where TFN, is the total farm nutrient production (lbs)for j where j=l=N, j=2= P205, j=3=
K20, M is the total farm manure production (1000 gallons), and ND,- is the jth nutrient

density of the manure (lbs/1000 gal). The P205 density of the manure changes based on

14

the phosphorus inclusion rate in the ration formulation, but the N and K20 content are
assumed to remain unchanged with ration changes.
3.2 Cropping Program

Crops acres planted on farm remove nutrients through nutrient uptake from
manure application and commercial fertilizer. In particular, crop use of manure nutrients
is determined by the crop yield and pre-existing nutrient levels of the soil (Feinerman,
Bosch, and Pease 2004). For example, in Michigan corn silage with an average yield of
22 tons/acre removes approximately 73 lbs/acre of P205 from the soil whereas corn grain
with an average yield of 150 bu/acre removes approximately 56 lbs/acre of P205
(Wamcke et al. 2004). Therefore, a farmer may choose to plant corn silage in saturated
phosphorus soil in order to decrease soil phosphorus levels. These differences in
phosphorus utilization/uptake demonstrate the importance of manure management
techniques on the cropping program and nutrient disposal.

The following characteristics of individual farms are needed to calculate the
nutrient removal of the crops planted: potential yield of crops, nutrient removal rates, and
nutrient credits. Nutrient removal and credit values were compiled from the Michigan
State University extension bulletin entitled, “Nutrient Recommendations for Field Crops
in Michigan (Wamcke et al., 2004) which are represented in Table 2. Nutrient removal
(lbs/acre) was calculated by multiplying the pounds per unit of nutrient removal in Table

2 by the potential yield of the crop planted.

15

Table 2. Nutrient removal rates for Michigan field crops

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. N removal N credit P205 K20
Crop Unrt (lbs luni t) (lbs luni t) removal removal
(lbs/unit) (lbs/unit)
Alfalfa Hay ton 45 40 + (% 13 50
Haylage ton 14 stand) 3.2 12
Barley Grain bu 0.88 0.38 0.25
Straw ton 13 3.2 52
Beans, dry Grain CM 3.6 1.2 1.6
edible
Bromgrass Hay ton 33 1 3 5 1
Canola Grain bu 1.9 0.91 0.46
Clover:grass Hay ton 41 1 3 39
Corn Grain bu 0.90 0.37 0.27
Silage ton 9.4 3.30 8
Oats Grain bu 0.62 30 + 0.25 0.19
Straw ton 13 0.5(%stand) 2.8 57
Orchardgrass Hay ton 50 17 62
Sorghum Grain bu 1.1 0.39 0.39
Sorghum- Hay ton 40 1 5 58
Sudangrass Haylage ton 12 4.6 l 8
Soybeans Grain bu 3 .8 30 0.8 1 .4
Srgar beets Roots ton 4.0 1.3 3.3
Wheat Grain bu 1.2 30 + 0.63 0.37
Straw ton 13 0.5(%stand 3.3 23

 

‘Source: MSU extension bulletin E-2904, Wamcke et al. 2004.

3.3 Manure Application Rate

Initial soil phosphorus content is determined by soil tests on farms. Current

environmental laws monitor nutrient levels in soil in an effort to alleviate detrimental

environmental effects of nutrient loading. Therefore, many states have defined

agronomic manure application rates dependent on the initial soil phosphorus levels

(Feinerman, Bosch, and Pease 2004). For example, Michigan uses the Bray Pl soil test

as specified by the Generally Accepted Agricultural and Management Practices for

Manure Management and Utilization (GAAMP) in accordance with the Michigan Right

to Farm guidelines to determine the phosphorus per acre soil content. This criterion

16

 

specifies three acceptable manure application rates: nitrogen removal, phosphorus
removal, and no manure application.

The relevant manure disposal application rate is determined by initial soil nutrient
stocks, manure nutrient density, and agronomic crop nutrient removal rate. The manure

application rate (gal/acre) for the respective nutrients in the manure was calculated as

NR- —NC
M4Rj,= ——’S—S—*1000,

ND!-

where MAst is the jth manure application rate for crop 5, NR], is the jth nutrient removal
level for crop s (lbs/acre), NC, is the nutrient credit for crop s (lbs/acre) which is given in
the form of nitrogen (N) credits based on N fixation in legume crops, ND, is the jth
nutrient density of the manure (lbs/1000 gal), and 1000 converts the manure application
rate to gallons per acre.

3.4 Manure Disposal Cost

The total cost to dispose of manure was calculated as

MDC: (LT +7'r,,+UT,,+1T ) *HR,

M2

1

n
where MDC is the manure disposal cost (3), n indicates field available for manure
spreading (whether owned, rented or through some other agreement), LT is the manure
loading time (hrs), 77”,, is the manure transportation time (hrs) which is a function of the
distance to field n, UT ,, is the manure unloading time (hrs) which is a function of field n
characteristics, IT is the manure incorporation time (hrs), and HR is the hourly rate ($/hr)
for manure disposal. An hourly rate is used rather than a cost based on mileage since the

distance manure must be hauled is function of the time needed for transport (V anette

l7

2006). The hourly manure disposal cost incorporates yearly machinery and labor costs
for loading, transportation, unloading, and incorporation time of manure (Harri gan 1997).
Each of the time components of the manure disposal cost is dealt with in turn below.

Loading time (LT) includes agitating the manure, maneuvering the spreader, and
pumping manure into the spreader. Loading time is a function of the quantity of manure
produced, which is dependent on the number and type of animal on the farm. It is also a
function of the pump, agitator and spreader used. Typical time allocations for these tasks
can be found in Extension bulletins (Harrigan 2001).

Transportation time (T1) is the time needed to transport a full load of manure
from the manure storage facility to the field and return the empty spreader. TI'is a
function of the quantity of the manure produced, manure transportation equipment
technology, and distance the manure must be hauled for disposal.

There are numerous spreader options for manure disposal, such as, tractor-drawn
tank, truck mounted, and nurse trucks to transport manure to remote locations. The
producer matches appropriate tractor and spreader type with farm size and hauling
distance. The average speed of the tractor varies with road conditions, distance, and
. whether the spreader is empty or full (Harrigan 1997).

The distance manure must be hauled for disposal is a function of initial soil
nutrient levels of available acres. As the soil nutrient content increases, less manure can
be applied necessitating further hauling distances. Available acres are a function of
owned and rented acres, as well as the availability of other acreage for spreading manure

that may be obtained through agreements (for a fee or not).

18

Unloading time (U7) is a function of the quantity of manure produced, manure
application rate, and manure spreader capacity. Manure application rate is a decreasing
function of the nutrient density of the manure, increasing function of crop removal rates,
and decreasing function of initial soil phosphorus content.

Incorporation time (17) is the amount of time needed to incorporate the applied
manure into the soil, which is a function of the acres utilized for manure application.
During incorporation it is assumed the tractor is driving at a constant speed.

