Operations and economic models for large milking parlors


Material Information

Operations and economic models for large milking parlors
Physical Description:
xxi, 299 leaves : ill. ; 29 cm.
Thomas, Craig V ( Craig Vincent ), 1951-
Publication Date:


Subjects / Keywords:
Milking parlors   ( lcsh )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )


Thesis (Ph. D.)--University of Florida, 1994.
Includes bibliographical references (leaves 287-298).
Statement of Responsibility:
by Craig Vincent Thomas.
General Note:
General Note:

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University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
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notis - AKF8497
oclc - 31920215
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Full Text







To my wife for her love, patience, and understanding;
to my son for his example of dedication, hard work, and self-discipline;
to God for the abundant blessings He gives me each day.


This dissertation would not have been possible without the
contributions of many kind and sincere people. I am most grateful to Dr.
Michael A. DeLorenzo, chair of my supervisory committee. Dr. DeLorenzo's
constructive criticism of my work, his untiring work ethic, and his excellent
example of adherence to the highest standards of scholarship have been the
single-most important components of my doctoral education.
Sufficient thanks are impossible for the help and friendship provided
by Mr. David Bray. Dave was most responsible for my return to graduate
school to pursue my doctoral degree. Without his support and assistance in
the securing of grant funds and other physical support, many of these studies

would not have been possible. Furthermore, his wealth of practical
knowledge and abundance of common sense in dairy management decision-
making have provided me with a solid foundation that will hopefully result
in my work having a real impact on dairy producers.
I am also extremely grateful to Dr. Roger Natzke, department chairman
and a member of my supervisory committee, for providing me with the

opportunity to return to school and pursue these studies. I am extremely
grateful for the provision of a departmental assistantship and many of the
resources so critical for the success of my projects.
I am also thankful for the assistance provided by the remaining
members of my supervisory committee, Dr. Richard Weldon and Dr. Ray

Bucklin. Many of the economic principles used in my analysis were first
learned in Dr. Weldon's agricultural finance course. I am very thankful for
the many hours he spent with me after class further elucidating economic
principles I found difficult to grasp. I will always remember him as one of the
finest classroom teachers in my doctoral education. I would like to thank Dr.
Bucklin for assisting me with many of the engineering aspects of my

dissertation. His assistance with the initial aspects of my parlor simulation
work was very important.
Sincere thanks are in order for Mr. Jake Martin. Jake provided
essential assistance in gathering much of the data necessary to calculate the
capital investment costs for the various parlors used in these studies. I am

especially grateful for his detailed documentation and timely delivery of this

George Bryan, computer programmer for Dr. DeLorenzo, contributed
immensely to my program. George allowed me to move into his office and
spent many hours helping me untangle hardware and software problems.
Without his assistance I am sure that my studies would have been

significantly delayed. I am also thankful for the days he assisted me at the

Dairy Research Unit installing and trouble-shooting the milking parlor
computer system. Without his expertise this critical system would not have
been available for use in my research.
I am also very thankful for the friendship, encouragement and

assistance provided by so many others in the Dairy Science Department.

Fellow graduate students, Bill Sanchez, Carlos Becceril, Doug McCullough,

Miguel Campos, Robert Smith, and others were very helpful and provided
valued advice during my studies. The personnel at the Dairy Research Unit,

especially David Herbst and Jim Hunter, played a very important role
necessary for the success of several research projects.
Finally, and most importantly, I thank my wife, Sherry, and son, Ryan,
for all of the encouragement, support, and patience they have exhibited. I
thank my wife for her return to full-time employment that was so necessary
for the successful completion of my studies. I am proud of her spirit in
overcoming the many obstacles she faced before and after securing
employment. I thank my son for the wonderful example he has been to me.

His constant dedication to hard work and self-discipline in the classroom and
on the basketball court have served as a constant reminder to me of the
preciousness of life's opportunities.



ACKNOWLEDMENTS ................................................................................ iii

LIST OF TABLES............................................................................................ ix

LIST OF FIGURES.......................................................................................... xiv

LIST OF ABBREVIATIONS........................................................................ xviii

A BSTR A C T ..................................................................................................... xx


1 INTRODUCTION..................................................................... 1

2 LITERATURE REVIEW .......................................................... 6

The Milking Parlor From an Operations Management
Perspective ........................................................................ 6

Factors Influencing Milking Parlor Performance........... 9

Time and Motion Study.................................................... 30

Simulation Modeling........................................................ 39

Economic Analysis of Milking Parlors.......................... 57

Economic Analytical Tools............................................... 64


Introduction......................................................................... 89

Materials and Methods...................................................... 91

Results and Discussion...................................................... 95

C conclusions .......................................................................... 111


Introduction......................................................................... 112

Materials and Methods...................................................... 114

Results and Discussion...................................................... 117

C conclusions ......................................................................... 127

PA R LO RS................................................................................ 129

Introduction......................................................................... 129

Materials and Methods...................................................... 131

Results and Discussion...................................................... 149

C conclusions ......................................................................... 160


Introduction......................................................................... 162

Materials and Methods...................................................... 164

Results and Discussion...................................................... 173

C onclusions......................................................................... 206

PA R LO R S................................................................................ 208

Introduction......................................................................... 208

Materials and Methods ...................................................... 216

Results and Discussion...................................................... 229

C onclusions......................................................................... 250

FUTURE RESEARCH .......................................................... 251

A PPEN D ICES ................................................................................................ 257

AND AMOUNTS OF MILKING LABOR......................... 257

CAPITAL BUDGETING MODELS..................................... 264

GETING M ODELS ................................................................. 266

REFEREN C ES................................................................................................ 287

BIOGRAPHICAL SKETCH ......................................................................... 299




3-1. Least squares ANOVA for lag and milk flow times............ 96

3-2. Partial regression coefficients for lag time data and
m ilk flow data........................................................................... 97

3-3. Least squares ANOVA for milk yield .................................. 102

3-4. Partial regression coefficients for milk yield data.............. 102

3-5. Shifted gamma distribution parameters for milk flow
time as a function of milk yield per milking, pulsation
ratio, and vacuum level.......................................................... 110

4-1. Milk yield characteristics of test herds by herd milk
yield category. ............................................................................. 118

4-2. Weibull distribution parameters for pooled and trun-
cated milk yield per milking as a function of herd milk
yield category and m onth ....................................................... 122

4-3. Comparison of observed and simulated means and
standard deviations for pooled and truncated milk
yield per milking by herd milk yield category and
m on th ......................................................................................... 124

4-4. Comparison of observed and simulated means and
standard deviations for monthly total herd milk yield
by dairy and herd milk yield category ..................................125

4-5. Minimum, maximum, and average absolute percen-
tage difference between observed and simulated means
for monthly total herd milk yield and percentage differ-
ence between observed and simulated yearly total herd
milk yield by dairy and herd milk yield category .............. 126

5-1. Definitions of parlor simulation model's stochastic
elem ents and activities............................................................ 138

5-2. Characteristics of dairies providing simulation data........ 142

5-3. Raw data means and standard deviations for parlor
simulation model elements and activities by dairy...........146

5-4. Element and activity fitted distributions for milking
parlor simulation validation models .................................. 150

5-5. Comparison between observed and simulated parlor
performance for validation dairies....................................... 153

5-6. Element and activity fitted distributions for herringbone
and parallel milking parlor simulation models................ 154

5-7. Comparison of simulated milking parlor performance
measures for three milking facility size categories ........... 156

6-1. Least squares ANOVA for turns per hour and milk
per stall per hour by size of parallel parlor and milking
system pulsation ratio and vacuum.................................... 174

6-2. Least squares means for turns per hour and milk
per shift per hour by size of parallel parlor........................ 174

6-3. Least squares means for turns per hour and milk
per stall per hour by milking system pulsation ratio
and vacuum ............................................................................... 177

6-4. Least squares means for turns per hour and milk
per stall per hour by various combinations of
milking system pulsation ratio and vacuum.................... 178

6-5. Least squares means for turns per hour and milk
per stall per hour by various combinations of
parallel parlor size and milking system pulsation
ratio.............................................................................................1... 79

6-6. Least squares means for turns per hour and milk
per stall per hour by various combinations of
parallel parlor size and milking system vacuum............. 179

6-7. Least squares ANOVA for turns per hour and milk
per stall per hour by parlor design, parlor size and
milking system pulsation ratio and vacuum..................... 181

6-8. Least squares means for turns per hour and milk
per shift per hour by parlor design ....................................... 181

6-9. Least squares means for turns per hour and milk
per shift per hour by parlor design and milking system
pulsation ratio........................................................................... 182

6-10. Least squares means for turns per hour and milk
per shift per hour by parlor design and milking
system vacuum ......................................................................... 182

6-11. Least squares ANOVA for turns per hour and milk
per stall per hour by size of parallel parlor, milking
procedures, and amount of milking labor.......................... 184

6-12. Least squares means for turns per hour and milk
per shift per hour by milking procedure............................. 185

6-13. Least squares means for turns per hour and milk
per shift per hour by amount of milking labor.................. 186

6-14. Least squares means for turns per hour and milk
per shift per hour by milking procedures and
am ount of m ilking labor ........................................................ 187

6-15. Least squares means for turns per hour and milk
per shift per hour by parlor size and milking
procedures.................................................................................. 188

6-16. Least squares means for turns per hour and milk
per shift per hour by parlor size and amount of
m ilking labor............................................................................. 188

6-17. Least squares ANOVA for turns per hour and milk
per stall per hour by parlor design, parlor size, milking
procedures, and amount of milking labor.......................... 191

6-18. Least squares means for turns per hour and milk
per shift per hour by parlor design ....................................... 192

6-19. Least squares means for turns per hour and milk
per shift per hour by milking procedure............................. 192

6-20. Least squares means for turns per hour and milk
per shift per hour by amount of milking labor.................. 193

6-21. Least squares means for turns per hour and milk
per shift per hour by parlor design and milking
procedures.................................................................................. 194

6-22. Least squares means for turns per hour and milk
per shift per hour by parlor design and amount
of m ilking labor. ........................................................................ 194

6-23. Least squares means for turns per hour and milk
per shift per hour by parlor size and milking
procedures.................................................................................. 196

6-24. Least squares means for turns per hour and milk
per shift per hour by parlor size and amount of
m ilking labor............................................................................. 196

6-25. Least squares means for turns per hour and milk
per shift per hour by milking procedures and
am ount of m ilking labor ........................................................ 197

6-26. Least squares ANOVA for turns per hour and milk
per stall per hour by size of parallel parlor and indivi-
dual cow milk yield per milking........................................... 198

6-27. Regression coefficients for turns per hour as a function
of individual cow milk yield per milking for various
sized parallel and herringbone parlors................................ 199

6-28. Regression coefficients for milk per stall per hour as a
function of individual cow milk yield per milking for
various sized parallel and herringbone parlors................. 200

6-29. Least squares ANOVA for turns per hour and milk
per stall per hour by parlor design, parlor size, and
individual cow milk yield per milking............................... 204

7-1. Costs of totally equipped parlors in three milking fac-
ility size categories including parlor building and
associated equipm ent............................................................... 218

7-2. Information used to calculate depreciation, capital
replacement, and property taxes for milking facility
capital budget m odels .............................................................. 219

7-3. Cash flow calculations in milking facility capital bud-
get m odels. .................................................................................. 220

7-4. Stochastic output from the simulation of various
m ilking facility alternatives................................................... 230

7-5. Lower and upper bounds on the willingness to pay
for various milking facility alternatives ............................. 231

7-6. Stochastic output from the simulation of various
milking facility alternatives operated at selected
pulsation ratio and vacuum combinations........................ 236

7-7. Lower and upper bounds on the willingness to pay
for various milking facility alternatives operated at
selected pulsation ratio and vacuum combinations......... 237

7-8. Stochastic output from the simulation of three milking
facility alternatives operated using selected combina-
tions of milking procedures and amounts of milking
lab or............................................................................................. 243

7-9. Lower and upper bounds on the willingness to pay
for three milking facility alternatives operated using
selected combinations of milking procedures and
am ounts of milking labor....................................................... 244



2-1. Operational view of dairy farm............................................. 8

2-2. Alternative problem-solving approaches........................... 40

2-3. Steps in a simulation study.................................................... 43

2-4. Schematic view of risk efficiency criterion......................... 74

3-1. Components of total machine-on time............................... 93

3-2. Milking time as a function of pulsation ratio
and vacuum level .................................................................... 99

3-3. Milking time as a function of pulsation ratio and
milk yield per cow per milking at a constant vacuum
(46.6 kPa) ..................................................................................... 101

3-4. Milk yield per milking as a function of pulsation ratio
and vacuum level .................................................................... 103

3-5. Histogram of sample data with overplot of fitted
gamma distribution for 50:50 pulsation ratio, 42.3
kPa vacuum, high milk yield per milking
(> 12.35 kg/cow )......................................................................... 108

3-6. Histogram of sample data with overplot of fitted
gamma distribution for 70:30 pulsation ratio, 50.8
kPa vacuum, high milk yield per milking
(< 7.41 kg/cow )........................................................................... 109

4-1. Comparison by herd milk yield category and month
of observed average daily bulk tank milk yield per
cow and simulated average daily milk yield per cow.......... 119

4-2. Histogram of pooled and truncated milk yield per
milking sample data with overplot of fitted Weibull
distribution for worst fitting distribution ........................... 120

4-3. Histogram of pooled and truncated milk yield per
milking sample data with overplot of fitted Weibull
distribution for best fitting distribution............................... 121

5-1. Flowchart of milking parlor simulation model logic ........ 133

5-2. Time-bar chart of network parlor simulation model
showing stochastic elements and activities........................ 135

5-3. Simplified schematic representation of network parlor
simulation model showing stochastic elements and
activities...................................................................................... 136

5-4. Performance comparison of four large parallel milking
p arlors. ......................................................................................... 159

6-1. Time-bar chart of hypothetical three-stall parlor
showing stochastic elements and activities of SLAM-
SYSTEM parlor simulation model .................................... 176

6-2. Parlor turns per hour as a function of individual
cow milk yield per milking for different size parallel
m ilking parlors. ......................................................................... 201

6-3. Milk per stall per hour as a function of individual
cow milk yield per milking for different size parallel
m ilking parlors. ......................................................................... 202

6-4. Parlor turns per hour as a function of individual
cow milk yield per milking for different size her-
ringbone and parallel milking parlors................................. 205

6-5. Milk per stall per hour as a function of individual
cow milk yield per milking for different size her-
ringbone and parallel milking parlors................................. 206

7-1. Cumulative probability distributions of net present
returns to ownership and non-parlor fixed costs for
double-20 herringbone and double-20 parallel milking
p arlors. ......................................................................................... 232

7-2. Cumulative probability distributions of net present
returns to ownership and non-parlor fixed costs for
double-32 parallel, two double-16 herringbone, and
two double-16 parallel milking parlors ............................... 233

7-3. Cumulative probability distributions of net present
returns to ownership and non-parlor fixed costs for
double-40 parallel, two double-20 herringbone, and
two double-20 parallel milking parlors ............................... 234

7-4. Cumulative probability distributions of net present
returns to ownership and non-parlor fixed costs for
double-20 parallel milking parlor operated at: 1) 60:40
pulsation ratio, 46.6 kPa vacuum; 2) 60:40 pulsation ratio,
50.8 kPa vacuum; 3) 70:30 pulsation ratio, 46.6 kPa vac-
uum;and 4) 70:30 pulsation ratio, 50.8 kPa vacuum......... 238

7-5. Cumulative probability distributions of net present re-
turns to ownership and non-parlor fixed costs for two
double-16 parallel milking parlor operated at: 1) 60:40
pulsation ratio, 46.6 kPa vacuum; 2) 60:40 pulsation
ratio, 50.8 kPa vacuum; 3) 70:30 pulsation ratio, 46.6
kPa vacuum; and 4) 70:30 pulsation ratio, 50.8 kPa
vacuum ....................................................................................... 239

7-6. Cumulative probability distributions of net present
returns to ownership and non-parlor fixed costs for
two double-20 parallel milking parlor operated at:
1) 60:40 pulsation ratio, 46.6 kPa vacuum; 2) 60:40
pulsation ratio, 50.8 kPa vacuum; 3) 70:30 pulsation
ratio, 46.6 kPa vacuum; and 4) 70:30 pulsation ratio,
50.8 kPa vacuum ....................................................................... 240

7-7. Cumulative probability distributions of net present
returns to ownership and non-parlor fixed costs for
double-20 parallel milking parlor operated using two
milking procedures (MP): 1) standard (predip, wipe,
attach), and 2) abbreviated (attach); and three levels of
milking labor (ML): 1) deficit (2 milkers), 2) standard
(3 milkers), and surplus (4 milkers) ..................................... 246


7-8. Cumulative probability distributions of net present
returns to ownership and non-parlor fixed costs for
two double-16 parallel milking parlor operated using
two milking procedures (MP): 1) standard (predip, wipe,
attach), and 2) abbreviated (attach); and three levels of
milking labor (ML): 1) deficit (2 milkers), 2) standard
(3 milkers), and surplus (4 milkers) ................. 247

7-9. Cumulative probability distributions of net present
returns to ownership and non-parlor fixed costs for
two double-20 parallel milking parlor operated using
two milking procedures (MP): 1) standard (predip,
wipe, attach), and 2) abbreviated (attach); and three
levels of milking labor (ML): 1) deficit (2 milkers),
2) standard (3 milkers), and surplus (4 milkers)................ 248



Excluding abbreviations of common weights and measures, the
following are used within the dissertation. Terms may or may not be
accompanied with long form descriptions in the text.

