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OPERATIONS AND ECONOMIC MODELS FOR LARGE MILKING PARLORS BY CRAIG VINCENT THOMAS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1994 To my wife for her love, patience, and understanding; to my son for his example of dedication, hard work, and selfdiscipline; to God for the abundant blessings He gives me each day. ACKNOWLEDGMENTS 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 singlemost 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 information. 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 troubleshooting 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 fulltime 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 selfdiscipline in the classroom and on the basketball court have served as a constant reminder to me of the preciousness of life's opportunities. TABLE OF CONTENTS PAGE ACKNOWLEDMENTS ................................................................................ iii LIST OF TABLES............................................................................................ ix LIST OF FIGURES.......................................................................................... xiv LIST OF ABBREVIATIONS........................................................................ xviii A BSTR A C T ..................................................................................................... xx CHAPTER 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 3 PREDICTING INDIVIDUAL COW MILKING TIME FOR MILKING PARLOR SIMULATION MODELS................ 89 Introduction......................................................................... 89 Materials and Methods...................................................... 91 Results and Discussion...................................................... 95 C conclusions .......................................................................... 111 4 SIMULATING INDIVIDUAL COW MILK YIELD FOR MILKING PARLOR SIMULATION MODELS................ 112 Introduction......................................................................... 112 Materials and Methods...................................................... 114 Results and Discussion...................................................... 117 C conclusions ......................................................................... 127 5 A NETWORK SIMULATION MODEL OF LARGE HERRINGBONE AND PARALLEL MILKING PA R LO RS................................................................................ 129 Introduction......................................................................... 129 Materials and Methods...................................................... 131 Results and Discussion...................................................... 149 C conclusions ......................................................................... 160 6 EFFECTS OF PARLOR SIZE, PARLOR DESIGN, MILKING SYSTEM OPERATING CHARACTERIS TICS, MANAGEMENT STRATEGIES, AND MILK YIELD ON THE PERFORMANCE OF LARGE HER RINGBONE AND PARALLEL MILKING PARLORS...... 162 Introduction......................................................................... 162 Materials and Methods...................................................... 164 Results and Discussion...................................................... 173 C onclusions......................................................................... 206 7 A STOCHASTIC ECONOMIC ANALYSIS OF LARGE HERRINGBONE AND PARALLEL MILKING PA R LO R S................................................................................ 208 Introduction......................................................................... 208 Materials and Methods ...................................................... 216 Results and Discussion...................................................... 229 C onclusions......................................................................... 250 8 SUMMARY AND RECOMMENDATIONS FOR FUTURE RESEARCH .......................................................... 251 A PPEN D ICES ................................................................................................ 257 A LEAST SQUARES MILKING PARLOR PERFOR MANCE MEANS FOR VARIOUS SIZES OF HERRINGBONE AND PARALLEL MILKING PARLORS OPERATED AT DIFFERENT COMBI NATIONS OF MILKING SYSTEM OPERATING CHARACTERISTICS, MILKING PROCEDURES, AND AMOUNTS OF MILKING LABOR......................... 257 B DAILY FEED COSTS USED IN MILKING FACILITY CAPITAL BUDGETING MODELS..................................... 264 C STOCHASTIC OUTPUTS FROM MILKING PARLOR SIMULATION MODELS SERVING AS INPUTS TO STOCHASTIC MILKING FACILITY CAPITAL BUD GETING M ODELS ................................................................. 266 REFEREN C ES................................................................................................ 287 BIOGRAPHICAL SKETCH ......................................................................... 299 viii LIST OF TABLES TABLE PAGE 31. Least squares ANOVA for lag and milk flow times............ 96 32. Partial regression coefficients for lag time data and m ilk flow data........................................................................... 97 33. Least squares ANOVA for milk yield .................................. 102 34. Partial regression coefficients for milk yield data.............. 102 35. Shifted gamma distribution parameters for milk flow time as a function of milk yield per milking, pulsation ratio, and vacuum level.......................................................... 110 41. Milk yield characteristics of test herds by herd milk yield category. ............................................................................. 118 42. Weibull distribution parameters for pooled and trun cated milk yield per milking as a function of herd milk yield category and m onth ....................................................... 122 43. 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 44. Comparison of observed and simulated means and standard deviations for monthly total herd milk yield by dairy and herd milk yield category ..................................125 45. 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 51. Definitions of parlor simulation model's stochastic elem ents and activities............................................................ 138 52. Characteristics of dairies providing simulation data........ 142 53. Raw data means and standard deviations for parlor simulation model elements and activities by dairy...........146 54. Element and activity fitted distributions for milking parlor simulation validation models .................................. 150 55. Comparison between observed and simulated parlor performance for validation dairies....................................... 153 56. Element and activity fitted distributions for herringbone and parallel milking parlor simulation models................ 154 57. Comparison of simulated milking parlor performance measures for three milking facility size categories ........... 156 61. 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 62. Least squares means for turns per hour and milk per shift per hour by size of parallel parlor........................ 174 63. Least squares means for turns per hour and milk per stall per hour by milking system pulsation ratio and vacuum ............................................................................... 