Manure contains nutrients which may reduce or eliminate the need for
commercial fertilizer application. Therefore, it is appropriate to calculate a fertilizer
value of manure to calculate the total manure disposal costs net of fertilizer. This
fertilizer value was only applied to manure disposed on farm and applied at the
agronomic phosphorus removal rate for both the phosphorus and nitrogen removal rates.
The P205 content of manure was calculated and multiplied by the US commercial
fertilizer price, $0.25/1b (Rausch 2006), to determine the fertilizer value of manure. This
value was subtracted from the MDC to obtain the total manure disposal costs net of
fertilizer value, NMDC
3.5 Phosphorus Disposal Cost

The dietary requirement for phosphorus in the dairy diet is calculated as the
summation of absorbed phosphorus needed for maintenance, growth, pregnancy, and
lactation divided by the absorption coefficients (NRC, 2001). For example, nutritional
requirements to produce 67 pounds of milk per day requires a dry matter intake of 52
pounds per day, of which 0.17 pounds of the ration is composed of phosphorus. This

daily phosphorus consumption level correlates to 0.04 pounds/cow of excess phosphorus

19

(NRC, 2001). Thus, there will always be at least 0.04 pounds/cow of phosphorus to
dispose through manure application indicating some disposal cost is unavoidable.
Therefore, the relevant disposal cost to consider when changing ration formulation is the
increase in disposal cost above this minimum unavoidable level that results from the
ration selected. Total farm phosphorus disposal cost was calculated from the NMDC as

NMDC — NMDC
P D C = Fed Re q ,

PFed'PReq

 

where PDC is the average cost to dispose of one excess pound of phosphorus ($/lb),

NMDCM is the farm manure disposal cost net of fertilizer value for the phosphorus fed

(above requirement), NMDC is the manure disposal cost net of fertilizer value for the

Ru:
minimum level of phosphorus to dispose (phosphorus requirement level), Pped is the
amount of phosphorus fed in the ration formulation (lbs), and PR“, is the amount of
phosphorus fed to achieve the nutritional requirement (lbs).

The daily total farm disposal cost of excess phosphorus was calculated by
multiplying PDC by the pounds of excess phosphorus fed in the total farm ration; This
procedure was repeated for a range of phosphorus inclusion levels in the total farm ration
to derive the phosphorus disposal cost function. Therefore, the PDC is a function of total

farm manure disposal costs.

20

Chapter 4: Ration Formulation

Dairy ration formulation is posited as minimizing costs while maintaining a
specified milk production level. The production function for milk production can be
represented as

y=f(L. F. 0),
where y is the milk yield, L is labor input, F is feed input, and 6 is defined as random
states of nature that affect milk production, such as weather and stress levels on cows.
The dairy producer evaluates different methods to decrease the cost of production
dependent on input levels. In particular, the dairy producer evaluates the nutrient
composition of different feeds to determine if a less expensive feedstuff can be
substituted in the ration to decrease input costs while maintaining nutritional
requirements for a specified milk production level.
4.1 Ration Formulation with Disposal Costs

The least cost ration formulation can be estimated using linear programming (LP).
This approach minimizes the costs of production while holding output (milk production)
fixed. LP has been widely used in the area of optimizing cost performance subject to
animal performance and the nutritional requirements that a specified performance level
dictates and hence is an appropriate model for this research problem (Waugh 1951; Black
and Hlubik 1980; France and Thornley 1984; Tozer 2000; Coffey 2001).

LP has three quantitative components: decision variables, an objective function,
and constraints. The decision variables describe a particular type of action, such as, the
amount of a particular feedstuff included in the ration formulation. The objective

function determines the optimal combination of decision variables to minimize total

21

ration costs. The constraints are restrictions for the decision variables. For this model
one constraint specifies that dry matter intake can not exceed 52 pounds of feed a day per
lactating cow.

The assumptions of linear programming also require the objective function and
constraints must be linear and completely deterministic. The decision variables must be
continuous, homogenous, and non-negative to allow integer or fractional values to be
used to obtain the optimal objective function (France and Thornley 1984).

Since linear programming is the most commonly used method of dairy ration
formulation we want to use a programming technique that can incorporate the nutrient
disposal cost directly in the current ration formulation LP. As stated previously, the
objective function and constraints must be linear and deterministic. The nutrient disposal
function is non-linear necessitating separable programming to replace this function with a
piecewise linear approximation (France and Thornley 1984). Separable programming is
a technique that allows nonlinear functions of single variables to be used in either the
constraints or objective functions of a linear programming problem. This non-linear
technique is used to find a global or local optimum to a large number of non-linear
problems allowing a linear approximation to a curve (Miller 1963).

The linear programming ration formulation with the nutrient disposal cost
function is defined as

n m
(1) Minimize C = ijxj + Zpkdk

j=l k=l
Subject to:

n
(2) 261ng > (=,<) bl
j=1

22

m
(3) Zlkdk =1
k=1
(4) Xj,/Ik 20, Vj,k

The objective function is specified in equation (1) where x] are quantities of feed
ingredients with price p,- and d}.- are the quantities of excess phosphorus (dependent on the
phosphorus feed intake level) with a nutrient disposal price pk. Equation (2) depicts the
bounds of the nutritional constraints where 0,} is the nutritional content of the i’h nutrient
in the f" feed ingredient. The right hand side variable b, represents the bounds of the 1"”
nutrient. Equation (3) specifies the constraint for the separablity row where M is a row of
ones. We want the LP to choose continuous activities (d. and d“) to ensure the Kuhn
Tucker conditions hold. Therefore, Md], is the proportion of the phosphorus disposal
activity based on the k’h level of phosphorus intake by the cow. Equation (3) must sum to
one to ensure all manure is disposed. Equation (4) defines non-negativity conditions.
This LP program produces the least cost combination of feed ingredients that meet the
nutrient requirements for the specified performance level with the incorporation of the
nutrient disposal cost function; therefore, solving for a joint decision.

Nutrient requirement parameter descriptions are presented in Table 3. The
feedstuffs available for ration formulation were divided into four feed source categories:
silage, hay, energy feeds, and by-product feeds. The nutrient content of the feedstuffs are
presented in Table 4. Only feedstuffs common to Michigan were included.

The nutrient requirement parameters are the b,- in equation (2) of the LP. For
example, the crude protein (CP) nutrient requirement for a cow producing 67 pounds of
milk per day is 8.44 pounds per lactating cow per day. This constraint is met by

multiplying the amount of a feedstuff fed by the nutrient content of the feedstuff. If this

23

ration fed 10 pounds of alfalfa 1.91 pounds of CP will be supplied, therefore the ration

still needs to supply 6.53 pounds of CP. The LP allocates the remaining 6.5 3 pounds of

CP by simultaneously assessing the tradeoffs of the nutrient contents and prices of

alternative feedstuffs as well as additional nutritional constraints.