2x = two times per day milking
3x = three times per day milking
CDF = cumulative probability distribution function
CPH = cows milked per hour
CPMH = cows milked per man per hour
CT = cycle time
DDT = detachment delay time
DHIA = Dairy Herd Improvement Association
FSD = first degree stochastic dominance
GSD = generalized stochastic dominance
IRR = internal rate of return
LT = lag time
MFT = milk flow time
ML = milking labor
MMY = monthly total herd milk yield
MP = milking procedures
MPS = milk per shift
MSH = milk per stall per hour
MT = milking time
MY = milk yield
MYM = milk yield per milking
NPR = net present returns to ownership and non-parlor fixed
NPV = net present value
n = willingness to pay premium
PDF = probability density function
PP = payback period
PR = pulsation ratio
Ra = absolute risk aversion coefficient
ROR = rate of return
Rr = relative risk aversion coefficient
SDRF = stochastic dominance with respect to a function
SSD = second degree stochastic dominance
TMOT = total machine-on time


TPH = turns per hour
VCR = video cassette recorder
WRT = work routine time
YMY = yearly total herd milk yield

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



Craig Vincent Thomas

April, 1994

Chairman: Michael A. DeLorenzo
Major Department: Animal Science

Two stochastic models were developed to determine the most
economical size, design, milking system operating characteristics, and

management strategy for large milking parlors. Model one was a network

simulation for large herringbone and parallel parlors. Element and activity
distributions used in the model were fitted to data from Florida dairies using
herringbone and parallel parlors. Comparison between simulated and actual
parlor performance for four large parlors showed less than .50% difference

between actual and simulated mean cows milked per hour and milk

harvested per milking. Factorial experiments using the parlor simulation

revealed that parallel parlors outperformed similarly sized herringbones.
Smaller parallel parlors (double-16, 20) operated more efficiently in processing
inputs and producing outputs than larger parlors (double-32, 40). Milking

system operating characteristics enhanced parlor performance when
pulsation ratio was widened or vacuum was increased. Parlor performance
increases diminished as increased amounts of milking labor were employed
and optimal amount of milking labor depended upon milking procedures
used. Minimal milking procedures required less milking labor and an
intense premilking routine required more milking labor. Parlor performance
decreased in terms of number of cows milked per hour but increased in terms
of milk harvested per milking as individual cow milk yield per milking
increased. Model two was a parlor economic simulation which used
stochastic inputs, cows milked per milking and milk harvested per milking,
from the parlor simulation and predicted net present returns to ownership
and non-parlor fixed costs. Parlor alternative economic differences were
measured assuming dairy producers would maximize daily parlor use. The
economic analysis indicated parallel parlors provided higher returns than
herringbones. When total parlor stalls were 64 stalls or greater; multiple,
small (two double-16 or two double-20) parallel parlors provided higher
returns than multiple, small (two double-16 or two double-20) herringbones
or a single, large (double-32 or double-40) parallel. Operating the selected
multiple, small parallel parlors at wide pulsation ratio (70:30) and high
vacuum (50.8 kPa) provided the highest returns. Parlor returns were
substantially higher when management strategies employing minimal
premilking procedures were used. Employment of minimal milking labor
was not associated with highest parlor physical performance, but increased
generally increased parlor returns.


The trend toward fewer and larger dairy farms has been rapidly
occurring in every region of the U. S. The change of scale in the dairy
industry has accelerated in the last decade, especially in Florida where it is not
uncommon to find dairy herds of 1,000 to 3,000 cows milked through one
milking parlor. As a result, the milking facility has become the heart of the

dairy enterprise, one of its largest capital investments, and a major source of
operating costs. Furthermore, in open housing systems typical of Florida and
other Sunbelt states the milking parlor can be a critical factor limiting daily
milk output from the dairy because it is often unable to milk the entire
milking herd in the allowed milking time.

In response, Florida dairy producers have been building increasingly
larger milking parlors. For example, in the past five years milking parlors
with 48 or more stalls have been constructed (e.g., double-sided parallel
parlors with 24 to 40 stalls per side) in Florida. No quantitative information
exists to guide dairy producers in predicting the level of physical or economic
performance to anticipate from various parlor sizes and designs and what
effects milking system operating characteristics and management strategies

exert on parlor physical or economic performance.
Numerous factors have been hypothesized to affect milking parlor
performance: 1) parlor size (Bickert et al., 1974), 2) parlor design (Armstrong,

1988; Armstrong et al., 1974; Armstrong et al., 1990; Armstrong and Quick,
1986; Bickert et al., 1974; Gamroth, 1992), 3) milking system operating
characteristics (Thomas et al., 1993), 4) individual cow milking time
(Gamroth, 1992), 5) milking procedures and routine (Armstrong, 1988;
Armstrong and Quick, 1986; Bickert, 1978; Gamroth, 1992), 6) amount of
milking labor (Armstrong, 1988; Gamroth, 1992; Sagi and Merrill, 1977), and
7) herd milk production level (Armstrong and Quick, 1986). Unfortunately,
the majority of these reports provide only anecdotal information and do not
provide dairy operators with information that will allow them to accurately
predict parlor performance resulting from changes in any of these factors.
Furthermore, most information available concerning parlor performance is
on relatively small parlors (e.g., double-16 or smaller), which leaves a critical
void in the literature because large dairy operators have primarily increased
parlor cow throughput by building increasingly larger parlors. For example,
in the past five years it has become common for large Florida dairies to build
parlors with 40 to 80 stalls.
What little information is available in the literature concerning milking
parlor economic performance is outdated and does not consider the large
parlor sizes and new designs currently used (Bickert et al., 1974; Willet et al.,
1982). Past economic analyses of milking parlors (Bickert et al., 1974; Willet et
al., 1982) only examined parlor performance from an input processing
viewpoint and did not consider the effects of parlor size, design, milking
system operating characteristics, and management strategies on milk output.
Additionally, these analyses considered parlor performance to be static and
dairy producers to be pure profit maximizers. Therefore, in analyzing
milking parlor economic performance the scientific community has failed to
address three very crucial aspects of real world management decision making:

1) a true profit equation where returns are a function of all input and output
quantities and prices, 2) variability in expected returns (i.e., risk), and 3) the
attitude of the decision maker towards the variable return (i.e., risk attitude).
Milking parlors are extremely complex systems that do not easily lend
themselves to experimentation to gain reliable decision-making information.
Therfore, some researchers (Bickert et al., 1972; Burks, 1989; Chang, 1992;
Micke and Appleman, 1973; Price et al., 1972) have studied milking parlors by
employing simulation modeling, a modeling technique in which the real
system (i.e., milking parlor, cows, and milking personnel) is imitated by a
computer program (Schriber, 1991). However, the applicability of past parlor
simulation models for use in decision making has been limited by their lack
of flexibility in assessing the impact on parlor performance due to the effects
of parlor size and design and changes in milking system operating
characteristics (e.g., milking system vacuum and pulsation ratio (PR)) and
management philosophies (e.g., milking procedures (MP), amount of milking
labor (ML)). Importantly, past parlor simulations either did not consider the
effect of milk yield (MY) on parlor performance (Price et al., 1972) or did not
allow a range of herd MY levels to be modeled (Bickert et al., 1972; Chang,
1992; Micke and Appleman, 1973). Valid milking parlor simulation models
useful in decision making should consider several alternative milking
system operating characteristics, management strategies, and herd MY levels
to assess the relationship between these factors and parlor performance.
Flexible modeling of MY allows parlor performance to be measured in terms
of milk output as well as cow throughput. The ultimate comparison and
selection of preferred parlor systems and operating philosophies should be
based on an analysis of outputs produced and inputs used and processed.

Projects in this dissertation were designed to produce models useful in
predicting milking parlor performance in response to a variety of milking
parlor designs, parlor sizes, milking system operating characteristics, and
management strategies; and to predict milking facility investment value in
response to these variables. Overall objectives were:

(1) to formulate an individual cow milking time (MT) prediction meth-
od suitable for use in milking parlor simulation models to simulate
a broad range of herds (i.e., MY level) and milking system operating
characteristics (i.e., PR and vacuum), and individual cow MY;

(2) to formulate a method of simulating individual cow milk yield
per milking (MYM) that would be suitable for use in milking parlor
simulation modeling and would allow seasonality and different
levels of herd MY to be modeled;

(3) to formulate a milking parlor simulation model for large herring-
bone and parallel milking parlors that accurately imitated a variety
of real parlor systems employing several different milking system
operating characteristics, management strategies, and herd MY
levels with performance predicted in terms of milk output and
cow throughput;

(4) to determine the effects of parlor size, parlor design, milking system
operating characteristics, management strategies (i.e., MP and
amount of ML), and herd MY on the performance of simulated
herringbone and parallel milking parlors;

(5) to develop a stochastic capital budgeting model to determine which
milking parlor prospects are preferred, economically, by dairy
decision makers, and the willingness of dairy decision makers to pay
for the economically preferred milking parlor prospects;

(6) and to determine which milking system operating characteristics and
management strategies are preferred, economically, by dairy decision
makers; and the willingness of dairy decision makers to pay for the
economically preferred combinations of milking system operating
characteristics and management strategies.


The Milking Parlor From an Operations Management Perspective

To properly evaluate milking parlor performance on large dairies the
parlor should be viewed from an operations management standpoint.
Operationally the dairy farm with its housing, feeding, milking, waste
handling systems, and so forth, is the plant. Within this plant various
individual systems (e.g., feeding and milking systems) perform operations to
physically transform raw materials (e.g., hay, grain, cows) into products. In

the case of a commercial dairy, the primary product is milk and the secondary
products are animals.
Operationally, dairy managers have generally organized their plants ac-
cording to a process layout (Chase and Aquilano, 1989). In this type of layout,
similar equipment (e.g., milking machines) is grouped together. Productive
units (i.e., cows) travel according to a sequence of established operations

where appropriate machinery is located to accomplish a given task in the
transformation process. Such plant layouts are common in manufacturing
industries. For example, most industrial plants are departmentalized so that
parts travel from one end of the plant to the other through departments that
successively transform raw materials into finished products. Primary
operations occur in the first department, then parts move on to secondary

operations followed by finishing operations and ultimate assembly of parts
into subunits and finished products. On a large dairy, this
departmentalization of operations results in areas reserved for feeding, health
care, milking, breeding and other activities essential to production.
The soundness of the process layout is manifested by its wide adoption
in nearly every industry. However, as with any process manufacturing
layout, the output capacity of the plant is finite, being no greater than the
department with the highest processing requirements. In other words, total
output is no greater than the output of the most restrictive "bottleneck"
(Figure 2-1). Generally, on large dairy farms this distinction falls on the
milking parlor because the number of cows that can be processed through the

parlor is less flexible than the cow population other departments in the
system can tolerate.
In manufacturing industries, bottleneck problems are handled utilizing a
concept known as capacity balance (Chase and Aquilano, 1989). The initial
and primary determinants of total plant output are forecasted product
demand and capacity of the most restrictive bottleneck. First, if required to
meet anticipated demand, capacity of the most restrictive bottleneck is
increased through capital asset acquisition. Capacity balance then strives to
balance the output of each department to exactly meet the input requirements
of each succeeding department. Appropriate non-bottleneck equipment is
utilized or idled to meet this requirement. In theory, the plant will be
designed to exactly match product output with forecasted product demand,
both in terms of quantity produced and timing of production. However, in
practice this balance is rarely, if ever, achieved. Forecasts are never 100%
accurate and demand is never constant over time. Furthermore, the best
operating level for each department often differs. Therefore, a compromise


between departmental production costs and lost sales due to unmet demand
or storage costs due to excess production must be reached to maximize profit.
Capacity balance for a large dairy farm is a somewhat different issue than
in manufacturing industries. The primary difference results from differences




Output limited by most
restrictive processing
Figure 2-1. Operational view of dairy farm.

in product demand. In the absence of quotas on milk production or waste

disposal constraints, the demand from an individual dairy is, for all practical
purposes, infinite. This occurs because the dairy producer operates in an
almost perfectly competitive market where he is a "price taker" for his
outputs. Therefore, the producer has no restrictions on total output from the

demand side, only from the cost side. To determine capacity balance he

should seek a total facility size that balances marginal revenue and marginal

cost yet does not outstrip his ability to manage effectively. Capacity will
therefore be highly dependent on the skill and temperament of the manager.

It is also assumed that dairy owners and managers are in business to
make money, i.e., they are profit maximizers or maximizers of some other
measure of economic success (e.g., maximization of expected utility).
Therefore, they make investments in expectation of positive returns and
decide among competing investments on the basis of their relative returns
for a given level of risk. Thus the choice among competing investments will
be the one that brings the highest return over its life at an acceptable level of
A critical factor in reaching this goal is minimizing the constraining

effects from the bottleneck which often has the greatest influence on the dairy
plant's total output--the milking parlor. Therefore, the primary interest will
be focused more heavily on product output rather than input processing.
Instead of focusing on how many cows a particular parlor can milk per unit
time dairy owner's and manager's attention should focus on the parlor's
milk output per unit time. Additionally, they should be concerned with
identifying and controlling the factors with the most influence on parlor milk
output. Placing the primary focus on the parlor's milk output also allows for
a complete investment analysis of milking parlors that examines the
investment value of various parlor sizes and designs and the sensitivity of
their value due to changes in critical variables affecting performance.

Factors Influencing Milking Parlor Performance

Milking parlor performance in terms of output per unit time is deter-
mined by three things: 1) animal factors, 2) machinery factors, and, 3) human

Animal Factors

Many factors inherent to the cow have an impact on variation of
individual cow MT. Sources of variation can be delineated into two basic

sources, variation within cows and variation between cows.
Several researchers (Beck et al., 1951a; Beck et al., 1951b; Foot, 1935;
Stewart et al., 1957; Touchberry and Markos, 1970) have noted that individual
cows have characteristic milk flow curves that show little variation with
time; however, extreme variation has been discovered in milk flow curves
between cows. Schmidt and van Vleck (1969) showed that regression models
containing no between-cow variables accounted for only 37% of the variation
in MT before machine stripping.
A recent milking speed study indicated that between cow variation for
MT was highly significant (P < .001) (Thomas et al., 1991). Twelve cows
producing from 13.9 to 41.5 kg of milk/d were examined. System vacuum
was set at 45.6 kPa. Although pulsation characteristics were varied; MT

average for the 288 total observations was 8.0 min with a wide range of 4.5 to
16.0 min.
Touchberry and Markos (1970) conducted an exhaustive study of
variation in MT by collecting 6703 MT observations on 243 lactations of 147
cows. The range in individual cow MYM (2x per day milking) was 2.25 to 22.5
kg with average MT before machine stripping of 4.20 min (SD = 1.39 min). On

average, 95.5% of the MYM was collected before machine stripping.