177 64. Least squares means for turns per hour and milk per stall per hour by various combinations of milking system pulsation ratio and vacuum.................... 178 65. 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 66. 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 67. 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 68. Least squares means for turns per hour and milk per shift per hour by parlor design ....................................... 181 69. Least squares means for turns per hour and milk per shift per hour by parlor design and milking system pulsation ratio........................................................................... 182 610. Least squares means for turns per hour and milk per shift per hour by parlor design and milking system vacuum ......................................................................... 182 611. 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.......................... 184 612. Least squares means for turns per hour and milk per shift per hour by milking procedure............................. 185 613. Least squares means for turns per hour and milk per shift per hour by amount of milking labor.................. 186 614. Least squares means for turns per hour and milk per shift per hour by milking procedures and am ount of m ilking labor ........................................................ 187 615. Least squares means for turns per hour and milk per shift per hour by parlor size and milking procedures.................................................................................. 188 616. Least squares means for turns per hour and milk per shift per hour by parlor size and amount of m ilking labor............................................................................. 188 617. 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.......................... 191 618. Least squares means for turns per hour and milk per shift per hour by parlor design ....................................... 192 619. Least squares means for turns per hour and milk per shift per hour by milking procedure............................. 192 620. Least squares means for turns per hour and milk per shift per hour by amount of milking labor.................. 193 621. Least squares means for turns per hour and milk per shift per hour by parlor design and milking procedures.................................................................................. 194 622. Least squares means for turns per hour and milk per shift per hour by parlor design and amount of m ilking labor. ........................................................................ 194 623. Least squares means for turns per hour and milk per shift per hour by parlor size and milking procedures.................................................................................. 196 624. Least squares means for turns per hour and milk per shift per hour by parlor size and amount of m ilking labor............................................................................. 196 625. Least squares means for turns per hour and milk per shift per hour by milking procedures and am ount of m ilking labor ........................................................ 197 626. 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........................................... 198 627. Regression coefficients for turns per hour as a function of individual cow milk yield per milking for various sized parallel and herringbone parlors................................ 199 628. 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................. 200 629. 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 71. Costs of totally equipped parlors in three milking fac ility size categories including parlor building and associated equipm ent............................................................... 218 72. Information used to calculate depreciation, capital replacement, and property taxes for milking facility capital budget m odels .............................................................. 219 73. Cash flow calculations in milking facility capital bud get m odels. .................................................................................. 220 74. Stochastic output from the simulation of various m ilking facility alternatives................................................... 230 75. Lower and upper bounds on the willingness to pay for various milking facility alternatives ............................. 231 76. Stochastic output from the simulation of various milking facility alternatives operated at selected pulsation ratio and vacuum combinations........................ 236 77. Lower and upper bounds on the willingness to pay for various milking facility alternatives operated at selected pulsation ratio and vacuum combinations......... 237 78. 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 79. 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 LIST OF FIGURES FIGURE PAGE 21. Operational view of dairy farm............................................. 8 22. Alternative problemsolving approaches........................... 40 23. Steps in a simulation study.................................................... 43 24. Schematic view of risk efficiency criterion......................... 74 31. Components of total machineon time............................... 93 32. Milking time as a function of pulsation ratio and vacuum level .................................................................... 99 33. Milking time as a function of pulsation ratio and milk yield per cow per milking at a constant vacuum (46.6 kPa) ..................................................................................... 101 34. Milk yield per milking as a function of pulsation ratio and vacuum level .................................................................... 103 35. 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 36. 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 41. 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 42. Histogram of pooled and truncated milk yield per milking sample data with overplot of fitted Weibull distribution for worst fitting distribution ........................... 120 43. Histogram of pooled and truncated milk yield per milking sample data with overplot of fitted Weibull distribution for best fitting distribution............................... 121 51. Flowchart of milking parlor simulation model logic ........ 133 52. Timebar chart of network parlor simulation model showing stochastic elements and activities........................ 135 53. Simplified schematic representation of network parlor simulation model showing stochastic elements and activities...................................................................................... 136 54. Performance comparison of four large parallel milking p arlors. ......................................................................................... 159 61. Timebar chart of hypothetical threestall parlor showing stochastic elements and activities of SLAM SYSTEM parlor simulation model .................................... 176 62. Parlor turns per hour as a function of individual cow milk yield per milking for different size parallel m ilking parlors. ......................................................................... 