Table 3. Nutrient Requirement Parameters

 

Nutrient Requirement

 

 

 

 

 

 

 

 

 

 

 

 

Parameters Abbreviations Description of the parameter
Dry Matter Intake DMI Amount of feed consumed by the
anrmal.
Neutral Detergent Fiber NDF Deterrnrnes the fiber requrrements for
the cow.
Crude Protein* CP Total amount of protein in the diet
Rumen Undegraded Protein“ RUP Amount of protern not degraded in the
rumen (bypass protern).
Rumen Degraded Protein“ RDP Amount of protern degraded 1n the
rumen.
Net Energy for Lactation NEL Amount of energy needed for
maintenance and lactatron.
Calcium Ca Mineral needed in ration
Phosphorus P Mineral needed in ration
Calcium to phosphorus limits C a:P 1203:1015 the mrneral relatronshrp 1n the
Ether Extract Fat Included 1n.ratron to control rntake,
erther 1n anrmal or vegetable form.
Total Digestible Nutrients* TDN Amount of ruminally available energy.

 

 

 

*Specifies intermediary equations used for the protein system. It was assumed that RUP+RDP=CP,
indicating the protein system is perfectly balanced for this model.

24

 

Table 4. Nutrient content of feedstuffs

 

 

Legume Cotton
Corn hay with Groun Seed,
Silage, grass , (1 Corn Soybean whole
Nutrient norma mid- Grain Meal, with
Parameter Units l maturity Alfalfa (dry) 48% CP lint DDGS
Dry Matter % 0.351 0.880 0.903 0.881 0.895 0.901 0.902
NDF lbs 0.450 0.472 0.416 0.095 0.098 0.503 0.388
CP lbs 0.088 0.191 0.192 0.094 0.538 0.235 0.297
RUP lbs 0.353 0.18 0.409 0.473 0.426 0.229 0.508
RDP lbs 0.647 0.82 0.591 0.527 0.574 0.771 0.492
NEL "/11? 0.725 0.5318 0.541 0.914 1.004 0.882 0.895
Ca lbs 0.0028 0.01 17 0.0147 0.0004 0.0035 0.0017 0.0022
P lbs 0.0026 0.0030 0.0028 0.003 0.007 0.006 0.0083
Mg lbs 0.0017 0.0027 0.0029 0.0012 0.0029 0.0037 0.0033
Fat lbs 0.032 0.02 0.025 0.042 0.01 1 0.193 0.1
TDN lbs 0.688 0.594 0.564 0.887 0.814 0.405* 0637*

 

Source: NRC, 2001.
"‘ Fat corrected TDN was used since the calories fi'om fat are not useful for generating microbial protein.
The calculation was as follows: [TDN-((Fat-.30)*2.25)], (Black 2007).

4.2 Relationships between Parameter Constraints and Feed Ingredients

There are many concerns when determining a dairy cow ration formulation. For
example, properly accounting for the metabolizable and microbial protein, fiber and fat
inclusion levels, dry matter intake, and the fermentability of the diet are all factors
considered in ration formulation. These factors are influenced by the feed ingredients
_ included in the ration formulation. DDGS is a feedstuff that causes concern in ration
formulation since affects each of the items above.

Modeling the protein system in dairy ration formulation is needed to ensure
adequate nutritional values for body maintenance and milk production. This is of
particular interest with DDGS which have a high proportion of protein bypassing the
rumen with protein quality below other possible sources. The protein system is driven by
metabolizable protein (MP) which is dependent on crude protein (CP), rumen degraded

protein (RDP), and rumen undegraded protein (RUP). The relationship between the

25

different classifications of protein is modeled in the total digestible nutrients (TDN)
requirements. MP is modeled as

MP = RUP + RDP,
where RUP is defined as bypass protein and RDP is composed of two items: microbial
protein and urea. TDN is modeled as an energy requirement per pound of microbial
protein to equate the supply of microbial protein through RDP to the crude protein
demand of the animal. TDN is a proxy for the ruminally available energy.

DDGS are typically included in the ration for a protein source, but are also a
source of fat, fiber, and phosphorus. In particular, energy in DDGS is primarily in the
form of digestible fiber and fat which has lead to numerous debates about the inclusion
levels of these nutrients in the diet (Jenkins 2002). Fat and fiber are important
components of the dairy ration. Fiber is a major source of energy for milk production,
but is only utilized once it is fermented in the rumen. Feeding excess fat may reduce the
microbial fermentation in the rumen. Consequently, fiber utilization is strongly related to
fat consumption. Feeding in excess of fat requirements may decrease dry matter intake
which concurrently decreases the amount of energy available for milk production.
Therefore, the inclusion of fat is an important factor when determining a dairy ration with
DDGS.

Schingoethe (2004) has recommended that the maximum inclusion rate of
distillers fed to dairy cows can be up to 20% of the dry matter intake of the lactating dairy
cow. This equates to about 10-11 lbs/cow/day of DDGS based on a DMI of 52
lbs/cow/day. Past studies have demonstrated that feeding more than this inclusion rate

will decrease milk production (Schingoethe 2004). Feeding 10-11 lbs of DDGS

26

corresponds to a 10% fat inclusion rate. Therefore, a ration with 52 pounds of DM1
includes approximately 5 pounds of fat (ether extract). Allen suggests limiting fat to 4-
8% of total DMI, which corresponds to an inclusion of 2-4 pounds of fat. Jenkins (2002)
evaluated 20 different fat inclusion studies and found that inclusion rates ranged from
1.5-6.8% of the dry matter intake (Jenkins 2002). This may conclude that high levels of
DDGS in the ration formulation may lead to excess amounts of fat in the ration which, in
turn, can suppress feed consumption and inhibit energy digestion through fiber. This
issue will be addressed through a sensitivity analysis limiting the percent of fat inclusion

in the ration formulation in Chapter 5.

27

Chapter 5: Application to Representative Dairy Farms

The application to representative dairy farms is divided into two sections. The
first application evaluates manure disposal technologies, nutrient disposal costs, and their
implications on the feeding decision for a 400 acre dairy farm with 200 lactating cows.
The second application is a 750 acre farm with 200 lactating cows, 40 dry cows, and 200
replacement heifers.
5.1 400 acre farm with only lactating cows

The representative herd for this analysis was based on an average Michigan dairy
farm milking 200 cows (Wittenberg and Wolf 2005). It was assumed the farm had 400
crop acres which is equivalent to two acres per cow of cropland to dispose of manure.
The ration formulated for this model was based on a representative lactating Holstein
cow weighing 1400 lbs, 120 days in milk, 3.0 body condition score, and a 3.5% fat
corrected milk with milk production of approximately 67 pounds of milk per day. These
assumptions require a daily DMI of 52 pounds of feed per cow per day.
5. 1. 1 Farm characteristics
Total farm manure production for this 200 cow herd was 1,139,157 gallons of manure
with a nutrient content of 61,610 pounds of nitrogen and 34,770 pounds of K20 in the
manure. The nutrient density of this manure was calculated as 31 pounds of N per 1000
gallons of manure and 31 pounds of K20 per 1000 gallons of manure.2 The nutrient
production and density of P205 change with the ration formulation and are presented in
Table 5. The daily base phosphorus requirement for lactating cows was 0.18 pounds of

phosphorus. Thus, the total herd consumed a minimum of 36 pounds of phosphorus per

 

2 Available N was used rather than N due to volatilization of N. Available N = 51 lbs/1000 gal * 0.35 * 12,
where 0.35 is the mineralization factor and 12 is the percent solids in the lagoon manure.