The results were generally in agreement with earlier workers (Beck et al.,
1951a; Beck et al., 1951b; Stewart et al., 1957). Touchberry and Markos (1970)
found that most of the total variation in MT was due to differences between
cows of the same breed group and due to differences between observations

within the same cow in the same lactation. Over 50% of the total variation in
MT was due to differences between cows. Because MYM and stage of lactation
were found to have such significant effects on MT and other milking rate
measures the variance components were adjusted for these two independent
variables. When these adjustments were made it was found that the
percentage of variation in total MT accounted for by differences between cows
of the same breed group was 55.7%. The second most important source of
variation in MT was differences found within a given lactation of the same
cow (31.8%). Breed differences accounted for only 4.5% and differences
between lactations of the same cow only 8.0%. They also found that the
percentage of total variation due to differences between observations within
the same cow in the same lactation fell significantly when adjusted for stage

of lactation and MYM. The percentage decreased from 48.4 to 31.8%.
The researchers developed three prediction equations for MT based on
regression coefficients for MYM plus maximum flow rate or MY in first
minute of milking or MY in first two minutes of milking. All three
equations were highly correlated with actual MT (R > .86). In all three cases
they concluded that the main evidence to be gained from the prediction
equations was that the time required to milk cows was primarily dependent
on MYM. Clough (1979) also reported on the relationship of average MYM
and average MT. Data collected from 28 commercial herds at the a.m.
milking showed a significant (P < .01) linear relationship between average
MY and average MT. The linear regression coefficient was .207 with an
intercept of 2.75.

Smith et al. (1974) obtained similar results in studies on the independent
effects of stage of lactation and MY on measures of milk flow rate. Data was
collected on 1402 milkings of 87 cows from three breed groups. Average total

MT (machine time + strip time) was 5.37 min (SD = .81 min). Average strip
time was 1.48 min (SD = .60 min). Average total MYM was 10.17 kg (SD = 1.19
kg) and average strip yield was 1.48 kg (SD = .98 kg). Cows within breed
groups were found to account for 48.9% of the variation in total MT. Breed
within lactation accounted for only 3% of total variation in MT while stage of
lactation within cow accounted for 33%. Unexplained variation in MT (i.e.,
differences between a.m. and p.m. time of milking, within cow within
lactation) accounted for 16% of the total variation in MT.
They conducted two analyses of variance for various milking rate

measurements using a mixed model which included effects due to year of
calving, month of calving, lactation number, breed group, cow within
lactation number and breed group, stage of lactation, milking system, time of
milking (a.m. versus p.m.) and interaction between stage of lactation and
milking system. The first model did not correct the effects for the influence of
MYM while the second model fitted partial linear and quadratic regressions
on MYM for the milking at which milking rates were observed. The analyses
revealed that stage of lactation and stage of lactation X milking system
interaction had a significant effect on MT when unadjusted for MYM. When
this adjustment was made, however, stage of lactation had no significant

effect on MT. The researchers concluded that changes in total MT from one
stage of lactation to another are primarily dependent on lactation trend in
MY, therefore, they concluded corrections in MT for stage of lactation were
much less important than corrections for MYM.
Little information is available on the effects of milk production on the
performance of milking parlors. Armstrong and Quick (1986), in a case study,
reported that increased levels of milk production decreased parlor

performance. In their study they compared the effects of average daily MY of

15.9 vs 27.7 kg/cow. They found that cows with higher average daily MY
decreased the number of cows milked per man per hour (CPMH) from 84 to
67. The decrease in parlor performance was primarily due to an increase in
the waiting time of the milkers. Waiting time for lower producing cows was
.9 s/cow versus 9.2 s/cow for higher producing cows.
Milking frequency is a management decision; however, its effect on the
time required to milk cows is thought to be primarily mediated through
changes in MYM (Barnes et al., 1989). The most common milking frequency
in the U. S. dairy industry is twice per day (2x) with roughly equal milking
interval between a.m. and p.m. milkings. However, three times per day (3x)
milking is not uncommon and reports in the literature indicate milk
production responses from no response to as much as a 32% increase (Elliot,
1959, Hanson and Bonnier, 1947, Pearson et al., 1979). A more typical
response would be that found by Gisi et al. (1986) which indicated a 12%
advantage in milk production for 3x versus 2x milked cows.

Machinery Factors

Several machinery related factors are known to influence the time
required to milk individual cows and it is known that milking parlor size and
design influence parlor performance. However, a paucity of information
exists on the influence of most milking machinery factors on milking parlor
performance or its interaction with milking parlor size and design The most
important machinery related factors, in addition to milking parlor size and
design, include milking system operating characteristics, milking parlor
mechanization and milking equipment malfunction.

Milking system operating characteristics

Much work has been done concerning the influence of milking system
operating characteristics on the time required to milk individual cows;
however, little is documented concerning its effect on the milking times of
groups of cows or parlor performance. The primary effects of milking system
operating characteristics on MT and MY of individual cows is mediated
through: 1) vacuum level, 2) pulsation rate, and 3) PR.
Numerous investigators (Baxter et al., 1950; Caruolo et al., 1955; Gregoire
et al., 1954; Schmidt and Van Vleck, 1969; Schmidt et al., 1963; Smith and
Petersen, 1946; Stewart and Schultz, 1958) have studied the relationship
between vacuum level, milking speed and MY. All of these studies showed a
decrease in MT and an increase in flow rate as vacuum level increased. For

example, Schmidt and Van Vleck (1969) found a significant (P < .05) negative
correlation between time before machine stripping and milking vacuum
level (-.40) and a significant (P < .05) positive correlation between milking
vacuum level and average and maximum flow rates (+.46).
Caruolo et al. (1955) investigated milking vacuum levels of 33.9, 44.0 and
57.6 kPa over an entire lactation and found significant (P < .05) decreases in
average MT as vacuum level increased. Average MT were 9.35, 7.20 and 6.12
min for 33.9, 44.0 and 57.6 kPa, respectively. Smith and Petersen (1946)
utilized milking vacuum levels of 33.9, 40.6 and 47.4 kPa and two different
PR. Analysis within a given PR indicated a linear relationship between
milking vacuum level and MT with each 6.8 kPa increase in vacuum level

resulting in a 25 s decrease in MT. Baxter et al. (1950) investigated vacuum

levels of 35.9, 53.8 and 69.1 kPa and found mean peak flow rates to increase
linearly for normally milked quarters and quadratically in cannulated

quarters. Another study conducted by Smith and Petersen examined vacuum
levels of 33.9, 42.3 and 50.8 kPa. Results indicated that as vacuum level

increased milking rate increased in a curvilinear fashion with the greatest
increase occurring between 33.9 and 40.6 kPa. Work summarized by British
researchers (Thiel and Mein, 1979) indicated perhaps why Smith and Petersen
(1946) found linear and curvilinear relationships between milking vacuum
level and MT. According to Thiel and Mein (1979) there is a curvilinear
relationship between vacuum and peak flow rate with the rate of peak flow
rate increase, decreasing with increasing vacuum levels. However, the peak
flow occurs just prior to reaching 50.8 kPa. Therefore, the differing
relationships described by Smith and Petersen (1946) may have been due to
the two milking vacuum ranges differing; with one including and one
excluding a data point beyond this inflection point.
Investigations into the relationship between vacuum level and udder
health have been somewhat confusing and controversial. Mochrie et al.

(1953a), Mochrie et al. (1953b), and Mochrie et al. (1955) were unable to detect
any significant effect of vacuum level on milk leukocyte counts or teat end
scores in either short or long term trials. More recent work by Spencer and
Rogers (1991) suggested that higher vacuum may aid in decreasing milking
machine malfunctions, such as teatcup liner slips, known to contribute to
increased rates of new intramammary infection (Spencer, 1989). They found
that lower vacuum levels had higher levels of liner slips, major vacuum
fluctuations, and unit fall offs. Mean frequencies of liner slips per milking
were 8.8 and 4.7 for vacuum levels of 42.0 and 50.0 kPa. Mean frequencies of
major vacuum fluctuations per milking were 11.2 and 6.2 for vacuum levels
of 42.0 and 50.0 kPa. Mean frequencies of unit fall offs per milking were .090
and .028 for vacuum levels of 42.0 and 50.0 kPa.

Pulsation rate has been shown (Schmidt and Van Vleck, 1969) to have
low but significant (P < .01) correlations with MT before machine stripping
(-.25), average flow rate (+.26) and maximum flow rate (+.22). However, most
research showed advantages gained in milking speed by increasing pulsation
rate were small and primarily gained by increasing pulsation rates from very
low levels (e.g., 20 to 35 cycles/min) to medium levels (e.g., 50 to 80
cycles/min)(Clough et al., 1953; Stewart and Schultz, 1958). Rosen et al. (1983)
found that machine-on time was decreased .44 min/milking by increasing
pulsation rate from 35 to 50 cycles/min and no further significant reduction
in time was gained by increasing the rate to 65 or 80 cycles/min. Schmidt and
Van Vleck (1969) examined pulsation rates of 40, 50, 60, 80 and 120 cycles/min.
In multiple regression analysis of their full model, no partial regression
coefficients showed a significant effect of pulsation rate on MT before
machine stripping, milking speed or strip yields. At best, in a reduced model,
increasing pulsation rate by 20 cycles/min resulted in a meager .18 min
decrease in MT before machine stripping. Thomas et al. (1991) found no
significant difference between pulsation rates of 50 and 60 cycles/min for MT,
milk flow rate, or MY. Also, in the short term they found no significant effect
of pulsation rate on somatic cell count.
Schmidt and Van Vleck (1969) found PR to have significant (P < .01)
correlations with MT before machine stripping (-.27), average flow rate (+.26)
and maximum flow rate (+.27). In multiple regression analysis for a full
model, partial regression coefficients showed a significant (P < .01) effect for
PR on MT before stripping (-.60), total MT (-.65), average flow rate (+.41) and
maximum flow rate (+.60). As a result of their analysis, they concluded that
quantitatively the three components that contributed the most to variation in
milk flow measurements were vacuum level, PR, and MYM.

Thomas et al. (1991) investigated PR of 50:50, 60:40 and 70:30 and found
significant (P < .05) effects on milking speed and MYM. Least-square means
for MT differed significantly (P < .05) between each PR and were 8.44, 8.00 and
7.47 min for 50:50, 60:40 and 70:30, respectively. Least-square means for
average flow rate differed significantly (P < .05) between each PR and were 1.5,
1.6 and 1.7 kg/min for 50:50, 60:40 and 70:30, respectively. There were also
significant (P < .05) differences between 50:50 and 70:30 for total MYM (12.1 vs
12.6 kg), fat yield per milking (.48 vs .52 kg) and 3.5% FCM yield per milking
(13.0 vs 13.8 kg). No significant interactions between pulsation rate and PR
were found. Pulsation ratio was not found to influence somatic cell counts in
the short term. In another study Thomas et al. (1993) found that widening PR
from 50:50 to 70:30 increased CPH by 3.6% (4.1 cows) in double-11 herringbone
parlors. This research also showed no differences between 50:50 and 70:30 PR
in various measures of udder health; such as bulk tank SCC, incidence of
clinical mastitis, and rate of culling due to mastitis.
Mahle et al. (1982) purported to show a relationship between udder
health and PR. Their work indicated a highly significant effect of PR on
Wisconsin mastitis test scores. The Wisconsin mastitis test scores were
higher for 50:50 and 70:30 than 60:40 PR and, although nonsignificant, 70:30
had the highest number of new intramammary infections due to
Staphylococcus aureus. However, applicability of results to dairy situations is
questionable because the animals used in the trial were beef heifers and
experimental postmilking challenge with Staphylococcus aureus was used
with no postmilking teat antisepsis employed. Reitsma et al. (1981) also
found a relationship between PR and udder health. They examined four time

durations when teatcup liners were more than half closed, 0, .17, .34, and .51 s.
Liners, except for 0 s duration, were open for .66 s. This translates into

approximate pulsation ratios of 100:0, 80:20, 66:34 and 56:44 for 0, .17, .34, and
.51 s durations, respectively. Cows were subjected to experimental bacterial
challenge with teats dipped before and after milking in a culture of
Streptococcus agalactiae and Streptococcus dysgalactiae. No postmilking teat
antisepsis was performed. Results showed a higher percentage of quarters
infected for 0 and .17 s (50 and 27.5%) duration than for .34 and .51 s (10.0 and
12.8%). However, the pragmatic significance of these results are questionable
due to experimental bacterial challenge and the absence of postmilking teat
antisepsis. The researchers indicated that the longer durations of liner
closure (.34 and .51 s) cover the range of PR normally provided in
commercially available milking systems and the proportion of infected
quarters on these treatments were similar to the those of controls in previous
experiments by Bramley et al. (1978). This work (Bramley et al., 1978) failed to
show significant differences in new infection rates between no pulsation and
a 2:1 PR even under premilking experimental bacterial challenge conditions
when postmilking teat antisepsis was performed. The same trial also failed to
show significant differences in new infection rates between PR of 2:1 and 8:1
under experimental bacterial challenge conditions without postmilking teat

Milking parlor size and design

Before discussing the effects of milking parlor size and design on
performance, it is pertinent to consider how milking parlor performance has
been measured. The most common method used to report milking parlor
performance in the United States is cows milked per hour (CPH) (Bickert et
al., 1974). Although this term is well known to dairy producers and appears
commonly in the popular press, it fails to account for differences between

parlor types and sizes for the number of milking personnel or for differences
in herd MY levels. This has given rise to another popular measure of
performance, CPMH, that takes into account labor differences among parlors
(Bickert et al., 1974; Kelso et al., 1979; Williams et al., 1981). Clough (1979)
stated that many have advocated measuring parlor performance in terms of
milk produced per hour or per man per hour.
Another performance measurement term gaining in popularity is turns
per hour (TPH) or sometimes called turn-ins per hour (Armstrong, 1990).
Turns per hour refers to how many times per hour the particular parlor
milks a number of cows equal to the number of parlor stalls. Turns per hour

can be measured by observing the milking routine for several successive
groups of cows and calculating the average time interval from opening of
entry gate for one group until the entry gate opening of the next group. This
interval is referred to as "turnaround time" or cycle time (CT) (Sagi and
Merrill, 1977). Once average CT is calculated TPH is calculated by dividing 60
min/hr by CT. Cows per hour can be calculated by multiplying TPH times the

total number of parlor stalls. Turns per hour has the same disadvantage as
CPH since it does not consider labor inputs; however, it does allow
comparisons across parlor sizes.
Another term seen in the literature is "steady state throughput" (Willet
et al., 1982). When parlor performance is measured in terms of steady state
throughput the time required for parlor set-up, clean-up, and group changes
are not included in calculating performance figures such as CPH or CPMH.
Therefore, this method fails to take into account significant factors affecting
parlor performance. Also, unfortunately, many references do not clearly state
whether performance figures were measured as total performance; where
these additional factors are included, or as steady state throughput.