201 63. Milk per stall per hour as a function of individual cow milk yield per milking for different size parallel m ilking parlors. ......................................................................... 202 64. Parlor turns per hour as a function of individual cow milk yield per milking for different size her ringbone and parallel milking parlors................................. 205 65. 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 71. Cumulative probability distributions of net present returns to ownership and nonparlor fixed costs for double20 herringbone and double20 parallel milking p arlors. ......................................................................................... 232 72. Cumulative probability distributions of net present returns to ownership and nonparlor fixed costs for double32 parallel, two double16 herringbone, and two double16 parallel milking parlors ............................... 233 73. Cumulative probability distributions of net present returns to ownership and nonparlor fixed costs for double40 parallel, two double20 herringbone, and two double20 parallel milking parlors ............................... 234 74. Cumulative probability distributions of net present returns to ownership and nonparlor fixed costs for double20 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 75. Cumulative probability distributions of net present re turns to ownership and nonparlor fixed costs for two double16 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 76. Cumulative probability distributions of net present returns to ownership and nonparlor fixed costs for two double20 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 77. Cumulative probability distributions of net present returns to ownership and nonparlor fixed costs for double20 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 xvi 78. Cumulative probability distributions of net present returns to ownership and nonparlor fixed costs for two double16 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 79. Cumulative probability distributions of net present returns to ownership and nonparlor fixed costs for two double20 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 xvii LIST OF ABBREVIATIONS 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 nonparlor fixed costs 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 machineon time xviii 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 OPERATIONS AND ECONOMIC MODELS OF LARGE MILKING PARLORS By 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 (double16, 20) operated more efficiently in processing inputs and producing outputs than larger parlors (double32, 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 nonparlor 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 double16 or two double20) parallel parlors provided higher returns than multiple, small (two double16 or two double20) herringbones or a single, large (double32 or double40) 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. CHAPTER 1 INTRODUCTION 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., doublesided 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., double16 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 decisionmaking 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. CHAPTER 2 LITERATURE REVIEW 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 21). 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 nonbottleneck 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 8 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 TRANSFORMATION INPUTS PROCESS OUTPUTS FEEDING ANIMALS MILKING MILK CAPITAL BREEDING . HEALTH ANIMALS LABOR WASTE Output limited by most restrictive processing requirement. Figure 21. 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 risk. 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 outputthe 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 factors. 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 betweencow 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 machineon 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. Leastsquare 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. Leastsquare 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 double11 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 antisepsis. 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 turnins 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 setup, cleanup, 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, nonroutine or emergency procedures requiring attention by the milker. Therefore the maximum number of cows a particular parlorequipmentlabor 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 performance. 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 (double4, 6, 8 and 10), polygon (24 stall), turnstyle (17 stall), and sideopening (double3). 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 rapidexit 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 4sided polygon and 3sided 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 twosided herringbone or parallel parlors. Bickert (1980) maintained that a double10, mechanized herringbone parlor will operate about 7% slower than an 18stall mechanized trigon parlor (92 vs. 98 CPH). Armstrong and Quick (1986) reported on a case study comparing a double16 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 twosided 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 double20 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 double20 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. Duallane exit alleys have been reported to increase CPMH by 7% in a double10 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 "rapidexit" milking parlor stalls. Rapidexit stalls are designed so each stall within a parlor side has a separate exit gate or the entire exitside 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 rapidexit equipped herringbone parlors in the range of double10's to double24'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 double10 herringbone, 13.8% (116 versus 132 CPH) in a double16 herringbone and 16.0% (150 versus 174 CPH) in a double24 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 inparlor 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 double8 or double10 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 double8 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 double8 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 double10 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 endtoend routine in a polygon parlor. The endtoend 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 32stall 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 endtoend routine (Armstrong and Quick, 1986). Gamroth (1992) reported a 20 to 30% reduction in parlor performance for a territorial vs taskoriented milking routine. In the territorial routine each milker performs all pre and postmilking tasks in a specified area of the parlor, while in the taskoriented 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 welloperated 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 2540% 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 double20 and double24 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 relationships. 