28

day or 10,749 pound per year. Phosphorus fed was increased by two pounds per herd per
day to generate the remaining phosphorus fed and excreted levels.3 This increase was
chosen to allow the increments between feeding decisions to be small enough for
implementation of separable programming.

The 400 crop acres were divided between corn grain, corn silage, alfalfa, and
soybeans. The percent of the total acres devoted to each crop was determined using mean
share values from the 2004 Michigan Dairy Farm Business Analysis Summary
(Wittenberg and Wolf 2005). Corn grain, corn silage, alfalfa and soybeans utilized 116,
76, 100, 108 acres, respectively. The average yield was assumed to be 150 bu/acre, 22
ton/acre, 6 ton/acre, and 45 bu/acre for corn grain, corn silage, alfalfa, and soybeans,
respectively. Nutrient removal for the different crops was calculated based on fertilizer
recommendations from the MSU Extension Bulletin E-2904 presented in Table 2
(Wamcke et al. 2004).

Manure was applied to the crops based on the GAAMP standards in accordance
with Michigan Right to Farm guidelines for manure application. Manure can be applied
to land at nitrogen removal rates if the soil test for phosphorus is less than 149 lbs/acre.
If the soil test level is in the range of 150-299 lbs/acre of phosphorus, manure may be
applied at phosphorus removal rates. If the phosphorus soil test is above 300 or more
lbs/acre manure may not be applied to the soil (Michigan Department of Agriculture,
2006). Based on the GAAMP standards each crop was split into the three hauling
categories, therefore, each crop has three application rates: nitrogen removal application
rate, phosphorus removal application rate, and no manure application. The nitrogen

removal application rate was included in this analysis since farmers want to apply at the

 

3 This is the equivalent of increasing phosphorus fed by 5 grams per cow per day.

29

highest application rate possible. It should be noted that applying at the nitrogen removal
rate increases the possibility of phosphorus loading. Therefore, in the subsequent years
nitrogen removal rate land may turn into phosphorus removal land. The most extreme
case of a farm scenario would be applying all manure at the phosphorus removal rates.
Nitrogen removal manure application rates for corn grain, corn silage, alfalfa and
soybeans were 4,365 gal/acre, 6,686 gal/acre, 7,436 gal/acre, and 4,559 gal/acre,
respectively. Phosphorus removal manure applications rates vary with the amount of
phosphorus fed in the ration and are presented in Table 5.

Table 5. Manure application rates and costs for varying levels of phosphorus in the
lactating cow dairy ration

Phosphorus intake (lbs/herd/year)
10,749a 12,093 13,436 14,780 16,123 17,467

 

P205 density of manure

 

 

(lbs/1000 gal) l4 17 20 22 25 28

Phosphorus excreted in

manure (lbs)b 7,088 8,431 9,775 11,118 12,462 13,806

Phosphorus excreted above

minimum nutritional 0 1,343 2,687 4,030 5,374 6,718

requirement (lbs)

Crop Manure Application Rate (gallons/acre)

Corn Grain 3,878 3,260 2,812 2,472 2,206 1,991

Corn Silage 5,073 4,265 3,679 3,234 2,885 2,605

Alfalfa 5,451 4,582 3,952 3,475 3,100 2,798

Soybeans 2,516 2,115 1,824 1,604 1,431 1,292
S/herd/year

Manure Disposal Costs

(MDC) 16,429 17,413 19,014 20,560 21,859 22,861

Manure Disposal Costs net of

fertilizer (NMDC)c 12,757 13,023 19,014 20,560 21,859 22,861

 

Source: Calculated from representative farm assumptions
aPhosphorus fed based on minimum nutritional requirements.
bMultiplying by 2.3 generates the P205 manure value.

cA fertilizer credit is not give to manure applied off farm

30

For a base case, it is assumed that all four crops had 20% of their acres in the
nitrogen manure application rate category, 50% in the phosphorus manure application
rate category, and 30% in the no manure application rate category. Applying these
assumptions the example farm with 400 crop acres had 280 acres available to dispose
1,139,157 gallons of manure. Owned acreage was available at a range of one to four
miles round trip. If the on-farm acres were not sufficient to dispose of all the farm
manure, it was assumed that 200 acres were available for off-farm manure application at
varying distances of 7-20 miles roundtrip.

The farm used a 200 horsepower tractor to pull a 6,000 gallon manure spreader.
A 100 horsepower tractor was used to operate a 70-90 horsepower manure pump. It was
assumed that the manure spreader was filled at an average loading rate of 1,300 gallons
per minute. Therefore, it took 4.6 minutes to fill a 6,000 gallon manure spreader.
Agitation and maneuvering the spreader from the storage to the roadside was assumed to
take 7.5 minutes (Harrigan 1997). It was assumed the tractor traveled at a constant speed
of 12 miles per hour with a full load of manure traveling distances less than a mile. The
tractor traveled at a constant speed of 14 miles per hour with full loads of manure
traveling further than a mile from the manure storage facility. A constant speed of 14 and
17 miles per hour was assumed for return trips less than a mile and greater than a mile,
respectively. The tractor traveled at a constant speed of four miles per hour while
unloading the manure. The manure spreader width was calculated as 20 feet, which
accounted for overlap of manure application. A 220 horsepower tractor was used for

manure incorporation traveling at a constant speed of 4 miles per hour. The tillage

31

equipment incorporated the manure at a swath width of 45 feet. The hourly cost for
manure disposal was valued at $150 (Vanette 2006).
5.1.2 Ration formulation specification

The nutrient and mineral content of feeds used in the model were specified from
the Nutrient Requirements for Dairy Cattle (NRC 2001) with the additional support of
Spartan Ration 3 (Vandehaar and Kriegel 2005). Feed ingredients were limited to those
typically available to dairy producers in Michigan. Nutritional constraints are specified
in Table 6. The feed ingredient prices included in this paper were compiled as a three
month average (October 2006-December 2006) of Chicago feed prices to represent prices

relationships and decisions (LMIC 2006).

Table 6. Nutrient constraints for lactating_c_ows

 

 

Constraint Sign Lactating
Coefficients Cows
DMI lbs/day <= 5 1 .92
NDF lbs/day >= 14.14
CP lbs/day >= 8.44
RUP lbs/day >= 3.88
RDP lbs/day >= 4.57
NEL Meal/day >= 1 8.92
Ca lbs/day >= 0.32
P lbs/day >= 0. 1 7
Fat lbs/day <= 2.2 1
TDN lbs/day >= 3 1 .3 1

 

Source: NRC and Spartan 3

The ration formulation was estimated using the modified LP, which jointly minimized the

feeding and nutrient disposal costs. The modified LP tableau is presented in Table 7.