These measures of parlor performance allow some degree of comparison
between parlors, but as Armstrong and Quick (1986) suggested, they fall short
of accounting for all performance differences among parlors. They suggested
that parlors can be more accurately compared by using time and motion
studies. Such methods are not new (Chetwynd, 1956) and have been used
extensively in the United States (Appleman and Micke, 1973; Armstrong,
1979; Armstrong, 1982; Armstrong and Seltz, 1972; McVeagh and Leonard,
1981; Merrill and Thompson, 1980; Burks, 1989; Burks, et al., 1989) and Great
Britain (Clough and Quick, 1967; Quick, 1967; Quick, 1968). The primary
measure of milking parlor performance that has resulted from time and
motion studies is work routine time (WRT). Work routine time is derived
by summing all the times required for milker(s) to perform all activities
related to milking one cow. Common elements of WRT are: 1) cow entry
into parlor, 2) premilking udder preparation, 3) milking machine attachment,
4) milking machine adjustment or reattachment, 5) postmilking teat dipping
or spraying, 6) cow exit from parlor, 7) operator absence from parlor, and,
8) miscellaneous (e.g., waiting, washing milking unit, treating sick cow, etc.).
As Armstrong and Quick (1986) suggested, "The time required for these
activities ultimately determines the number of cows that can be milked per
hour by each operator" (p. 1169).
Armstrong and Quick (1986) suggested that WRT is advantageous as a
measure of milking parlor performance since it takes into account all factors
influencing speed: 1) type, size, and design of parlor and associated
equipment, 2) skill of ML, 3) number, type, and duration of MP, 4) animal
related factors influencing MT (e.g., level of MYM), and, 5) presence and
frequency of any milking equipment malfunctions, non-routine or
emergency procedures requiring attention by the milker. Therefore the

maximum number of cows a particular parlor-equipment-labor combination
can milk per hour is found by dividing 60 min/hr by WRT measured in
minutes per cow. However, this method still fails to account for parlor down
time due to nonmilking events such as premilking parlor setup, postmilking
parlor cleanup and shift changing.
Sagi and Merrill (1977) examined theoretical throughput capacities of
large herringbone parlors and reported that the slope of the curve associating
WRT with parlor performance was very steep. They concluded that even
decreases as small as .1 min/cow in WRT had a major impact on large parlor
The scientific literature has scant information on the effects of milking
parlor size and design on milking parlor performance. Most information
available is in the form of popular press articles and Cooperative Extension
Service bulletins. What information that does appear describing actual parlor
performances, even in refereed journals, consists primarily of data collected
from case studies and does not attempt to describe statistically the sources of
variation for milking parlor performance.
The classic journal article on the subject appeared as a symposium paper
in the March 1974 issue of the Journal of Dairy Science (Bickert et al., 1974).
This article lists expected performance figures (CPH) for the following parlor
types and sizes: herringbone (double-4, 6, 8 and 10), polygon (24 stall),
turnstyle (17 stall), and side-opening (double-3). The source of the parlor
performance figures were time and motion studies and computer
simulations; but the variation associated with these performance figures was
not given. However, the authors did offer anecdotal information on the
subject. For example, they indicated that the size of herringbone milking
parlors had an effect on efficiency. They maintained that efficiency per stall

decreases in long row (i.e., > 8 stalls/side) herringbone parlors. According to
the authors, increasing parlor length decreases efficiency because it takes more
time for cow entry and, in the absence of rapid-exit stalls, it also increases cow
exit time. Furthermore, since the majority of parlor designs require an entire
side of cows to enter and exit simultaneously, the cows on one side will only
milk as fast as the slowest milking cow on the side. Therefore, as number of
stalls per side increased the effect of the slowest milking cow was exacerbated.
One report (Armstrong, 1988) indicated that in a herd of 1,500 cows the
removal of 12 slow milking cows (>12 min/milking) decreased the total herd
milking time by 45 min.
These effects have led to the development of milking parlors with more
than two sides (e.g., the 4-sided polygon and 3-sided trigon). The logic for this
development was that by dividing the same number of stalls over more sides
the slow milking cow does not have as great an effect on polygon and trigon
parlors as it would on the two-sided herringbone or parallel parlors. Bickert
(1980) maintained that a double-10, mechanized herringbone parlor will
operate about 7% slower than an 18-stall mechanized trigon parlor (92 vs. 98
CPH). Armstrong and Quick (1986) reported on a case study comparing a
double-16 herringbone parlor vs a 32 stall polygon parlor. Each parlor used
the same number of operators, followed similar MP and average daily MY
(27.7 kg/cow) was the same. The primary differences in WRT between the
two parlors were cow entry, cow exit and operator wait. The polygon had a
16.9 s/cow advantage in WRT and milked 35.7% (112 vs. 152 CPH) more CPH.
A relatively new milking parlor design called the parallel parlor was
developed in the late 1970's in Holland and is currently undergoing a wave of
popularity in the United States (Armstrong et al., 1989). This design is similar
to herringbone parlors in that it is a two-sided parlor. However, the cows

stand perpendicular to, and facing away from, the milker pit. The first
parallel parlor in the United States was reported to have been built in 1981.
Commercially manufactured models of parallel parlors have only come into
existence in the past five years. Armstrong et al. (1990) reported a slight
performance advantage of parallel parlors over similarly sized herringbone
parlors. They found the WRT in a similarly equipped double-20 herringbone
and parallel parlor to be 40.0 s/cow versus 38.5 s/cow, respectively. This
translated into a 3.9% CPH performance advantage for the double-20 parallel
parlor (187 vs 180 CPH).
Other important considerations in milking parlor design include such
items as the design of holding pens, parlor entrances and exits, and parlor
return lanes. Armstrong et al. (1990) recommended that the escape area
adjacent to rapid exit stalls be 3.0 m in width. Dual-lane exit alleys have been
reported to increase CPMH by 7% in a double-10 herringbone (Armstrong et
al., 1974). Constructing parlors and holding areas with common floors, no
steps, ramps or turning required for parlor entry are also reported to improve
parlor performance (Armstrong and Quick, 1986). Armstrong (1988) also
reported on the innovation of "rapid-exit" milking parlor stalls. Rapid-exit
stalls are designed so each stall within a parlor side has a separate exit gate or
the entire exit-side of a parlor half rises in unison to release all cows
simultaneously. Armstrong (1988) reported increases in CPH of 9.3 to 16.0%
for rapid-exit equipped herringbone parlors in the range of double-10's to
double-24's. The percentage increase in parlor performance, measured as
CPH, was reported to increase as parlor size increased. For example, the
reported performance increase was 9.3% (75 versus 82 CPH) in a double-10
herringbone, 13.8% (116 versus 132 CPH) in a double-16 herringbone and
16.0% (150 versus 174 CPH) in a double-24 herringbone.

Milking parlor mechanization

In the early 1970's, milking equipment manufacturers began marketing
an increased number of devices for mechanizing milking parlors. Such items
became available as automatic milking machine detachers, automatic feed
bowl covers for parlors with in-parlor feeding systems, power operated parlor
gates, and holding pen crowd gates. According to Bickert et al. (1974) these
innovations have a positive impact on milking parlor performance. For
example, they reported that the addition of a crowd gate in a double-8 or
double-10 herringbone increased performance by 5 CPH. The addition of
automatic detachers to these two parlors is reported to decrease the number of
required operators from one to two with only a slight reduction in CPH
performance. Support of these conclusions is found in the work of
Armstrong and Seltz (1972) which showed that machine stripping and
detachment accounted for 22% of a milker's time in a double-8 herringbone.
According to Thompson (1981), and supported by the data of Bickert et al.
(1974), automatic detachers may be more advantageous as parlor size
increases. In parlors with automatic detachers Thompson (1981) pointed out
that operators do not have to return to the cow to manually detach the unit.
Therefore, fewer operators can operate more units without danger of
overmilking plus time normally spent in detaching units manually can be
reassigned to other duties.
A relatively new innovation from Great Britain in parlor mechanization
is automatic postmilking spraying of antiseptic teat dip in exit alleys
(Armstrong and Quick, 1986). This technology was reported to reduce WRT
by 9.4% (5.2 s/cow decrease) in a double-8 herringbone and increased CPMH

by 6. Its effectiveness in terms of cost and efficacy in comparison with
standard teat dipping techniques was not reported.

Milking equipment malfunction

Appleman and Micke (1973) reported that milking equipment problems
and adjustments varied from 2.2 to 8.2% of WRT. They reported the primary
component of milking equipment malfunction affecting milking parlor
performance was due to milking machine teatcup liner slippage and machine
fall off. Micke and Appleman (1973) reported that, on average, 2.6% of WRT
was spent attending to minor problems (e.g., machine adjustment). These
data also support the idea that the major source of time spent attending
equipment malfunctions are primarily due to teatcup liner slippage. Spencer
and Rogers (1991) have shown that lower levels of milking vacuum increase
milking machine malfunctions. Milking vacuum of 50 kPa averaged 4.7 liner
slips per milking and .028 unit fall offs per milking while milking vacuum of
42 kPa averaged 8.8 liner slips per milking and .090 unit fall offs per milking.
The increase in WRT resulting from these events was not reported. Baxter et
al. (1990) studied the effect of teatcup liner design on milking equipment
malfunctions. Their data on two commercially available teatcup liners
showed significant differences in their slip characteristics (5.99 major slips per
cow milking vs 1.73). It has also been shown that Jersey cows require up to
four times more milking machine adjustment time than Holsteins (Blake et
al., 1978). Armstrong and Quick (1986) also reported that the presence of stray
voltages in the parlor have a negative impact on WRT. In one case study the
correction of a stray voltage problem in a double-10 herringbone resulted in a
decrease in WRT of 6.8 s/cow and an increase in CPH of 7.7.

Human Factors

Human factors have an important influence on milking parlor
performance and the time required to milk individual cows and groups of
cows. However, this area has seen less investigation than those previously
discussed. The most important human related factors include MP and
milking routine and milking personnel training, skill and motivation.

Milking procedures and milking routine

Milking procedures are an important factor in determining WRT. The
contribution of MP to WRT will be determined by the number of procedures
performed and the length of time required to perform them (Armstrong and
Quick, 1986). Also, the organization of MP into a milking routine have an
impact on parlor performance. For example, according to Bickert (1978) a
circular routine is superior to an end-to-end routine in a polygon parlor. The

end-to-end routine has been traditional in herringbone parlors and was used
in polygons when they were first introduced. This method consists of one
operator at one end of the parlor and the other operator at the other end. The
circular routine was adapted for the polygon parlor and consists of two
operators working clockwise (or counterclockwise). One operator prepares
cows and attaches milking units with the second operator dipping teats and
handling cow entry and exit. In a 32-stall polygon the circular routine has
been reported to decrease WRT 6.7 s/cow, increase CPMH by 9.4 and increase
CPH by 19 when compared to the end-to-end routine (Armstrong and Quick,
1986). Gamroth (1992) reported a 20 to 30% reduction in parlor performance
for a territorial vs task-oriented milking routine. In the territorial routine

each milker performs all pre- and postmilking tasks in a specified area of the
parlor, while in the task-oriented routine each milker performs a specific
premilking task on all cows then assists other milkers after performing their
assigned premilking task on the last cow of a parlor side.
Merrill and Thompson (1980) suggested that MP procedures should be
designed to achieve three objectives: 1) produce clean and normal milk,
2) achieve high MY, and, 3) sustain good udder health. In order to achieve
these objectives they advised that milkers should only attach milking
machines to cows with clean, dry, properly stimulated udders and teats;
should minimize teatcup liner slippage during milking; should promptly
remove milking machines at the end of milking and should immediately dip
all teats in a disinfectant solution. Obviously most well-operated dairies will
perform similar tasks in a similar order to achieve these objectives.
However, climatic conditions, housing conditions, presence or lack of an
automatic wash and drip dry pen will affect the length of time for performing
udder preparation tasks. Armstrong (1988) suggested that udder preparation
accounts for 25-40% of WRT. For larger herds he recommended separate and
equally sized washing and drying pens in the parlor holding area. From a
design standpoint one could say that increasing milking parlor performance
begins in the cow's environment. By decreasing the soil load on udders and
teats or removing it prior to parlor entry one can either decrease time
required for a task or perhaps even eliminate the task entirely.
Premilking udder preparation also plays an important role in
stimulating milk letdown which shortens MT. Sagi et al. (1980) demonstrated
that cows milked out significantly (P < .001) faster when quarters were
stimulated prior to milking. In their trial teats were forestripped and
manually massaged with warm water and paper towels for 30 s vs machine

attachment with no premilking udder preparation. The treatment providing
manual stimulation had a one minute shorter MT (4.4 vs. 5.4 min).
However, when total premilking udder preparation time (30 s) plus delay in
machine attachment (30 s) were considered there was no difference in the
treatments. No significant differences in MY or fat percentage were detected
between these two treatments. Thomas (1981) found similar results when
various premilking udder preparations and machine attachment delays were
studied. This data indicated little differences in total time required to prepare
and milk cows among low or high stimulus intensity premilking udder
preparations when machine attachment delays were short (<30 s) for low
stimulus treatments and long (1 min) for high stimulus treatments.
There is also a great deal of difference in MP preferences among dairy
owners and managers. For example, work by Pankey et al. (1987) suggested
that premilking application of a sanitizing teat dip decreased new mastitis
infections due to coliform and other environmental mastitis pathogens by
50%. However, it was recommended that a 30 s contact time be allowed to
insure germicide effectiveness. Many dairy producers have adopted
predipping as a regular part of their premilking udder preparation
procedures. Armstrong et al. (1990) claimed that including predipping in the
premilking procedures reduces parlor performance by 15 to 20% in double-20
and double-24 parallel and herringbone parlors.

Milking personnel

Another important area that has received little attention concerns the
human element of milking, i.e., the person that performs the MP. As with

most manual tasks; there is a great deal of variation in skill levels of dairy

employees and in the time required for them to carry out these tasks. It is also
recognized by those in the industry that there are interactions between
human physical, mental and emotional characteristics and in facility design
and operation. For example, interactions between cow platform height and
milker height (Vos, 1974). Most of these interactions have been studied via
trial and error methods; thus, there is a need to better quantify these
Another relationship that appears in the literature but has received little
to no rigorous scientific examination is the relationship between parlor size
and number of milking personnel. Sagi and Merrill (1977) approached this
problem by basing units per milker as a function of WRT, allocated machine
unit time, and CT. Their algorithm for calculating personnel requirements
was presented graphically using theoretical projections which they deemed
possible and reasonable. Their model indicated that in an automated parlor
one milker can handle a double-8 parlor and achieve a CT of 12 min.
According to their model increasing parlor size beyond this point would
require an additional milker to maintain the same CT. However, they do
warn that it has been estimated that idealized parlor performance is often 20
to 25% higher than actual performance and that performance declines even
further when parlor preparation and cleaning time are considered. They

indicated that parlor preparation and cleaning time can amount to 30% of
total milking time or one-fourth minute per cow in moderate size
herringbone parlors.
Armstrong (1988) suggested that assessment of human factors was the
most subjective portion of measuring parlor performance. One area he was
able to quantify concerned the length of milking shift and its effect on parlor
efficiency. Data were collected in 42 milking parlors. Thirty of the parlors ran

a straight 8 hr shift. In these parlors peak milker performance occurred about
1.0 hr into the shift and then steadily declined until about .5 to 1.0 hr before
the end of the shift when anticipation of the end of the shift increased milker
efficiency. In the other 12 parlors the milker was given a 15 to 30 min break at
about the midpoint of the shift. In these parlors the beginning of the shift

was similar in that peak performance occurred about 1.0 hr into the shift and
was followed by a steady decline. However, with a formal rest period the
second half of the shift was a mirror image of the first half with a rapid
increase in efficiency immediately after the break to peak levels then a decline
in performance until the .5 to 1.0 hr period before the end of the shift when
performance once again increased. The area of employee management and
motivation begs further investigation.
Armstrong (1988) also reported on another interesting aspect of the
human side of milking cows. In a case study of a double-10 herringbone he
examined the effect of "parlor pressure" on performance. He reported that
subsequent to a 450 cow increase in herd size, and no changes to the milking
system or milking personnel, parlor performance increased 33% (60 vs 80
CPH). Work routine time decreased from 60 to 45 s/cow. The increase in
parlor efficiency was attributed to the desire of the milking personnel to
finish the shift in eight hours.