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 double8 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 onefourth 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 double10 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 welltrained 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 worktask 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 study. Work involving the interaction of workers and machines and groups of workers are primarily studied using workermachine charts, activity charts and horizontal timebar 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 semicovertly, 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 realtime 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 slowmotion (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 "micromotion", 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 workermachine 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 motiontime 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 elements: 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 wellunified 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 22). 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 "whatif" questions and it is impossible to answer questions concerning proposed systems not yet in existence. I I I Experimentation Simulation Mathematical on the modeling real system Increasing realism Increasing abstraction Figure 22. Alternative problemsolving 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., closedform) 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, closedform 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 discretecontinuous 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 customerservice 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 23)(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 23, one should be aware that simulation has an evolutionary nature. Therefore, movement between steps is not completely a oneway 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 23. 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) Tracedriven 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 KruskalWallis 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 such as GPSS/H, SIMAN, SIMSCRIPT 11.5 or SLAM II. 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 nonstationary (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., tracedriven 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, MannWhitney, twosample chisquare, etc.). They referred to this method as the correlatedinspection approach. Another more reliable approach suggested by Law and Kelton (1991) is the confidenceinterval 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 warmup 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 computerbased 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 machinereadable 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 endusers. Simulation Studies Applied to Milking Parlor Performance Price et al. (1972) simulated small (4 to 12 stalls) sideopening 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 sideopening 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 sideopening 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 modeling. 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., sideopening 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 sideopening and herringbone parlors was shown to be for oneman 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 analysis. 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 falloff), 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 sideopening 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., pseudotrace 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 double2, sideopening 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 double15 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 choices. The most recent parlor simulation study was conducted by Chang (1992). This simulation, entitled OPSIM, employed objectoriented 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 double6 to double10 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 double13 herringbone with a double13 parallel parlor indicated a 3.7% CPH advantage for the parallel configuration. 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, workforce 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 onehalf hour of parlor setup time, one hour for group changes and onehalf 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 double4, 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 double4 herringbones to double10 herringbones and 16stall 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 aftertax 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 aftertax 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 aftertax, 15 yr fixed system costs. Annual, aftertax 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 aftertax fixed and operating costs for variable herd sizes were then developed using the annual aftertax fixed costs plus operating costs per hour times the number of cows in the milking herd. The equations were used to make an annual, aftertax cost per cow comparison for each system at varying herd sizes from 50 to 500 cows. Results of the analysis indicated that the leastcost system for herds of 250 cows or less was the unmechanized double4 herringbone ($161 annual cost/cow, 250 cow herd). Depending on herd size (50 to 250 cows) the unmechanized double4 herringbone had from a $1/cow to a $233/cow advantage in annual aftertax 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 leastcost system was often the smaller parlors (double6, 8); however, the leastcost advantage was usually obtained at the cost of more hours per milking. For example, at a 350 cow herd size the double8 was the leastcost system at $137/cow and a 6.5 hr milking time. The double10 was the next leastcost 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 12stall 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 12stall 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 Where 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 aftertax value of revenue is a constant; therefore, the equation can be written as NPVa = NPV + #a Where 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 Where 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 attitude. 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 time. 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) U'(X) Where 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) U'(X) or, Rr(X) = XxRa(X) Where 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 nondairy and percentage of total assets that were nonfarm 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 24, 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 Efficiency Criterion Risk Efficient Set Risk Inefficient Set (contains all risky projects (contains all risky projects not preferred by decision maker) preferred by decision maker) Figure 24. 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 meanvariance 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 meanvariance criterion in agriculture because the outcome distributions for many risky decision prospects in agriculture have been found to be nonnormal. 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 meanvariance 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 where U'(X) >0 (i.e., o F(X) > G(X) if 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) if 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., 1981). 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 