32

 

Emama

 

 

 

cod Nd- wed- mod and 3.838;;
2: _ _ 30m 0.383%
3.5 Red awed 28
RN _.o mmod Em
26 good cmood m
de mmood wmood «0
m2: Nb.— mvg Amz
nmé mavd Seed and
warm womd mmmd gm
34.x Sad wwod m0
3 .3 wwmd med “52
mm. ~ m Noad Emd ~35
1 . . owe—mm Bob wfltfloaa

mid :Em mm: mm c E o mOQQ :80

323%: maeaameam 3.5 ”5.525

 

 

 

958 $552“— ..8 .5935. .3 vow—=52 .h «Bah. .

33

5.1.3 Results

Two least-cost rations were formulated. The first ration minimized feed cost without
phosphorus disposal cost considerations. The second ration simultaneously minimized
joint feeding and nutrient disposal cost decision by incorporating phosphorus disposal
costs. The phosphorus disposal cost function exhibits increasing returns to scale, which
violates the second order conditions for solving the linear program with separable
programming. To correct for this problem we iteratively solved (restricted entry method)
for the separable row to determine what region the manure disposal activity would locate.
This region was then used to solve the ration formulation. LP results are presented in

Table 8.

Table 8. Lactating cow LP Ration Comparisons

 

 

 

 

Ration Ration
Formulation Formulation
Independent joint with
of disposal phosphorus
Feed Ingredient Cost/unit costs disposal costs
lbs/cow/day
Corn silage $25/ton 20.57 21.93
Legume Hay with grass $100/ton -- --
Ground Corn $2.50/bu 17.94 19.06
Calcium Carbonate $20/cwt 0.71 0.63
Cottonseed, whole with lint $160/ton -- 0.41
Soybean mean, 48% CP $190/ton 2.78 4.92
DDGS $120/ton 10.03 5.07
$/cow/day
Feed Cost 2.6749 2.7068
Disposal Cost 0.2093 0.0129
$/herd/year

Herd Feed Cost 195,267.7 197,596.4
Herd Disposal Cost 15,278.90 941.70
Total Herd Cost 210,546.6 198,538.1

 

Source: Calculated from data
* This ration does not include a mineral and vitamin premix

34

DDGS are a source of protein and energy, but also provide large amounts of
phosphorus. Therefore, including the phosphorus disposal cost in ration formulation
allows us to evaluate the consequences of including particular feedstuffs. Including the
excess phosphorus disposal cost function reallocated the feed ingredients in the ration as
the additional disposal costs became large enough to off-set the cost savings of feeding
cheaper sources of energy and protein. In particular, the amount DDGS in the ration
formulation decreased by 50% whereas the soybean inclusion increased by 77%. This
occurred because the cost of excess phosphorus disposal was greater than the value of the
low cost protein source. In the base case protein and energy was supplied by DDGS with
a phosphorus content of 0.0183 pounds per pound fed and was replaced by soybean meal,
with phosphorus content of 0.0070 pounds per pound fed when phosphorus disposal costs
were included (NRC 2001).

Incorporating the nutrient disposal cost increased the total cost of the ration but
lowered aggregate feed and disposal cost. The ration formulation independent of
disposal costs had a yearly per cow feed and disposal cost of $1,052.73 with total manure
disposal costs applied at environmentally compliant phosphorus rates, of $76.39/cow, and
feed cost of $976.34/cow. The phosphorus disposal case had a yearly total cost of
$992.69/cow, which was composed of a $987.98/cow feed cost and $4.71/cow
phosphorus disposal cost. Thus, the base case incurred a phosphorus disposal cost which
was not recognized in the total ration cost. Incorporating the excess phosphorus disposal
cost function increased feed cost by 1%, but decreased excess phosphorus disposal costs
by 90% resulting in a total cost savings of $51 .50/cow/year. This is a yearly cost savings

of $12,008 for the 200 cow herd.

35

For operations with an adequate land base to dispose of manure, the feeding
decision may not change with the inclusion of the nutrient disposal cost. The key
underlying component to this problem is a function of land availability and initial soil
nutrient levels. If all manure can be applied only at the phosphorus application rate due
to high soil nutrient levels additional off farm land may be needed for manure
application. This leads to increased time required to dispose of the same amount of
manure (gallons) and hence increases the cost of nutrient disposal.

Figure 1 depicts excess phosphorus disposal costs for two manure application
cases for the representative 200 cow farm. The base case used the assumptions described
in Section 5.1 of the thesis. The alternative case was developed to compare excess
phosphorus disposal costs when the manure application rate was limited to that of only
phosphorus removal for the available crop acres. Therefore, it was assumed that 0%,
70%, and 30% of all crop acres are in the nitrogen, phosphorus, and no manure
application rates, respectively. Both cases applied a phosphorus fertilizer credit to
manure applied on farm. If manure was applied off farm a nutrient fertilizer credit was
not given since the producer is not benefiting from the manure applied on off farm

acreage.

36

 

 

22000
20000
1 8000 ~
1 6000
14000
1 2000

 

 

 

 

 

 

 

 

 

S

 

 

 

8000
6000

4000 _.
2... _///~—/ __
0 ~ . T T . . . T f . .
10749 11421 12093 12764 13436 14108 14780 15452 16123 16795 17467
Phosphorus fed (Ibalherdlyear)

 

Disposal Cost (Slherdlyear)

 

 

 

 

 

 

 

 

 

[—a— Base Case —o—Altemative Gas—e]

 

 

Figure l. 200 cow excess phosphorus disposal costs as determined by incremental
increases in whole farm phosphorus intake

The base case began off farm manure disposal when phosphorus fed was greater
than 12,093 lbs/herd/year. The alternative case began disposing manure off farm when
the whole phosphorus consumed was greater than 10,749 lbs/herd/year. Under both
manure disposal strategies 280 acres were available for manure application. However,
the alternative case had to dispose manure off farm earlier due to lower manure
application rates at the phosphorus removal level. Therefore, once the alternative case
fed more than the recommended amount of phosphorus manure disposal went off farm.
The fertilizer valuation of the manure did affect the total ration cost (but not the feeding
decision) and should be considered when making ration decisions as it could, for example
in land that was deficient in phosphorus, lead to feeding higher levels of phosphorus in

the livestock ration.

37

5. 1.4 Sensitivity Analysis

Past research has recommended the maximum inclusion rate of DDGS in the daily
feeding decision is 20% of DM1 (Schingoethe 2004). The base case for the
representative farm had a DMI of 52 lbs/cow/day. The base case fed 10 pounds of
DDGS cow/day, which is the maximum inclusion level as specified by Schingoethe. The
phosphorus disposal case fed 5 pounds of DDGS cow/day which corresponds to a 10%
inclusion rate. This suggests that the optimal inclusion rate for DDGS may be below the
maximum potential level when the cost of environmental regulations is included.

The relationship between fat constraints, DMI, and DDGS inclusion was
discussed in Chapter 4. A sensitivity analysis was performed to determine if fat was a
limiting constraint in ration formulation, such that changing the fat constraint limited the
amount of DDGS included in the ration formulation. Fat inclusion levels of 4, 4.5, and
4.7% were evaluated.4 An inclusion rate of 4.7% corresponds to the maximum DDGS
inclusion level as specified by Schingoethe. Results are presented in Table 9.