Time and Motion Study

Time and motion study refers to a broad base of knowledge concerning
the scientific and systematic study of work methods for the purposes of:
1) determining preferred work systems and methods, 2) standardizing work
systems and methods, 3) estimating the time required by a properly trained

worker to perform specific tasks at a normal pace, and 4) provide assistance in
training new workers in preferred work systems and methods (Barnes, 1980;
Jay, 1981; Mundel, 1985).
Although the two areas, motion study and time study, are difficult to
separate they do refer to two distinct concepts (Mundel, 1985). Specifically the
aim of motion study is to determine or design the preferable method of
performing work. The criteria most often determining work method
preference is cost. However, other aspects such as effectiveness, accuracy,
reliability, economy of time, effort, and material are often just as critical.
Chase and Aquilano (1989) defined a work task continuum with three
levels: 1) manual tasks which view the human body as an engine performing
strenuous manual tasks with strength and muscle fatigue as the limiting
factors determining output, 2) motor tasks primarily controlled by the central
nervous system with effectiveness measured in terms of speed and precision
of movements, and 3) mental tasks that involve rapid decision making with
effectiveness measured in terms of response time and error rate. Although
individual tasks may be readily categorized into one of the three categories, a
specific job may contain elements of all aspects of the continuum.
Jay (1981) pointed out that all human work is composed of the basic
building blocks of human motion. These human motions can be aggregated
to form work elements (e.g., striking a nail with a hammer). Work elements
can then be further aggregated to form a task or job. Tasks are often
associated with some unit of output (e.g., a nail driven into a board). He also
suggests breaking work elements down into three levels: 1) level one divides
work into elements based on whether they are performed by man or
machines, 2) level two delineates between work elements that are repetitive

or occasional, and 3) level three separates work elements based on those
requiring constant or variable effort.
Time study specifically refers to a variety of procedures to determine the
time required to perform a task or its elements, under standard measurement
conditions, by a human, a machine, or combination of the two. Barnes (1980)
defined time study as the method "...used to determine the time required by a
qualified and well-trained person at a normal pace to do a specified task" (p.
257). He indicated that the result from a time study will be the "standard
time" for the task.
Mundel (1985) pointed out that time and motion studies provide an
important source of information to the management process since they assist
the manager in: 1) determining quantitative output objectives over a given
time span, 2) planning of production programs, 3) determining workload,
4) determining resources needed to perform a given workload, and
5) evaluating the accomplishment of objectives and any need for revision of
objectives or initiation of corrective action to meet the production plan.

Motion Study Methodology

The overall objective in motion studies is to determine what work
methods are being used and to devise ways to eliminate or improve the
methods so that productivity may be increased. The techniques used in
motion study are dependent upon the overall objective of the study and the
point on the work-task continuum where the tasks involved fall. For
example, work involving intricate motor tasks (e.g., hand assembly of
electronic components) would require a somewhat different technique than
work primarily involving manual tasks (e.g., chopping wood).

A common tool used to study work methods is the construction of charts
(Chase and Aquilano, 1989). The format of work method charts differs based
on the whether the focus of the study is on: 1) the overall production system,
2) workers located at fixed workplaces, 3) workers interacting with machines,
or 4) workers interacting with other workers (Chase and Aquilano, 1989). In
most cases the study of work methods takes place simultaneously with time
Work involving the interaction of workers and machines and groups of
workers are primarily studied using worker-machine charts, activity charts
and horizontal time-bar charts (Chase and Aquilano, 1989; Mundel, 1985).
The basic format of these charts is similar where the individual elements of
the work being performed, whether by man or machine, are represented by
bars corresponding to the time required by the elements. By simultaneously
charting machine elements and worker task elements, or elements performed
by multiple workers, the relationships between elements performed by the
different entities can be elucidated.
Naturally the construction of work method charts requires observation
of the work being performed. Observation can be accomplished obtrusively
or unobtrusively. Obtrusive observation would involve the actual physical
presence of the observer in the workplace; while unobtrusive observation
would be accomplished semi-covertly, for example by a video camera. Each

method is not without its advantages and disadvantages. Mundel (1985)
pointed out that the most serious limitations of obtrusive observation are
with respect to the amount of information that can be recorded per unit time
in real-time data collection due to the limitations of the human eye, ear and
hand. He pointed out that this method of measurement is limited in the

number of simultaneous events that can be measured and is subject to
serious errors when extended beyond its limits.
Partially due to these limitations of obtrusive studies there has been
increasing reliance on unobtrusive work study methods (Barnes, 1980;
Mundel, 1985). These methods primarily involve the use of movie or video
cameras (Burks, 1989). This method has the advantage of providing a
permanent record of the work study and measurement errors can be
decreased by multiple reviewing of the film or videotape in slow-motion
(Burks, 1989). Mundel (1985) especially recommended this method when
analyzing work involving long cycles, variable cycles, or coordinated worker
activity. Additionally, some studies, for example on "micro-motion", are
virtually impossible using other methods. This method, however, is not
without its disadvantages. For example, positioning of cameras) must be
done with care to get a full view of the workplace, especially when studying
multiple worker or worker-machine processes (Barnes, 1980).

Time Study Methodology

Chase and Aquilano (1989) discussed four accepted methods of
measuring the time required to perform a human task:
1) Time study, which involves separating the task into individual ele-
ments and timing each element individually with a timing device
such as a stopwatch. After a number of repetitions the element times

are averaged and a standard deviation is calculated. To derive a
standard time for use in determining work standards the elemental
times are first adjusted by a subjective performance rating to obtain a

normal time. Normal time is then adjusted for time allowances (i.e.,
breaks, unavoidable delay and worker fatigue) to obtain standard time.
2) Elemental standard time data, which calculates standard time for a new
job by breaking the job into its elements and calculating its standard
time based on historical elemental standard time data that has been
codified into published tables or a computer database.
3) Predetermined motion-time data, which is similar to the elemental
standard time method except the standard time for a new job is con-
structed using codified historical data based on the basic motions
involved in the task elements of the new job.
4) Work sampling, which involves a periodic sampling of the work
activity under study. Based on the sample results inferences about the
activity are made. This method is primarily used to study work act-
ivities where the observer is not interested in breaking tasks into their
individual elements. For example, it could be used to determine what
proportion of time a secretary spends typing, filing, mailing, etc.

Mundel (1985) indicated that the method of time study used will be
dependent upon the nature of the work, the time for repetition of each work
element and the uses of the time standard. Barnes (1980) suggested the
following steps in conducting a time study: 1) secure and record information
concerning the operator and operation being studied, 2) divide the operation
into elements, each with a complete description, 3) observe and record the
time taken by the operator for each element of the operation, 4) determine the
number of cycles to be timed, 5) rate the operators performance, 6) check to
insure the required number of cycles have been timed, 7) determine
allowances, and 8) determine the standard time for the operation.

Chase and Aquilano (1989) indicated that the two most important aspects
of a time study are proper breakdown of the task into elements and
determination of the proper number of observations to record. Jay (1981)
maintained that proper element description is the most important part of
conducting a valid time study. He advised conducting pilot studies to insure
a complete understanding of the task and accurate identification of its
elements. Mundel (1985) identified seven criteria for separating tasks
1) Elements should be easily detected and have a definite endpoint. He
stated that the most desirable endpoint is one that permits a means of
anticipating its occurrence, thus the observer is prepared to read and
record the time.
2) Elements should be as small as is convenient to time. He suggested that
with stopwatch timing the smallest practical time unit is about .04 min
(3 s). For elements with shorter times he recommends the use of
movie films or videotapes. For elements too small to measure ac-
curately Jay (1981) recommends a method called differential timing. In
this method, for example, several identical adjacent repeated elements
are timed followed by another timing of the sequence dropping the last
element. The element time can then be obtained by subtraction.
3) Elements should be as unified as possible. This means that an element
should be a well-unified group of motions involving one object rather
than a series of motions with multiple objects.
4) Hand work time and machine work time should be separated. This
distinction is necessary since the underlying sources of time variation
are much different in hand operations vs machine operations.

5) Separation between internal work time and external work time should
be made. Internal work time is hand work performed while a machine
is in control of elapsed time for the process. External work time is
hand work performed when the hand work itself controls the elapsed

work time of the process.
6) Constant work elements should be separated from variable elements.
Whether a work element is constant or variable is a function of the
relation between the work element and the unit upon which the work
is performed. For example, the time required to turn on a machine is
usually independent of the size of the machine since it only requires

turning on a switch. However, the time required to place a nut on a

bolt can be dependent on nut size, thread pitch and density, etc.
7) Regular and irregular work elements should be kept separate. Work
elements that do not appear in every work cycle should be measured
separately and then prorated to its associated regular element.

Barnes (1980) indicated that time study is a sampling process of element

times; therefore, the sample must be of proper size to insure that element
times collected are representative of reality. He indicated that most timing
studies use a 95% confidence level and a 5% level of precision. Niebel
(1982) suggested a sample size algorithm based on cycle length (one cycle is
defined as the time to complete one sequence of all elements involved in a

repetitive task) and the number of times the cycle occurs on an annual basis.

For example, when cycle time is less than .7 min but greater than .5 min, and
the cycle is repeated more than 10,000 times annually, the required sample
size is 60. In general, the required sample size decreases as cycle time
increases or number of annual cycles decreases.

Time and Motion Study Methodology in Milking Parlors

Armstrong and Quick (1986) provided a review of time and motion
studies as applicable to the analysis of milking parlors. They defined the work
elements involved in the milking task as the elements of WRT. They
suggested eight typical elements: 1) cow entry, 2) feed cows, 3) udder washing,
4) udder drying, 5) milking machine attachment, 6) milking machine
detachment, 7) postmilking teat dipping or spraying, 8) cow exit, and 9)
miscellaneous. Miscellaneous elements included waiting, adjusting units,
reattaching units, washing units, floor washing, out of parlor, cow treatment
and milking mastitis cows. They emphasized the importance of specific break
points in the definition of work elements but do not make any specific
recommendations. A discussion on the relative merits of continuous vs
flyback timing was also made. These two methods of timing are very
commonly used in timing studies. The continuous method consists of
starting the timer at the beginning of the first element in the work cycle. The
time that each successive element ends is recorded, the timer continues to
run, and the individual element times are obtained by subtraction. In flyback
timing the running timer is zeroed at the beginning of each element and only
element ending times are recorded. They indicated that continuous timing
has the disadvantage of additional computations but times and frequencies of
unusual events are more easily noticed. They recommended time studies
that include all milkings due to differences in milk production per cow.
Researchers at the University of Kentucky (Burks, 1989; Burks et al., 1989)
conducted time and motion studies on milking parlors to provide input data
to a milking parlor simulation model (PARSIM). These researchers
videotaped actual milkings at thirteen dairies. Subsequent to filming, the

videotapes were analyzed with a video cassette recorder (VCR) linked to a
computerized event time recorder. Using this methodology the researchers
were able to record the multiple times for 38 different parlor work elements
and events. Once the work element and event time data were extracted from
the videotapes it was fitted, using a computer program (Law and Vincent,
1993), to eight different probability distributions and tested to determine
which fitted distribution best represented the individual data sets. The
program generated distribution parameters for each work element and event
distribution which were then used in the milking parlor simulation model
called PARSIM.

Simulation Modeling

Purpose of Simulation

In general, simulation is a modeling technique where a real system is
imitated by a computer program (Schriber, 1991). The real system is
represented in the computer program by a mathematical model which
contains the logical and quantitative relationships necessary to provide an
accurate abstraction of the real system (Law and Kelton, 1991). Simulation is a
modeling technique widely used in the field of operations research and
management science. A 1983 survey of operations researchers and
practitioners (Harpell et al., 1989) found that simulation ranked second
among quantitative techniques used most often. Cook and Russell (1976)
found that 89% of Fortune 500 companies used simulation in their decision

making processes. Black et al. (1989) stated that simulation modeling was a
valuable research tool in the animal sciences because it is "merely a

formalisation of the process used by all research scientists whereby ideas and
concepts about the operation and control of a system under study are
developed from data obtained during experimentation" (p. 5). They go on to
point out another benefit of simulation modeling is that in the process of
building a simulation model areas requiring further experimentation and
expansion of knowledge are revealed.
Schriber (1991) suggested that there are three general scientific
approaches to problem solving (Figure 2-2). In order to gain reliable decision
making information about complex systems the decision maker can take one
of the three approaches. For complex systems the most reliable would be
experimentation on the real system. In this case experiments would be
conducted on the real system and data would be collected and statistically
analyzed to estimate the answers) to the questions) of interest. This has
obvious limitations. For example, it is usually not economically feasible to
"tinker" with complex production systems to answer a variety of "what-if"
questions and it is impossible to answer questions concerning proposed
systems not yet in existence.

Experimentation Simulation Mathematical
on the modeling
real system

Increasing realism Increasing abstraction

Figure 2-2. Alternative problem-solving approaches.

The mathematical model approach describes the exact logical and
quantitative relationships of the system and has the advantage of providing

an exact analytical (i.e., closed-form) solution to the problem of interest.
However, modeling of this nature requires the highest degree of abstraction.
With this degree of abstraction, enough reality of complex systems can be lost
to seriously decrease the value of the solution.
The simulation approach is similar to the mathematical model approach
in that the system is described in terms of a mathematical model expressing
the system's logical and quantitative relationships. However, due to the
complexity of the system an analytical, closed-form solution is not attainable.
Instead simulation numerically exercises the model to determine the effects

of the inputs on the output performance measures (Law and Kelton, 1991).

Three basic types of simulation modeling are described by Pritsker (1986):

1) discrete simulation modeling, 2) continuous simulation modeling, and 3)
combined discrete-continuous simulation modeling. In discrete simulation
modeling the state variables change discretely at specified points in
simulation time. These discrete changes are called event times which are
instantaneous occurrences that may change the state of the system. In discrete

models the values of the state variables do not change between event times.
For instance, in a bank customer-service simulation model the teller is either
free or busy and their status only changes at the discrete times of the
beginning or completion of customer service.
In continuous simulation modeling state variables may change
continuously over simulated time. Differential equations are typically

employed to give the relationships for the rates of change of the state
variables over simulation time. Simulation modeling of the position and
velocity of a spacecraft is an example where continuous simulation modeling
has been employed. Pritsker (1986) also pointed out that it may be useful to
model some processes involving discrete events with continuous simulation

modeling. This is particularly useful when the level of aggregation of the
modeling effort is above the level of the discrete state variable. As an
example, Pritsker (1986) cited that in modeling the population of a particular
fish species in a lake, a continuous representation would probably be
preferred even though the population of the species changes discretely.

Simulation Methodology

Simulation modeling consists of nine steps (Figure 2-3)(adapted from
Law and Kelton, 1991; Pritsker, 1986; Schriber, 1991). Pritsker (1986) indicated
that, although the steps involved in a simulation study follow the outline of
Figure 2-3, one should be aware that simulation has an evolutionary nature.
Therefore, movement between steps is not completely a one-way process
because additional insights are gained into the problem and additional
questions become of interests as the study proceeds.

Problem formulation

This step in a simulation study consists of defining the problem to be

studied including the objectives of the study. An essential ingredient of this
step is a detailed and intimate description of the system to be modeled. This
would include the operational characteristics of the system and any and all
alternatives for operation of the system to be considered.

Model building

This step in a simulation study consists of forming a conceptual model
of the system and determining which characteristics of the system will be rep-

Figure 2-3. Steps in a simulation study.

resented in the model. Such a determination requires a complete
understanding of the structure and operating rules of the system. Pritsker

(1986) suggested that model building involves art as well as science and

should not include unnecessary detail, yet be sufficiently complex to

realistically describe the important characteristics of the system. He described
three crucial questions to answer: 1) which simplifying assumptions are
valid, 2) what elements should be included in the model, and 3) what
interactions occur between elements? He further suggested that this process

is highly evolutionary with a series of "cuts" being made where models are
built, analyzed and critiqued so that inaccuracies can be discovered and
confidence can be created in future models. This phase is also critical since
the specification of the model will determine its data requirements.

Data acquisition

The source of the data for the simulation study can be from observation
of existing systems or may have to be estimated for systems not yet in
existence. Production systems contain a number of possible sources of
randomness; for example, processing time, machine operating time, machine

repair time, etc. (Law and Kelton, 1991). When data are collected from the

observation of an existing system it is necessary to specify the probability
distributions of these random inputs to the simulation model. Law and
Kelton (1991) describe three approaches (in increasing order of desirability) of
specifying a distribution of data collected on an input random variable:
1) Trace-driven simulation approach where the actual collected

data values themselves are used directly in the simulation.

2) Empirical distribution approach where the collected data values

themselves are used to mathematically construct a probability
distribution function.
3) Theoretical distribution approach where the collected data are fitted

to a theoretical distribution function (e.g., Poisson, exponential, etc.).

Law and Kelton (1991) described several important issues in the
assessment of the correct theoretical distribution function for a data set.
These issues include: 1) assessment of sample independence,
2) hypothesization of distribution family (e.g., Poisson, exponential, normal,
etc.), 3) estimation of parameters, and 4) determination of the how well the
theoretical distribution fits the data. Another important issue concerns
assessing the homogeneity of different data sets. They described the use of the
Kruskal-Wallis hypothesis test for homogeneity. Homogeneous data sets,
which are identically distributed, of the various input random variables are
advantageous because they can be merged to form pooled data sets.

Model translation

This step in a simulation study involves translating the conceptual
model with its logical and quantitative relationships describing the system
into a computer program. The translation can employ a general purpose
language such as FORTRAN, Pascal, or C; or a specific simulation language


Model verification

Once the conceptual model has been translated into a computer
program the computerized version of the model must be verified. The
purpose of this step is to insure that the logic of the conceptual and
computerized models are in agreement. Schriber (1991) succinctly summed
up the purpose of verification as answering the question: "Are we building
the model right?" (p. 13). He recommended that synthetic data be used in the
verification process because this step focuses on the logic of the computerized

model, not on the data to be used in the simulation. By using synthetic data,
model output can be compared with manual calculations. Additionally,
verification of the model with synthetic data allows the researcher to proceed
with parallel collection of real data and even modification of the nature of the
real data collected.

Model validation

After the conceptual model has been translated into a verified

computer model the simulation must be validated. The validation process is
concerned with how well the simulation model truly represents the actual
system. Schriber (1991) described the purpose of validation as answering the
question: "Are we building the right model?" (p. 13). He warned that great
care must be taken in this step because it is easy to computerize an invalid
conceptual model. Pritsker (1986) suggested that the "comparison yardstick"

to be used in the validation process should be actual output from the real
system coupled with experiential knowledge of the real system's behavior.
Law and Kelton (1991) described a three step approach to model
validation. They first recommended developing a simulation model with
high "face validity". A model with high face validity is one that seems

reasonable to persons knowledgeable concerning the system under study.

Two primary features of this aspect of validation are: 1) intense observation
of systems similar to the system under study, and 2) an abundance of
communication with persons intimately involved with regular use of
existing systems similar to the system being modeled.
A second recommendation in the validation process is empirically-
testing the assumptions of the model. This step involves a quantitative test

of the assumptions made during model building. Important considerations
here include: 1) adequacy of data fit to the theoretical probability distribution
chosen, 2) representativeness of data chosen to build the model, and
3) homogeneity of data if data sets have been merged for use in the model.
They cited sensitivity analysis as a useful tool in the validation step.
Sensitivity analysis is used to determine the magnitude of change in the
simulation model output if the value of an input parameter is changed, the
input probability distribution is changed, or the level of detail in a subsystem
of the model is changed. Statistical experimental designs are often employed
in sensitivity analysis. They also recommended the use of the method of
common random numbers in sensitivity analysis so that the sensitivity of the
model to changes in a state variable are not confounded with other changes
that occur as a property of the stochastic nature of the simulation process.
Law and Kelton (1991) described the third test of a simulation model's
validity as the most definitive test of validity. This test is concerned with
how well the simulation model's output represents that expected from an
actual system. If a system similar to the simulation model exists, the
simulation model is considered valid if its output compares "favorably" with
the output of the actual system. Two ways were suggested as approaches to
accomplish this aspect of validation. First the Turing test where people with
knowledge of the system are asked to examine unmarked data sets from the
simulation model and the real system and then differentiate as to which data
set is from the simulation model and which is from the real system. Inability
of these "experts" to agree on which data set is simulated and which is real is
taken as evidence of model validity. Second, a quantitative approach where
differences in output values from the simulation model and the real system
are analyzed.

The authors expressed skepticism concerning a number of statistical

tests that have been proposed for quantitative evaluation. Their skepticism is
based on the fact that the output processes of all real and simulated systems
are non-stationary (i.e., output observation distributions change over time)
and autocorrelated (i.e., output observations are correlated with each other).
Therefore they concluded that classical statistical tests may not be directly
applicable. They also suggested that because a simulation model is only an
approximation of the real system that the null hypothesis that the real system
and the simulation model are the same is always false. Therefore, they feel it
is more useful to ask whether differences in the simulation model and the
real system are significant enough to seriously affect any conclusions made
using the model.

One recommended approach for model validation involves using actual
observed data (i.e., trace-driven simulation approach) rather than samples
from the input probability distributions. They maintained that by using this
method the model and the real system will experience exactly the same
observations from the input random variables and a more valid and precise
statistically comparison can be made (e.g., using statistical methods such as t
test, Mann-Whitney, two-sample chi-square, etc.). They referred to this
method as the correlated-inspection approach.
Another more reliable approach suggested by Law and Kelton (1991) is
the confidence-interval approach based on independent data. This method
requires the collection of a large amount of output data from the real and
simulated systems. Once the output data is collected output means from the

real and simulated systems are calculated and a confidence interval for the
difference between the output mean of the real system and the simulated
system is constructed. The authors stated that this confidence interval is

preferable to testing the null hypothesis that the means are equal because:
1) as previously mentioned, the model only approximates the real system;
therefore, the null hypothesis that the systems do not differ is always false,
and 2) a confidence interval gives more information than a hypothesis test
because the confidence interval provides information on whether the means
are unequal and by what magnitude. They also pointed out that just because
the means are statistically different does not necessarily indicate the
simulation model is an invalid representation of the real system. They

suggested that the decision of whether a statistically indicated difference in
the simulation model and real system is of practical significance is a
subjective decision based on the purpose of the model and the utility function
of the user.

Design and perform experiments

This step consists of planning and designing the experimental conditions
under which the simulation model will be exercised. This would include
such things as the alternatives to consider in independent simulations, initial
conditions to specify, length of warm-up period, length of simulations and
number of independent simulation replications to make within each
alternative simulation. Law and Kelton (1991) pointed out that most
simulation studies are merely rigorous exercises in computer programming
in that they begin with heuristic model building and coding, but end with a
single replication of the simulation to produce "the answer". They pointed
out that because simulation is a computer-based statistical sampling
experiment, appropriate statistical designs and simulation replications must

be used to obtain meaningful data for analysis and decision making.

Analysis of results

This step consists of analyzing the simulations and their replications
from the previous step to estimate the values of system performance and to

rank competing alternatives in system design or operation. A primary

statistical tool recommended for analysis by Law and Kelton (1991) is the
Welch confidence interval for the difference between the performance
means) of simulations run for two, or more, competing alternatives. This
procedure employs a t test with an estimated degrees of freedom derived from
each alternative's number of replications and performance variable

variance(s) to construct a confidence interval for the difference between each

alternative's performance variable(s) meanss. A Welch confidence interval
that contains zero results in a failure to reject the hypothesis of no difference
between each alternative's performance variable means) at the specified
level of a with the conclusion that the alternatives do not significantly differ
in performance.

Implementation and documentation

The final step in a simulation study is implementation and
documentation. Documentation involves the preparation of an exhaustive
written report detailing all important aspects of the study including

objectives, conceptual model assumptions, data collection methods, computer

programming of the conceptual model, verification and validation
procedures and results, a machine-readable copy of the model, sample output,
etc. (Schriber, 1991). Implementation concerns actual use of the simulation
model in the decision making process. The degree of implementation will

depend on the modeler's success in developing an accurate simulation and in
his ability to communicate it to potential end-users.

Simulation Studies Applied to Milking Parlor Performance

Price et al. (1972) simulated small (4 to 12 stalls) side-opening and
herringbone parlors using the GPSS III simulation language. The authors
indicated that construction of a valid parlor simulation model must take into
account all the important aspects and interactions between cow, man,
facilities and milking machine.
Price et al. (1972) used a three step process in building their parlor
simulation model. Step one involved building a conceptual model
identifying all activities involving cows and men in the system. The
conceptual model was presented as a flow diagram for a side-opening parlor
identifying seven key activities: cow entry, cow feeding, udder washing,
machine attachment, individual cow MT, machine removal and cow exit.
They indicated that additional activities were added to the conceptual model
for the herringbone parlor but these were not identified nor was a flow
diagram presented.
The second step concerned the establishment of operational priorities
among the key activities. These operational priorities served as the decision
rules guiding the simulation model. Five operational priorities, in
decreasing order of priority, were formulated: 1) remove machine from cow,
2) cow entry and feeding, 3) wash udder and check for injuries, 4) check for
mastitis and attach machine, and 5) take sick cow to sick bay. They indicated
that the philosophy behind this ordering of priorities was to keep
overmilking at a minimum while maintaining efficiency of parlor operation.

Step three in the simulation model building process was collection of
data for the key activities and the identification of the probability distributions
for each activity data set. Five different distributions were used in the
simulation model: 1) time to let cow in parlor, secure in stall and feed a
predetermined amount of grain (mean = 10 s, variance = 4 s), 2) time for
udder washing and checking for injuries (mean = 15 s, variance = 4 s), 3) time
to check for mastitis and attach machine (mean = 20 s, variance = 4 s),
4) individual cow MT (mean = 330 s, variance = 160 s), and 5) time to remove
machine and let cow out of parlor (mean = 10 s, variance = 2.25 s). Although
not explicitly stated, these distributions seem to only apply to side-opening
parlors. Because this study was concerned with initial model development,
data from other researchers was used. These data did not contain the raw
values, only means and ranges. Therefore, the researchers assumed each
activity was normally distributed. The researchers agreed that this could
affect the results and that identification of the exact form of the activity
probability distributions was a very important element in simulation
Upon completion of the model 27 different tests on milking parlors were
made using computer runs of the model. Each test included herd sizes from
50 to 700 cows in increments of 50. No indication was made of the procedures
used, if any, to verify and validate the simulation model before these
experimental model runs were conducted. They presented graphs relating
MT as a function of herd size, parlor design (i.e., side-opening or
herringbone), and number of parlor stalls. They concluded that the biggest
savings in MT was from increasing parlor size from four to six stalls and that

each further increase in size brought smaller and smaller decreases in MT.

The researchers also presented a discussion and a graph on percent
parlor utilization as a function of manpower ( one, two or three milkers) and
number of stalls. However, the exact definition of percent parlor utilization
was not given. The graphs show percent parlor utilization decreasing as both
the number of milkers increase or number of parlor stalls decrease. The
highest utilization, approximately 80%, for side-opening and herringbone
parlors was shown to be for one-man parlors with 12 stalls.
Information was also presented concerning the time cows must wait for
machine removal as a function of manpower and number of stalls.
Automatic detaching was not considered in the model. The graphs showed,
for both parlor designs, that the time cows must wait after milk flow has
ceased for machine removal increased as manpower decreased or the number
of stalls increased.
In their concluding remarks the researchers indicated that simulation

modeling of milking parlors could be an important technique with additional

improvement and refinement. They suggested, in addition to the increased
data collection and probability distribution identification needs, four key
improvements should be made: 1) vary travel time of milkers from stall to
stall depending on which stall the operator starts from and which stall he
travels to, 2) inclusion of a routine element for special treatment of a cow
with mastitis, 3) a more detailed breakdown of the operator routine elements,
and 4) study of the effect of changing the priority ordering using sensitivity
Another milking parlor simulation study was conducted by Micke and
Appleman (1973). This study essentially made refinements to the model
developed by Price et al. (1972). Micke and Appleman (1973) expanded the
milker action inputs to include 11 items. Items they included that were not

in the previous model were: 1) movement of milker into holding pen to
drive cows into the parlor, 2) separation of udder preparation into washing
and drying subunits, 3) machine stripping, 4) postmilking teat dipping,
5) correction of major problems (i.e., treating mastitis cows and collecting
abnormal milk, operator going to milk room, equipment problems other
than unit fall-off), and 6) correction of minor problems (i.e., adjust unit to
correct liner slip). Top priorities were assigned to correction of minor
problems and unit removal. Lowest priorities were assigned to machine
stripping and entry of milker into holding pen. A schematic of the
conceptual model for one cow moving through a side-opening parlor is
presented and the authors indicated that similar procedures were applicable
to herringbone parlors. They suggested that the only changes needed in the
model for herringbone parlors was to make certain that all stalls on one side
are vacant before cow entry and that all cows on one side must be ready for
release before cow exit is initiated.
The distributions of activity times used in the model were presented in

tabular form. The researchers indicated that the activity time data were from
the time and motions studies of Appleman and Micke (1973). Each activity
time had six to 13 reference points; however, interpolation between data
points was made to generate 21 data points for each activity between
accumulated probabilities of .00 to .999. There is no indication that the data
were used in an attempt to define probability density functions for the activity
distributions (i.e., pseudo-trace driven). No indication was made of the
procedures used, if any, to verify and validate the simulation model.
The authors only reported on the results of one simulation scenario, a
double-2, side-opening parlor with four units and one operator. The primary
output of their model included four measures of parlor efficiency: 1) time

required to milk 120 cows, 2) CPMH, 3) average time cows were in a stall, and
4) percent utilization of milking units; and two measures of milker efficiency:
1) percent utilization of milker's time, and 2) frequency of entry into holding
pen to chase cows into parlor. Other outputs included average times for such
items as herd MT, overmilking and individual operator activity times.
Disappointingly, the authors made no comparisons between different parlor
designs or parlor operating strategies; nor did they make any indications
concerning operation of the simulation model in terms of number of
replications or recommended statistical analysis of model output.
A more recent milking parlor simulation model (PARSIM) has been
built by researchers at the University of Kentucky (Burks, 1989; Burks et al.,
1989). The researchers used the SLAM II simulation language (Pritsker, 1986)
to model the performance of four milking parlor designs: side opening,
herringbone, polygon, and trigon. The upper range of parlor sizes modeled
included a double-15 herringbone, 24 stall trigon, and 32 stall polygon. The
simulation model was built from data collected on thirteen different milking
parlors located in Kentucky. Output from the model included means and
standard deviations for several parlor performance measures including group
throughput rate (CPH), herd throughput rate (CPH), and operator utilization.
The model simulated individual cow MYM and MT from equations
developed from the work of Touchberry and Markos (1970). However, the
model did not include parlor milk output as a response variable.
The validation procedures employed by the researchers involved
running the simulation model thirty replications on six different parlor
configurations. The output from these simulation model runs, in terms of
steady state CPH, were then compared to observed values reported by
Appleman and Micke (1973), Bickert (1980), and Armstrong and Quick (1986)

for parlors of the same size and design. The comparisons were made solely
on the basis of percent difference of PARSIM results vs the previously
reported values for parlor performance. The results indicated that PARSIM
predicted CPH from 19.2% lower than, to 2.4% higher than, the performance
reported by others (Appleman and Micke, 1973; Bickert, 1980; Armstrong and
Quick, 1986). The researchers made no attempts to compare model outputs
with those actually achieved on the dairies included in the study. In their
concluding comments the researchers suggested that PARSIM was a useful
tool to aid dairy producers in the selection of milking parlors, degree of parlor
automation, and milking parlor management philosophy. However, they
made no attempts to elucidate the economic ramifications of such decision
The most recent parlor simulation study was conducted by Chang (1992).