At fat inclusion levels of 4.5 and 4.7% of DM1 including the phosphorus disposal
costs produces the total least cost ration. At a fat inclusion level of 4% including the
excess phosphorus disposal cost does not decrease the total ration cost, but rather
increases the total ration cost by $2810.50/herd/year. This result demonstrates that
restricting the fat constraint at low levels may limit the amount of DDGS included in the
ration. However, at higher fat inclusion rates the nutrient disposal cost was needed to
account for excess nutrients. High levels of fat can suppress feed consumption.
Therefore, incorporating the disposal cost not only limits the amount of phosphorus

excreted, but also controls fat.

 

4 Fat inclusion levels below 4% generated infeasible solutions for the LP.

38

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39

LP ration formulation formulates the least cost ration considering the price of feed
ingredients and the substitutability among alternative feedstuffs. Therefore, a sensitivity
analysis was performed on to determine at what level prices must increase to change the
ration formulation. Using the prices from the ration formulation as a base, one price was
changed at a time, holding all other prices constant to determine how the feeding decision
changed based on feed prices alone. The base prices used for the analysis and the feeding
ration results of the scenarios are presented in Table 10. Scenario 1 evaluated changes in
the DDGS price. In order to change the ration fed the DDGS price needed to increase by
6% to $126/ton. Under Scenario 1 the amount of DDGS fed decreased by 43% from the
base case to feed a ration similar to the one implemented with the phosphorus disposal
costs included. Scenario 2 evaluated changes to the soybean price. In order to change
the ration fed, the soybean price needed to increase by 50% to $285/ton. Under scenario
2, the amount of DDGS fed decreased, but minimally. Under Scenario 2, the ration
formulation was still overfeeding phosphorus by 16%, indicating the nutrient disposal
cost function should be implemented to control the amount of phosphorus fed in excess
of nutritional requirements. Scenario 3 evaluated changes in the corn price. In order to
change the ration fed corn prices needed to increase by 60% to $4/bu. Scenario 3 feeds
more DDGS than the original base case (and the maximum inclusion level), which leads
to phosphorus fed in excess of nutritional requirements by 43%. Since Scenario 3
increased the inclusion rate of DDGS, this price scenario was run in the phosphorus
disposal case. Under pricing Scenario 3, the phosphorus disposal case feeds 10 pounds of

DDGS. Therefore the disposal cost is decreasing the amount of DDGS in the ration, but

40

still requiring manure disposal off farm due to the high phosphorus content of the

manure .

Table 10. Ration formulations undegrice changes

 

 

 

 

Scenarios
Base 13 2b 3°
Feed ingredients S/unit Lbs/cow/day
Silage $25/ton 20.57 21.83 15.3 21.34
Legume Hay, with grass $100/ton -- -- 3.68 --
Ground Corn $2.50/bu 17.94 19.06 20.86 12.08
Calcium Carbonate $10/cwt 0.71 0.64 0.6 0.78
Soybean meal, 48% $190/ton 2.78 4.74 1.92 5.94
DDGS $120/ton 10.03 5.76 9.67 11.90
$/cow/day
Feed Cost 2.6749 2.7164 2.8150 3.2356
Disposal Cost 0.2093 0.129 0.2027 0.2106
Total Ration Cost 2.884 2.8454 3.0177 3.4462

 

llDDGS price was valued at $126/ton
bSoybean meal price was valued at $285/ton
cCorn price was valued at $4/bu

This price analysis allowed us to evaluate how price changes effect the feeding
decision while holding farm characteristics constant. Of course, not all prices will‘be
held constant in the real world. In particular, corn and DDGS prices are correlated.
However, due to the increase of ethanol production and its dependence on com, corn
prices will continue to change in the future indicating a structural change in the corn
market. If corn prices continue to increase, producers may substitute more DDGS in the
ration formulation for corn grain as indicated in Scenario 3 of the price analysis. This is
causes concern due to the high phosphorus content of DDGS. Therefore, including the
phosphorus disposal cost allows the producer to make the most efficient joint decision for
the farm incorporating not only feed costs, but also disposal costs which are directly

correlated with the feed inclusion levels.

41

5.2 750 acre farm with lactating cows, dry cows, and heifers

As the costs of nutrient management vary with farm characteristics it is useful to
examine another case farm. This representative total farm herd had 200 lactating cows,
40 dry cows and 200 replacement heifers. The ration formulated for the lactating cows
was based on a Holstein cow weighing 1400 lbs, 120 days in milk, 3.0 body condition
score, and a 3.5% fat corrected milk with milk production of approximately 67 pounds of ‘
milk per day. The ration for dry cows was based on a cow 240 days pregnant weighing
1,500 pounds with a target average daily body weight gain of 1.32 pounds. The heifer
ration was based on a heifer 12 months old weighing 717 pounds with an average daily
target weight gain of 1.6 pounds in order to calve at 24 months.
5. 2.1 Farm characteristics

Total farm manure production for this representative herd was 1,799,466 gallons
of manure with a nutrient content of 96,522 pounds of nitrogen and 63,218 pounds of
K20 in the manure. The nutrient density of this manure was calculated as 31 pounds of
available N per 1000 gallons of manure and 36 pounds of K20 per 1,000 gallons of
manure. 5 The nutrient production and density of P205 changes with the ration
formulation and are presented in Table 11. The daily nutritional phosphorus requirement
was 0.18, 0.05, 0.04 pounds of phosphorus per lactating cow, dry cow, and heifer,
respectively. Thus, the total herd consumed a minimum of 46 pounds of phosphorus per
day or 16,787 pounds per year. At this feeding level the total herd excreted 11,903
pounds of phosphorus (27,377 pounds of P205) per year, which corresponds to a P205

manure nutrient density of 15 pounds per 1,000 gallons of manure. Therefore, 11,903

 

5 Available N was used rather than N due to volatilization of N. Available N = 51 lbs/1000 gal * 0.35 " 12,
where 0.35 is the mineralization factor and 12 is the percent solids in the lagoon manure.

42

pounds of phosphorus is the minimum, unavoidable level of disposal that results from
base nutritional requirements specified. The manure disposal costs were estimated by
increasing phosphorus fed by 3 pounds/herd/day. This increase was chosen to allow the
increments between feeding decisions to be small enough for implementation of
separable programming.

The representative Michigan dairy farm land base was 750 acres with the
cropping program of corn grain, corn silage, alfalfa, and soybeans. The percent of the
total acres devoted to each crop was determined using mean values from the Michigan
dairy farm survey (Wolf et al. 2007). Corn grain, corn silage, alfalfa and soybeans
utilized 200, 140, 190 and 200 acres, respectively. The average yield was assumed to be
150 bu/acre, 22 ton/acre, 6 ton/acre, and 45 bu/acre for corn grain, corn silage, alfalfa,
and soybeans, respectively. Nutrient removal for the different crops was calculated based
on fertilizer recommendations for average crop yields from MSU Extension Bulletin E-
2904 (Wamcke et al. 2004). It was assumed that the silage and alfalfa (forage) acreage
was owned whereas the corn grain and soybean acreage was rented. Therefore, it was
assumed rented acreage was further from the farm, indicating a potential for increased
nutrient disposal costs.