This simulation, entitled OPSIM, employed object-oriented programming

techniques and focused on operator activities to model WRT. Parlor
performance was predicted in terms of cow throughput (CPH), which the
author described as the most important index of parlor performance. OPSIM
also predicted individual WRT element times; however, no descriptions of
the underlying probability distributions for any of the individual activities of
the model were given. Individual cow MY was reported to be a model input

in the validation process, but no explanation was provided on how
individual cow MY was used in the model nor did the model predict parlor
performance in terms of parlor milk output per unit time. Twelve dairies
with herringbone parlors ranging from double-6 to double-10 were used to
validate the simulation. The reported correlation between predicted and

observed cow throughput was 88.6% which would be relatively low for

predictive purposes. Simulations comparing a double-13 herringbone with a

double-13 parallel parlor indicated a 3.7% CPH advantage for the parallel

Economic Analysis of Milking Parlors

Capacity Planning and Facility Layout

A critical question to address before considering a complete economic
analysis of any manufacturing facility component is the capacity required.
This is especially critical when the component has the highest processing
requirement and is thus most limiting output. According to Chase and
Aquilano (1989), the capacity decision is one of the most critical of all strategic
business decisions because it essentially defines the firm's competitive
boundary. Furthermore, it plays a major role in determining cost structure,
response rate to product market, work-force composition and requirements,

level of technology, and management requirements.

A basic definition of capacity is simply "the rate of output that can be
achieved from a process" (Chase and Aquilano, 1989, p. 273). In terms of the
milking parlor, Welchert et al. (1980) advised that capacity requirements
should be based on a match between parlor throughput (CPH) and herd size
with six hours allowed for milking at steady state throughput rates. This
provides allowances for one-half hour of parlor setup time, one hour for
group changes and one-half hour for parlor cleanup. Bickert (1980) stated that
the following factors should be considered when determining parlor capacity:
1) milking herd size, 2) ML availability, 3) time available for milking, 4) herd
MY level, 5) degree of mechanization, 6) capacity cushion to allow for herd
expansion, 7) initial investment costs, 8) annual ownership costs, and 9)

personal preference. He also pointed out that facility layout (i.e., parlor type)
should be the first consideration because this factor influences building size,
location, cow traffic patterns, milking routine and degree of mechanization
that can be used effectively. Clough (1979) offered similar advice, but also
added that in addition to any forecasted changes in herd size; consideration
should also be given to possible changes in management during the useful
life of the parlor that would affect performance.

Milking Parlor Investment and Operating Costs

Capital budgeting is the process of determining the profitability of an
investment (Levy and Sarnat, 1990). Daugherty et al. (1989) suggested four
possible methods of analyzing the profitability of an investment in a dairy
facility: 1) payback period (PP) which calculates the number of years to pay for
an investment, 2) simple rate of return (ROR) which calculates the rate of
return, adjusted for depreciation, of a project, 3) net present value (NPV)
which calculates the total net discounted cash flows of an investment, and 4)
internal rate of return (IRR) which calculates the breakeven discount rate
based on the point where total net discounted cash flows of an investment
equal zero. In their economic analysis of an investment in a dairy facility
Daugherty et al. (1989) used the NPV method. They cited problems with PP
and ROR because both do not consider the time value of money and PP does
not consider the possibility that an investment with a longer PP may be more
profitable than one with a shorter PP. They chose the NPV method as the
best method of comparing competing investments because the calculations
lead to a single value and it considers the time value of money. However,

they do point out that the selection of the discount rate and planning horizon
to be used are a possible concern.
Daugherty et al. (1989) pointed out that validity of investment decisions

in a dairy facility are highly dependent on accuracy of underlying data. They
cited five sources of data as most critical. First was investment costs which
are all costs involved in bringing the investment on line including
construction costs, material costs, livestock costs, equipment costs, hauling
costs, licenses, fees, communication costs, etc. They cited four stages in
estimating investment costs. Per animal unit costing which precedes the
design phase and was based on past projects and proprietary information.
They suggested that the accuracy of this estimate was in the range of plus or
minus 20%. Costs per square foot, cubic yard, linear foot, etc. estimates should
be used to refine those of the preceding stage. This estimate considers
approximate building sizes and production strategies (e.g., milking frequency,
parlor type, mechanization, etc.). The accuracy of this estimate was expected

to be plus or minus 15%. System installation subcontract cost estimates were
cited as estimates which complement and clarify those of the preceding phase.
Here equipment manufacturer representatives provided detailed cost
estimates of complete systems (e.g., milking equipment, stalls, etc.). The
accuracy of this estimate was expected to be plus or minus 10%. Finally,
detailed unit cost method was cited as the most accurate ( 5%) and

considered a complete and detailed listing of quantities of all items required
including materials, equipment, labor, etc. They indicated that this method
was rarely used by dairy producers; however, contractors typically use them to
prepare competitive bids. They stated that most dairy producers base
investment decisions on information obtained by the per animal unit cost
and system installation subcontract basis.

The second important area requiring accurate input data was capital
replacement costs. This area was important because many portions of the
investment have differing lengths of useful life. Therefore, it is critical to
accurately predict useful life of system components and accurately project
replacement costs. The third area is related to the second and concerns capital
sales. Because capital items are anticipated to be replaced it was important to
establish accurate salvage values for the items. The authors provided a word
of caution here and stated that planners must realistically determine if a
market exists for capital items or if past history shows that these items end up
collecting rust behind the farm shop. The fourth item requiring accurate
estimates was annual net cash flow which obviously depends on accurate
estimates of all factors affecting expenses and revenues. The fifth item was
the discount rate. The authors suggested that the discount rate chosen should
be the minimally acceptable rate of return on the investment. The authors
pointed out that the rate used will depend on whether the investment was
financed with debt, equity, or combination.
Another important consideration was the planning horizon. The
authors indicated two factors which determine length of planning horizon:
1) economic life of investment assets, and 2) subjective judgment of the
entrepreneur that reflects their risk attitude. Thus, for example, the planning
horizon might be considerably reduced if the entrepreneur considered that
external forces (e.g., technological change, government policy, organizational

changes, market conditions) increased the risk of the investment.

The first attempt to analyze investment costs for modern milking
parlors was conducted by Bickert et al. (1974). They analyzed investment costs
for double-4, 6, 8, and 10 herringbone parlors based on performance obtained
via time and motion analysis. Investment costs for building and equipment

were based on 1973 costs ($1.39/m2 for parlor, $.74/m2 for holding pen) which
they noted would vary by geographical location and equipment
manufacturer. Similar to performance data, cost data were reported in a
sequential fashion as varying degrees of mechanization were added to the
base cost of the milking parlor. Annual milking costs per cow were calculated
using two basic methods: 1) constant herd size of 300 cows, or 2) variable herd
size based on eight hours per milking. Both methods assumed that the entire
milking was performed at the steady state rates given by their time and
motion analysis. Costs of ownership were calculated using a $9,000 annual
per operator labor charge, 12 yr depreciation for buildings, 7 yr depreciation on
equipment, 8% interest on the unpaid balance, insurance at $4.65 per $1,000 of
investment, repairs were charged at 2.5%/yr on buildings and 5%/yr on
equipment. They found that ownership costs decreased as parlor size and
degree of mechanization increased due to increased capacity and efficiency
allowing for larger herd sizes over which to spread fixed costs.
An updated and more comprehensive approach to this investment
decision was examined by Willet et al. (1982). The major objectives of this
work were to identify least cost milking systems for dairy herds of 50 to 500
milking cows in the western United States. The study compared estimated
costs and returns for parlors ranging in size from double-4 herringbones to
double-10 herringbones and 16-stall polygons. Building and equipment cost
estimates were obtained from contractors and milking equipment dealers in
northwest Washington and labor estimates from a survey of Washington
dairies. Cost criteria used in evaluating the various parlor systems were the
equivalent annual after-tax cost per cow. These figures were derived by
spreading costs over a 15 yr period and adjusting them for income taxes and

discounting them using a 12% interest rate. The discounted after-tax costs
were then converted to an equivalent annual cost per cow.
Labor costs were estimated for each system based primarily on steady
state throughputs estimated from previous work (Bickert et al., 1974).
Additional time for parlor preparation, cleanup and downtime was added
based on two parlor labor surveys of 175 Washington dairies. Some
adjustments of parlor steady state throughputs were also made as a result of
the survey information.
The research estimated total costs as a sum of fixed costs and operating
costs. Fixed costs included depreciation, interest on investment, property
taxes, insurance and repairs. Cost were assumed to be constant for each parlor
regardless of size, but adjusted on a per cow basis as herd size increased.
Initial capital investment costs, equipment replacement costs, property taxes,
repairs and insurance were projected over an assumed 15 yr project life.
Investment tax credit, tax deductible expenses (assuming a 24% tax rate), and
salvage values were subtracted from the projected costs. A 12% discount rate
was used on remaining costs to obtain after-tax, 15 yr fixed system costs.
Annual, after-tax fixed system costs were obtained by amortizing the present
value over the 15 yr.

Three operating costs were estimated: 1) labor ($7/h), 2) electricity
(.9 kWh/hp of vacuum pump), 3) gas heating (from average survey data
estimates). Operating costs were calculated based on herd MT; therefore, their
contribution to the overall cost of a particular parlor depended upon total
herd MT (based on 2x milking). Operating costs were expressed on an annual
hourly basis by multiplying the cost per hour times 730 (1 hour milking time,
2x milking for 365 d). All costs were tax deducted at the 24% rate. Linear
regression equations for estimating average annual after-tax fixed and

operating costs for variable herd sizes were then developed using the annual
after-tax fixed costs plus operating costs per hour times the number of cows in
the milking herd.
The equations were used to make an annual, after-tax cost per cow
comparison for each system at varying herd sizes from 50 to 500 cows. Results
of the analysis indicated that the least-cost system for herds of 250 cows or less
was the unmechanized double-4 herringbone ($161 annual cost/cow, 250 cow
herd). Depending on herd size (50 to 250 cows) the unmechanized double-4
herringbone had from a $1/cow to a $233/cow advantage in annual after-tax
cost. This advantage narrowed as herd size approached 250 cows where the

labor savings due to mechanization began to show a positive effect. As herd
size increased the least-cost system was often the smaller parlors (double-6, 8);
however, the least-cost advantage was usually obtained at the cost of more
hours per milking. For example, at a 350 cow herd size the double-8 was the
least-cost system at $137/cow and a 6.5 hr milking time. The double-10 was
the next least-cost system at $139/cow and only a 5.6 hr milking time.
Therefore, the total difference in annual costs for these systems at this herd
size is only $700. The authors asserted that in this situation the average dairy
producer would rather pay the $700 and reallocate the 328.5 hr of annual labor
to other tasks, especially if the dairy producer was doing the milking.
The researchers were adamant in their warnings to dairy producers that

the results of this study were absolutely dependent on the fixity of the
assumptions. They particularly noted that changes in cow throughput in the
various parlors would have a significant effect. For example, throughput
figures for the 12-stall trigon were set at 62 CPH as a result of the survey of
Washington dairy producers. However, other investigators reported a
performance figure of 74 CPH (Bickert et al., 1974). If the higher performance

figure was used the annual cost per cow of the 12-stall trigon dropped by $9.84,
thus requiring adjustment of any comparison.

Economic Analytical Tools

Sensitivity Analysis

Sensitivity analysis is a common, pragmatic investment analysis
technique that allows some quantitation of a project's risk (Levy and Sarnat,
1990). The technique simply involves a best estimate of the project's

revenues and costs, which are used to calculate the project's NPV. Revenue

and cost estimates of the project are subjected to various changes to reveal
how changes (i.e., the various individual revenue and cost components)
affect the project's NPV (Whisler, 1976). This allows investors to determine if
a particular project meets or falls short of the decision criteria as various

scenarios are examined, and to determine which variables have the greatest

potential effect on a proposed investment's NPV (Huefner, 1972). The NPV
equation is:

NPV = l + (1- T) n (t t Cmt
t=1 (1 +k)t t=( (1+k)t t=1 (1+k)t


NPV = net present value,
Io = initial investment outlay,
Rt = gross revenue in year t,
C1,t = cost component 1 in year t,
Cm,t = cost component m in year t,
t = number of years in project's life (t = 1,..., n),
Tc = corporate tax rate,
k = cost of capital (i.e., discount rate).

By using this formula investors can analyze the impact of an a percentage
error in each revenue and cost estimate. For example, assuming an a% error
in revenue, the new NPV is given by
n (aRt)
NPVa =NPV +(1- -Tc)
t= (1+k)

Therefore, as a increases NPVa becomes more favorable; and vice versa, as a
decreases NPVa becomes less favorable than originally estimated. NPVa is a

linear function of a and after-tax value of revenue is a constant; therefore, the
equation can be written as
NPVa = NPV + #a


S=(1- Tc)i
t=1 (1+k)t

The same relationship holds for each cost component which may be
expressed as:

NPVa = NPV + va


n=( Cm,t
t=1 (1+k)t

Expressing the components as linear equations allows the construction of
simple linear graphs in which the relationship of the revenues and costs to
changes in a are easily visualized (Levy and Sarnat, 1990).

Risk Efficiency Analysis

Overview of risky decision making

Traditional neoclassical microeconomic theory states that producers are
pure profit maximizers (McCloskey, 1985). This simplistic view of producer
behavior does not accurately reflect reality because of its failure to account for

two important facets affecting real world decisions of managers: risk and risk
Risk is a term for which it is difficult to find a standard definition
(Young, 1984). Young (1984) indicated that the literature suggested several
alternative concepts of risk such as probability of loss, variance of profit, and

the size of maximum possible loss. These risk concepts can be based on
subjective expectations of decision makers where the probability of loss or
spread of a profit distribution is based on the decision makers personal
assessment of probabilities. Alternatively, Young (1984) suggested that risk
may be based on objective measures of expectation computed from historical
or experimental data. Sources of risk in agricultural production are diverse,
for example: 1) biological variation inherent in crop and livestock
production, 2) interaction between biological systems and variable weather
and environmental conditions, 3) variation in input supply and product
demand, 4) variation in input and output prices, and 5) effect of government
policies on input and output supply, demand, and prices (Boisvert & McCarl,
1990). When risk becomes an added consideration in the profit maximization
paradigm the objective of the producer becomes the maximization of expected

profit. Thus, before the consideration of risk, for a given set of input and
output prices, there is only one optimal value of the fixed and variable inputs
that define the maximum profit level. When risk becomes a consideration,

regardless of its source, profit maximization is no longer a single valued
function but a distribution of possible outcomes determined by the stochastic
nature of the production function, fixed and variable input usage, input
prices or output price.
Unfortunately even the maximization of expected profit paradigm has
proved to be an abstract and ineffective model in explaining and predicting
many types of economic and financial behavior (Robison et al., 1984). The
failure of the expected profit paradigm primarily arises from its failure to
account for the decision maker's attitude toward risk, or, in other words, the
decision maker's attitude toward the distribution of expected profits presented
by various risky prospects. When risk attitude becomes an added
consideration in the expected profit maximization paradigm the objective of
the producer becomes the maximization of expected utility. The expected
utility model clearly distinguishes between the decision maker's expectations,
that is his or her perception of uncertainty, based on subjective or objective
concepts of probability; and his or her preferences for each profit distribution
presented by the risky prospect.
The maximization of expected utility model was originally developed by

Von Neuman and Morgenstern (1947) and Luce and Raiffa (1957) and is based
on a set of axioms describing decision maker behavior. Essentially these
axioms are conditions or assumptions that require decision makers to behave
rationally in choosing among risky prospects. When the axioms hold, the
theorem follows that the selection of the optimal risky prospect is based on
maximization of expected utility (Robison et al., 1984).
Decision makers are classified on the basis of the shape of their utility

function which describes the relationship between utility and wealth (e.g.,
utility as a function of the outcome value for a risky prospect)(Robison et al.,

1984). Most decision makers are considered to be risk averse and have
concave utility functions indicating diminishing marginal utility as wealth
increases. Such a utility function indicates that the risk averse decision
maker will prefer a prospect with a perfectly certain outcome to one with an
equal expected, but stochastic, outcome.
Thus, the risk averse decision maker is only willing to pay a price for the
risky prospect that would yield the same level of utility as if the prospect were
certain. This value is referred to as the certainty equivalent (i.e., CE) of the
risky prospect. Thus, the expected utility of the risky prospect (i.e., EU(X)) is
equal to utility of the certain prospect (i.e., UE(X)). For the risk averse
decision maker the certainty equivalent (XCE) of the risky prospect is always
less than its expected monetary value (i.e., XCE < E(X)). The monetary
difference between the expected value of the risky prospect and the certainty
equivalent (i.e., E(X) XCE ) is called the risk premium. Risk premiums for
risk averse decision makers are always positive and represent the amount of
monetary compensation the risk averse decision maker requires to express
indifference between the risky prospect and an equivalent amount received
with certainty. Or, alternatively, the risk premium can be viewed as the
insurance premium the risk averse decision maker is willing to pay in order
to avoid the risky prospect. Therefore, as a prospect becomes more risky (i.e.,
its distribution becomes more variable), or the more highly risk averse the
decision maker becomes (i.e., the greater the concavity of his or her utility
function); the higher the risk premium becomes for a risky prospect.
Two other classes of decision makers also exist: risk neutral and risk
preferring (Robison et al., 1984). Risk neutral decision makers are
characterized by linear utility functions indicating an indifference to risk and
constant marginal utility as wealth increases. Due to the linearity of their

utility functions, risk neutral decision makers order risky prospects entirely
on the basis of the magnitude of the prospects expected value. Risk neutral
decision makers require no compensation, nor will they pay, to participate in
the risky prospect, thus their risk premium equals zero. Risk preferring
decision makers are characterized by convex utility functions indicating a
preference for the risky prospect vs an equivalent amount with certainty and
increasing marginal utility as wealth increases. Therefore, risk preferring
decision makers have a negative risk premium indicating the amount of
money they would be willing to pay to participate in the risky prospect versus

receiving the expected value of the risky prospect with certainty.
Research has indicated that agricultural producers do not always exhibit
risk averse behavior (Officer and Halter, 1968; Conklin et al., 1977). Halter and
Mason (1978) found nearly equal numbers of farmers were risk averse, risk
neutral and risk preferring. Whittaker and Winter (1980) also found that the
degree of risk aversion exhibited by farmers was not necessarily constant over

The second derivative of a decision maker's utility function (i.e., U"(X))
is indicative of the risk attitude of a decision maker (Robison et al., 1984).
That is, a negative U"(X) indicates concavity of the function and thus risk
aversion, and a positive U"(X) indicates convexity of the function and thus
risk preferring behavior. However, due to the ordinality of utility functions
the magnitude of U"(X) cannot be used to compare individual decision
maker's risk attitudes. This situation arises because the utility function is
only unique up to a positive linear transformation; therefore, the value of
U"(X) can be varied arbitrarily by multiplying the utility function with a
positive number (King and Robison, 1981; Pratt, 1964; Zentner et al., 1981).

Working independently, Arrow (1971) and Pratt (1964) developed
measures of an individual decision maker's risk attitude that are insensitive
to arbitrary transformations of the utility function. These measures are
referred to as the absolute risk aversion coefficient (Ra) and relative risk
aversion coefficient (Rr). The measure of absolute risk aversion is given by

Ra(X) U"(X)


X = Income or wealth

Therefore, the sign and magnitude of the Ra indicates risk attitude class

and the degree to which the belief is held by the decision maker. Decision
makers with a positive Ra are risk averse and the degree to which risk
aversion is held increases in size as the Ra increases. Decision makers whose
Ra equals zero hold a risk neutral risk attitude. Decision makers with a
negative Ra hold a risk preferring risk attitude and the degree to which risk is
preferred increases as the Ra becomes more negative (Robison et al., 1984).

Absolute risk aversion measures decision maker risk attitude
independent of wealth. Therefore, two decision makers with identically
positive Ra, but unequal levels of wealth, hold the same attitude toward a
given risky prospect. For example, two decision makers with the same Ra,
one with a net worth of $1 million and the other with a net worth of $100,000,
would hold the same attitude toward a risky prospect worth, for example,

$1,000. Boisvert and McCarl (1990) pointed out that values for Ra are local
(i.e., applicable at a specific level or narrow range of wealth) not global (i.e.,
applicable at all levels of wealth) measures of the degree of risk attitude.
Global measures of risk attitude are considered by Robison et al. (1984) to be

impossible to measure empirically; therefore, most studies on farmer risk
attitudes have dealt with local measures of risk attitude.
The measure of relative risk aversion is given by

Rr(X) = -X U"(X)
Rr(X) = XxRa(X)


X = Income or wealth

Like Ra, the sign and magnitude of Rr indicates risk attitude class and the
degree to which the belief is held by the decision maker. Relative risk
aversion measures decision maker risk attitude as wealth changes. Therefore,

two decision makers with identically positive Rr, but unequal levels of
wealth, do not hold the same attitude towards a given risky prospect. Rather,
they hold the same risk attitude toward risky prospects that equal the same
proportion of their wealth. For example, if two decision makers have the
same Rr, one with a net worth of $1 million and the other with a net worth of

$100,000, they would hold the same attitude toward a risky prospect worth, for
example, $10,000 and $1,000, respectively.
Tauer (1986) examined risk preferences of New York dairy farmers using
the risk interval approach developed by King and Robison (1981). The
researcher used a survey questionnaire to place dairy farmers into one of
eight risk preference groups, based on an interval for Ra, at two income
levels. The eight intervals for Ra included two that were risk preferring, one
centered around risk neutrality, and five that were risk averse. The two
annual income levels chosen, $15,000 and $30,000, were defined as the
amount of money available for family living expenses, farm operation

expansion, and accelerated debt repayment for the next year. Results
indicated that 34 percent of farmers surveyed fell in risk averse intervals for
Ra, 39 percent were risk neutral, and 26 percent were risk preferring. As a
group, these dairy farmers exhibited decreasing absolute risk aversion.
The researcher also merged the farmers into three risk preference groups
(averse, neutral, preferring) and examined if a relationship existed between
risk preference group and farmer age, years of education, dollars of equity,
farmer's estimated value of owner labor and management, and annual
income. Although the results were, at best, tenuous; the researcher did report
that risk neutral or preferring attitudes seemed to increase with age, level of
education, net worth, high income, and a lower value placed on owner labor
and management.
Analysis of the impact of the three risk attitude classes on farm operation

generally revealed that: 1) risk averse dairy farmers participated more heavily
in government crop programs, 2) risk averse dairy farmers contracted herd
size in contrast to herd size expansion for risk neutral and risk preferring
dairy farmers, 3) risk preferring dairy farmers had greater percent equity and
higher cash savings per $1,000 of cash expense, and 4) risk preferrers and risk
averse dairy farmers were more diversified, as measured by percentage of

receipts that were non-dairy and percentage of total assets that were non-farm
assets. The author suggested that the reasons why risk averse and risk
preferrers tended to diversify may be for the entirely different reasons of risk
reduction (risk averse) and speculation (risk preferred). However, due to the
relatively weak statistical strength of these measures the author warned that

either risk attitude may not play a major role in dairy farm decision making

or the interval approach to measuring the Ra may not have been accurate.

Risk efficiency criteria

A risk efficiency criterion is a decision rule that provides the decision
maker with an orderly process for evaluating the desirability of alternative
risky prospects (Selley, 1984). Most risk efficiency criteria have their basis in
expected utility theory because their choice criterion is expected utility
maximization and they incorporate information on decision maker
expectations (risk) and decision maker preferences (risk attitude)(King and
Robison, 1984). Thus, for risky prospect A to be preferred over risky prospect
B, according to a risk efficiency criterion, EU(A) > EU(B).
The purpose of a risk efficiency criterion, presented diagrammatically in
Figure 2-4, is to separate the set containing all risky prospects under
consideration by the decision maker (i.e., choice set) into a risk efficient set
containing those risky prospects preferred by the decision maker and a risk
inefficient set containing those risky prospects deemed undesirable by the dec-
ision maker (King and Robison, 1984).
Although the expected utility model is the basis for much of decision
theory under uncertainty, serious problems arise in its practical application
(King and Robison, 1984). The primary problem encountered is the accurate
measurement of decision maker preferences. If the analyst is able to

accurately estimate the decision maker's utility function the choice set of risky
prospects can be reduced to a single optimal risky prospect that maximizes the
decision maker's expected utility. However, as suggested by King and
Robison (1984) there are a number of difficulties that render utility function
estimation a difficult, expensive and inexact process. Risk efficiency criteria
overcome this problem by not requiring a full specification of the decision
maker's utility function. Instead assumptions are made concerning the form


Risk Efficient Set Risk Inefficient Set
(contains all risky projects (contains all risky projects not
preferred by decision maker) preferred by decision maker)

Figure 2-4. Schematic view of risk efficiency criterion.

of the utility function. Additionally, many risk efficiency criteria make
assumptions concerning the outcome distributions of the risky prospects in

the choice set.
The assumptions concerning decision maker's risk attitudes (i.e., form of
utility function) and risk (i.e., nature of risky prospect's outcome
distributions) allows a wider and less difficult application of the expected
utility theory to real world risky decision making. However, the increased
ease of application does not come without cost. The primary cost arises as a

Choice Set

(contains all available risky prospects)

result of assumptions concerning decision maker risk preferences. An
efficiency criterion applies for all decision makers whose preferences conform
to the assumptions made concerning the form of the utility function used by
the criterion. That is, for risky prospect A to be preferred over risky prospect B
according to the risk efficiency criterion the EU(A) > EU(B) for every utility
function satisfying the restrictions placed on preferences by the criterion. As a

decision criterion seeks to apply to an increasingly broad class of decision
makers, in terms of risk preferences, there is a decrease in its ability to
discriminate between risky prospects. Usually the less restrictive the
assumptions concerning decision maker preferences the less discriminatory
the criterion becomes. This can result in a decrease of the risk efficiency
criterion's discriminatory power to a point where it is unable to separate the

choice set of risky prospects into a risk efficient and inefficient set. Or, there
may be enough members in the risk efficient set that the criterion has failed
to serve as a meaningful guide for the decision maker (Boisvert and McCarl,
1990; King and Robison, 1984; Selley, 1984).
Assumptions concerning the probability distributions of the risky
prospects can also be a source of problems (Boisvert and McCarl, 1990). Some
risk efficiency criteria, for example mean-variance efficiency criterion, require
the outcome distributions for the risky prospects to be normally distributed
(or the decision maker's utility function to be quadratic). As suggested by
King and Robison (1984) this requirement decreases the applicability of the
mean-variance criterion in agriculture because the outcome distributions for
many risky decision prospects in agriculture have been found to be


Stochastic dominance

Stochastic dominance is a simple, commonly used, yet powerful decision
criteria for risky decision making (King and Robison, 1984). Stochastic
dominance provides an approach for ordering risky prospects which is
consistent with the expected utility framework, does not require complete
specification of decision maker preferences (i.e., utility functions), and does
not impose any restrictions on the outcome distributions of the risky
prospects under consideration (Zentner et al., 1981). The stochastically
efficient set is found by making pairwise comparisons of the cumulative
probability distribution functions (CDF) of the risky prospect's outcome
distributions under consideration. By using the CDF, stochastic dominance
enjoys an advantage over many other decision criteria because the CDF
inherently contains all the information on the risky prospect's outcome

distribution. Therefore, unlike for example the mean-variance criterion,
stochastic dominance considers not only the distribution's first (i.e., mean)
and second (i.e., variance) moments but also all higher moments (e.g.,
skewness, kurtosis), which are important considerations for most decision
makers. Stochastic dominance relies on the fundamental property that
decision makers prefer low outcomes to be associated with low probabilities
and high outcomes to be associated with high probabilities.
Stochastic dominance criterion is actually a family of criteria with
varying degrees of discriminatory power in reducing the choice set to a risk
efficient, or stochastically dominant set, and a risk inefficient set, or
stochastically dominated set. The three primary stochastic dominance
criterion are first degree stochastic dominance (FSD)(Quirk and Saposnik,
1962), second degree stochastic dominance (SSD)(Fishburn, 1964; Hanoch and

Levy, 1969; Hadar and Russel, 1969), and generalized stochastic dominance
(GSD)(Meyer, 1977), also referred to as stochastic dominance with respect to a
function (SDRF). The differences in stochastic dominance criteria result from
differences in the restrictiveness of their assumptions concerning decision
maker preferences (i.e., utility functions).

First degree stochastic dominance

First degree stochastic dominance is the least restrictive and least
discriminatory of stochastic dominance techniques. The only assumption
concerning risk preferences in FSD is that the underlying utility functions of
the decision makers exhibit positive marginal utility for some performance
measure, X. In other words, the first derivative of the utility function is
positive. Therefore, the ordering of risky prospects obtained via FSD is
applicable to all classes of decision makers; risk averse, risk neutral, and risk
preferring. As mentioned, all stochastic dominance techniques are based on
the CDF of the risky prospects' outcome distributions, thus FSD considers all
dimensions of risk; central tendency, dispersion, skewness, etc. The decision
rule for FSD states that risky prospect outcome distribution F is preferred to G
if F(X) is less than G(X) for all x, and at least one x, that is for decision makers

U'(X) >0 (i.e., o
F(X) >- G(X)
F(X) < G(X)
for all x and the inequality is strict for at least one value of X.

In graphical terms this implies that no points on the CDF of F ever lie to
the left of those on the CDF of G and at least one point on F lies to the right of
G. Thus, for equal probabilities, the value of the outcome distribution for
risky prospect F is equal to, or higher, than risky prospect G, but never lower.

The generality of the risk preference assumptions in FSD do not allow

discrimination between risky prospects whose CDF intersect. Thus, FSD can

fail to eliminate many risky prospects from the choice set (King and Robison,

1984; Zentner et al., 1981).

Second degree stochastic dominance

Second degree stochastic dominance is more restrictive than FSD because

it holds only for risk averse decision makers.. Thus, the underlying utility

functions of these decision makers must exhibit positive, but decreasing
marginal utility for the performance measure, X. In other words, the first
derivative of the utility function is positive and the second derivative is

negative. Therefore, the ordering obtained via SSD is not applicable to

decision makers who are risk neutral or risk preferring. Like FSD, SSD

considers all dimensions of risk; central tendency, dispersion, skewness, etc.

The decision rule for SSD states that risky prospect outcome distribution F is
preferred to risky prospect outcome distribution G if the accumulated area
under F(X) is less than the accumulated area under G(X) for all x, and at least

one x, that is for decision makers where

U'(X) > 0 and U"(X) < 0 (i.e., 0 < Ra(X) < o),

F(X) >- G(X)
Sx F(X) dX < j G(X) dX
Joo Jo

for all x and the inequality is strict for at least one value of X.
Graphically, SSD implies that distributions F and G can intersect;
however, distribution G will never be a candidate for the risk efficient set if its
low outcome values have a higher probability of occurrence. This situation
arises because, regardless of how attractive G may be at the high end of its
CDF, risk averse decision makers are primarily concerned with minimizing
the probability of a low outcome (King and Robison, 1984; Zentner et al.,
Second degree stochastic dominance is a more widely used and is a more
highly discriminatory risk efficiency criterion than FSD (King and Robison,
1984). However, the ranking of risky prospects obtained with SSD are invalid
if the risk averse assumption on decision maker risk attitude is violated.
Research (Officer and Halter, 1968; Conklin et al., 1977; Halter and Mason
1978; Whittaker and Winter, 1980; Tauer, 1986) has indicated that many
agricultural producers exhibit risk neutral and risk preferring risk attitudes.
Thus, the risk efficient (inefficient) set obtained using SSD may include risky
prospects that are not (are) preferred.

Generalized stochastic dominance

Generalized stochastic dominance allows for greater discrimination
among risky prospects than FSD or SSD. However, GSD places the highest
degree of restriction on decision maker risk preferences. Consequently, GSD
has the least breadth of applicability across classes of decision makers. In GSD,
as developed by Meyer (1977), an underlying utility function for decision
makers is not assumed. Rather, an upper and lower bound on Ra must be

specified and the GSD algorithm solves for a utility function, using optimal