Manure application and disposal technology (disposal equipment, disposal times)
were assumed to be the same as those specified for the 200 cow lactating cow herd in
section 5.1.1. Nitrogen removal manure application rates for corn grain, corn silage,
alfalfa and soybeans were 4,354 gal/acre, 6,669 gal/acre, 7,417 gal/acre, and 4,547
gal/acre, respectively. Phosphorus removal manure applications rates vary with the

amount of phosphorus fed in the ration and are presented in Table 11.

43

Under the whole farm analysis, the phosphorus density of the manure decreased
compared to the representative farm with only lactating cows. The volume of the
manure increased with the addition of the dry cows and heifers, however, the nutrient
density of the manure produced by the dry cow and heifers is lower than that of the
lactating cows. Therefore, the total nutrient density of the manure decreased allowing for
higher manure application rates.

Table 11. Manure application rates and costs for varying levels of phosphorus in

the total dairy ration
Phosphorus fed (lbs/herd/year)

 

 

 

 

16,787a 17,966 19,145 20,324 21,503 22,683
P205 density of manure 15 17 18 20 21 23
(lbs/1000 gal)
Phosphorus excreted in
manure (lbs)b 11,903 13,082 14,261 15,441 16,620 17,799
Phosphorus excreted above
base nutritional requirement 0 1,179 2,358 3,538 4,717 5,896
(lbs)

Manure Application Rate (gallons/acre)
Com Grain 3,875 3,526 3,234 2,987 2,775 2,591
Corn Silage 5,069 4,612 4,231 3,908 3,630 3,390
Alfalfa 5,446 4,955 4,545 4,198 3,900 3,642
Soybeans 2,514 2,287 2,098 1,938 1,800 1,681
$/herd/year

Manure disposal costs
(MDC) 27,256 29,413 31,418 33,303 36,1 10 38,746
Manure disposal costs net of
fertilizerc (NMDC) 20,931 22,375 23,738 33,303 36,110 38,746

 

' Phosphorus fed based on minimum nutritional requirements.
b Multiplying by 2.3 generates the P205 manure value.
cA fertilizer credit is not given to manure applied off farm.

44

For a base case, it was assumed that the corn silage and soybeans had 0% of their
acres in the nitrogen manure application rate category, 70% in the phosphorus manure
application rate category, and 30% in the no manure application rate category. It was
assumed that the corn grain and alfalfa crops had 20%, 50%, and 30% of their crop acres
in the nitrogen, phosphorus, and no manure application rates, respectively. Applying
these assumptions the representative farm with 750 crop acres had 525 (70%) acres
available to dispose 1,779,566 gallons of manure.

Owned acreage was available at a range of one to four miles round trip. It was
assumed rented acres were available at a range of 7-10 miles round trip. This farm had
46, 69, 69, 123, and 217 acres available at the round trip distances of 0.5, l, 2, 3, 10
miles, respectively. If the owned and rented acres were not sufficient to dispose the farm
manure, it was assumed an additional 200 acres were available for off-farm manure
application at varying distances of 10-20 miles roundtrip.

5. 2.2 Ration formulation Specifications

The nutrient and mineral content of feeds used in the model were specified from
the Nutrient Requirements for Dairy Cattle (NRC 2001) with the additional support of
Spartan Ration 3 (Vandehaar and Kriegel 2005). Feed ingredients were limited to those
typically available to dairy producers in Michigan. Nutritional constraints for lactating
cows, dry cows, and heifers are specified in Table 12. The feed ingredient prices
included in this paper were compiled as a three month average (October 2006-December
2006) of Chicago feed prices to represent prices relationships and decisions (LMIC

2006)

45

The total farm ration formulation was determined using a stacked LP. Therefore,
the lactating cow, dry cow, and heifer rations were solved simultaneously using the
available feedstuffs presented in Table 4 and nutrient constraints presented in Table 12.

A characterization of the stacked LP with the separable row is presented in Table 13.

Table 12. Nutrient constraints for lactating cows, dry cows, and heifers
Constraint Lactating Dry

 

Coefficients Sign Cows Cows Heifers
DMI lbs/day <= 51.92 31.37 24.91
NDF lbs/day >= 14.14 8.54 7.12

CP lbs/day >= 8.44 3 .96 2.12
RUP lbs/day >= 3 .88 1.74 0.18
RDP lbs/day >= 4.57 2.22 1 .94
NEL Mcal/day >= 18.52 6.87 --

NEM* Mcal/day >= -- -- 9.19
Ca lbs/day >= 0.32 0.07 0.08
P lbs/day >= 0.17 0.05 0.04

F at lbs/day <= 2.21 0.85 0.68

TDN lbs/day >= 31.31 14.69 12.66

 

Source: NRC and Vandehaar and Kriegel, 2006.
"' Since heifers are not lactating there net energy requirement is specified as, NEM is Net Energy for
Maintenance.

46

Table 13. Stacked LP tableau for total farm

 

 

 

 

 

 

 

 

 

 

  

Lactating Cow Dry Cows Heifers g Transfer Rows Phosphorus disposal
Lactating Corn Corn Corn Lactating Dry
Cow Units Silage DDGS Silage DDGS Silage DDGS Cow Cow Heifers 16787 17966 22683 LHS Sign
DMI lbs 0.351 0902 <:
NDF lbs 0.45 0.388 >=
CP lbs 0.088 0.297 >=
RUP lbs 0.353 0.508 >:
RDP lbs 0.647 0.492 >=
NEL Meal/day 1.45 1.97 >:
Ca lbs 0.0028 0.0022 >:
P lbs 0.0026 0.0083 >:
Fat lbs 0.032 0.1 <2
TDN lbs 0.688 0.637 >=
Excess P lbs 0.78 2.98 ~1 <-
Dry Cow
DMI lbs 0.351 0.902 <
NDF lbs 0.45 0.388 >=
CP lbs 0.088 0.297 >=
RUP lbs 0.353 0508 >2
RDP lbs 0.647 0.492 >:
NEL Meal/day 1.45 1.97 >2
Ca lbs 0.0028 0.0022 >:
P lbs 0.0026 0.0083 >=
Fat lbs 0.032 0.1 <2
TDN lbs 0.688 0.637 >=
Excess P lbs 0.78 2.98 —1 <=
Heifers
DMI lbs 0.351 0.902 <=
NDF lbs 0.45 0.388 >=
CP lbs 0.088 0.297 >=
RUP lbs 0.353 0.508 >=
RDP lbs 0.647 0.492 >=
Nem Meal/day 1.45 1.97 >=
Ca lbs 0.003 0.0022 >=
P lbs 0003 0.0083 >=
Fat lbs 0.032 0.1 <=
TDN lbs 0688 0.637 >=
Excess P lbs 0.78 2.98 —1 <=
Separable Row 1 1 l
Phos horus Disposal l l 1 -7300 ‘8053 14653 <:

 

 

 

47

 

 

5. 2.3 Results

Two least-cost rations were formulated. The first ration minimized feed cost
independent of phosphorus disposal considerations. The alternative case simultaneously
minimized feeding and nutrient disposal decisions by incorporating phosphorus disposal
costs. The phosphorus disposal cost function exhibits increasing returns to scale, which
violates the second order conditions for solving the linear program with separable
programming. To correct for this problem we iteratively solved (restricted entry method)
for the separable row to determine what region the manure disposal activity would locate.
This region was then used to solve the ration formulation. Total farm LP ration
comparisons are presented in Table 14.

Several important effects are apparent when the nutrient disposal costs were
included in the ration formulation decision. Including the excess phosphorus disposal
cost function reallocated the feed ingredients in the lactating and dry cow ration as the
additional disposal costs became large enough to off-set the cost savings of feeding
cheaper sources of energy and protein. In particular, the quantity of DDGS fed to the
lactating cows decreased by 58% whereas the quantity of soybean meal fed increased
from 0.10 lbs/cow/day to 2.11 lbs/cow/day. DDGS fed decreased by 100% for the dry
cows while soybean meal fed increase of 39%. This occurred because the cost of excess
phosphorus disposal was greater than the value of the low cost protein source. The
protein and energy supplied in the base case was transferred from DDGS with a
phosphorus content of 0.0083 pounds per pound fed to soybean meal with a phosphorus

content of 0.0070 pounds per pound fed (NRC 2001).

48

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49

Incorporating the nutrient disposal cost increased the total cost of the ration‘but
lowered aggregate feed and disposal cost. The base case had a daily herd (lactating and
dry cows as well as heifers) feed and disposal cost of $808.07 with total manure disposal
costs applied at environmentally compliant phosphorus rates, of $37.60/herd, and feed
cost of $770.47/herd. The phosphorus disposal case had a daily total cost of
$781 .58/herd, which was composed of a $775.60/herd feed cost and $5.98/herd
phosphorus disposal cost. Thus, the base case incurred a phosphorus disposal cost which
was not recognized in the total ration cost. The base model fed 56 pounds of daily
phosphorus to the herd which produced 43 pounds of excess phosphorus. The
phosphorus disposal case fed 53 pounds of phosphorus to the herd which produced 39
pounds of daily excess phosphorus. Incorporating the excess phosphorus disposal cost
function increased feed cost by 1%, but decreased excess phosphorus disposal costs by
84% resulted in a total cost savings of $9,671 .62 for the herd per year. Of course, actual
cost savings will differ for each farm.

Available land in close proximity to the farm which has phosphorus capacity is a
key factor in determining excess phosphorus disposal costs. To examine the sensitivity
of disposal costs to the initial soil phosphorus content assumptions, Figure 1 depicts
excess phosphorus disposal costs for two manure application cases for the representative
farm. The base case assumptions described gives a fertilizer credit to manure applied on
farm at the phosphorus application rate valued at $0.25/lb of P205. If manure was
applied off-farm, a fertilizer credit was not given. The alternative case was developed to
compare excess phosphorus disposal costs when the manure application rate was limited

to that of only phosphorus removal for the available crop acres. Therefore, it was

50

assumed that 0%, 70%, and 30% of all crop acres are in the nitrogen, phosphorus, and no
manure application rates, respectively. The alternative case valued excess phosphorus

disposal costs with a nutrient fertilizer credit valued at $0.25/lb of P205.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Disposal Cost (Slherdlyear)
a;
8
O

 

 

 

 

 

 

 

 

 

 

 

I I T I I I I I I

16787 17376 17966 18556 19145 19735 20324 20914 21503 22093 22683
Phosphorus fed (Ibdherdlyea r)

 

—o— Base Case +Altemative Case

 

 

 

 

Figure 2. Total farm excess phosphorus disposal costs as determined by
incremental increases in whole farm phosphorus intake

Off farm manure disposal for the base case began when whole farm phosphorus
consumed was greater than 19,735 pounds per year. In contrast, the alternative case
began off farm disposal when whole farm phosphorus consumed was greater than 17,966
pounds per year. Under both manure application cases 525 acres were available for
manure application. However, in the alternative case the farm manager had to dispose of

manure off farm at lower phosphorus inclusion levels in the ration due to the lower

51

manure application rates at the phosphorus removal rates resulting in higher disposal
costs.

For operations with an adequate land base to dispose of manure, the feeding
decision may not change with the inclusion of the nutrient disposal cost. The key
underlying component to this problem is a function of land availability and initial soil
nutrient levels. If all manure can be applied only at the phosphorus application rate due
to high initial soil nutrient levels, additional off farm land may be required for manure
application. This leads to increased time required to dispose of the same amount of
manure (gallons), and hence increased costs of nutrient disposal, as we saw in this total

farm as well as the 200 lactating cow farm.

52

Chapter 6: Conclusions

It is a standard economic result that private costs should be modified to the social
cost level when externalities are present. Increasing environmental regulations, and the
cost of implementing them, are affecting farm management decisions. This thesis has
demonstrated that excess farm nutrient disposal costs can be quantified and included in
the ration formulation. Nutrient disposal costs are a function of manure production
levels, land availability, manure hauling technology, and manure application rates, among
other factors. In particular, manure disposal costs are highly sensitive to the initial soil
nutrient levels of land available for disposal and manure application rates.

The results of this thesis demonstrate that it is possible, and relatively simple, to
modify the ration formulation to include excess phosphorus disposal costs. The inclusion
of the phosphorus disposal cost function reallocated feed ingredients to achieve lower
levels of phosphorus in the ration. In particular, the results from the two representative
farms demonstrate the sensitivity of increased phosphorus levels in the ration fed and its
effects on nutrient disposal costs and formulated rations.6

The price analysis on the 400 acre farm with 200 lactating cows demonstrated the
dependency of the feeding decisions on market prices. These decisions surrounding
relative market prices between various feed inputs will become an increasingly important

topic with the current market change in the corn sector and the increasing emphasis on

the ethanol industry.

 

6 The ration formulations generated for this thesis are not necessarily suggested to be utilized by dairy
producers, but were estimated for illustrative purposes to demonstrate the nutrient disposal cost could be
incorporated into a modified LP for ration formulation. The LP is relatively simplistic and does not include
the complex relationships of amino acids and their eflects on the protein system

53

Finally, the total farm phosphorus balance demonstrated that once again including
the phosphorus disposal function reallocates feed ingredients in the ration formulation.
Land availability becomes a more important factor under this scenario as well, due to
increased animal density.

With the increasing availability of by-product feeds animal nutritionists and
producers need to be aware of the total cost rather than solely the input cost of feedstuffs.
To fill this need a tool to determine the lowest total cost ration incorporating input feed
and environmental costs at an operational level has been developed. The new modified
LP with the inclusion of the phosphorus disposal cost function accomplishes this goal by
presenting the farmer with a decision making tool that can be adapted to farm specific
situations. Incorporating the disposal costs in commercial ration formulation would

facilitate environmentally sound least cost feeding decisions.

54

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