QPTEMUM SAERY CQW REPLACEMENT POLlClES TO MAMMEZE [NCQM-E GVER FEED COST Them E0» the Degree of DH. D. MICHIGAN STATE UNWERSETY Richard W. Rundeil 1967 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\\ \\\\\\\\\\i 4 l\\ 3 1293 10424 4177 This is to certifg that the thesis entitled Optimum dairy cow replzcement policies to maximize income over feed cost. presented by Rich rd ii. iiundell has been accepted towards fulfillment of the requirements for Dc'r Ph'D' degree in_. 61 y I L’ r professor Date /‘1/(4//(7 30/ /9(/ 0-169 ‘ ‘Mh .4 ABSTRACT OPTIMUM DAIRY COW REPLACEMENT POLICIES TO MAXIMIZE INCOME OVER FEED COST by Richard W. Rundell Simulation of a dairy herd over a period of 15 years was used to examine replacement strategies among six Opera— tionally practical systems of culling cows which would max- imize income over feed costs. The strategies or criteria used to remove the lower ranking cows to a relatively con- stant herd size were: (1) Mature Equivalent (M.E.) milk production, (2) M.E. gross milk income, (3) actual milk production, (4) actual gross income, (5) income over feed cost, and (6) present value of eXpected gross income of cow and her subsequent replacements. Two each of prices of milk, fat differential, feed, and Operational costs totaled 24 x 6 x 2 replications per trial or 192 replications. The following were treated as stochastic variables: (a) variation in milk production and milkfat percentage between cows and between lactations of the same cow, (b) chance of a calf being a heifer or bull, (c) chance of involuntary death or removal of cows and youngstock, and (d) chance of month of the year of involuntary removals. Richard W. Rundell The mean and variance of the base herd approximated the aver— age Michigan DHIA Holstein population in 1966. The sire value, approximating the best bulls used in A.I. was identi— cal for any given year through all strategies and replica- tions, but improved over time at the rate of 130 lb milk per year. Culls or cows removed because of low rank in each respective strategy were removed at the most profitable point to cull in their respective lactations by equating the milk income of the marginal month with the sum of the month's feed costs and monthly Operational charges. Practical use Of this simple method of determining when to cull cows within a lactation was demonstrated. A complete factorial design to analyze the generated data showed no significant differences between strategies under alternative combinations of prices in average income including salvage over feed cost per cow discounted to the present. This income was affected by the level of milk price (P<1.0l), feed cost (P <.Ol), Operational cost (P <.Ol), and fat differential (P< .05). When salvage value was omitted, average income over feed cost per cow per year for the 15 years was $385.94 under the culling strategy of actual gross income and was (P<:.Ol) larger than that of M.E. milk production at $385.56 or M.E. gross income at $383.66. Richard W. Rundell Average milk production per cow, fat production per cow, genetic value per cow, culling rate and average herd size differed (P<:.Ol) among strategies while gross income from milk was not significantly different. By mutually orthogonal contrasts, average milk production over the 15 years (14,247 lb) under the strategy of income over feed cost was significantly less than the average of the other five; average milk production under the M.E. milk strategy (14,357 lb) was higher (P< .01) than under the strategy of M.E. gross (14,266 lb) and the strategy Of actual milk yielded (P<:.Ol) more milk over 15 years than did actual gross. Fat production tended to rank the reverse of milk production among strategies. Both culling rate and herd size were higher under the two M.E. strategies. The average genetic milk value of the cows remaining in the herd at the end of each year was highest for the strategy of M.E. milk when averaged over the 15 years. OPTIMUM DAIRY COW REPLACEMENT POLICIES TO MAXIMIZE INCOME OVER FEED COST BY Richard w-‘-‘.'""i§unde11 A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree Of DOCTOR OF PHILOSOPHY Department of Dairy 1967 f ‘l “3.: “I f‘) RAN v u3 ,. 1 q‘ ACKNOWLEDGMENTS The author wishes to eXpress his appreciation to Dr. C. A. Lassiter, Chairman, and the Department Of Dairy for the assistantship and opportunity to pursue this study. Special thanks are due to Dr. John A. Speicher, the author's major professor, for his encouragement, guidance, and coun- sel throughout the entire period Of this study. Sincere thanks are due to Dr. John L. Gill for his counsel and technical assistance. The author is indebted to members of the Department Of Agriculture Economics for their COOperation and advice during all phases of this program. The author is eSpecially grateful to his wife Irene and daughter Lelia for their patience and understanding throughout the period Of this doctoral study. ***** ii TABLE OF CONTENTS Page INTRODUCTION . . . . . . . . . . . . . . . . . . . . . 1 REVIEW OF LITERATURE . . . . . . . . . . . . . . . . . 3 EXPERIMENTAL PROCEDURE . . . . . . . . . . . . . . . . 34 General Procedure and Derivation of Parameters . . . . . . . . . . . . . . . . . . 34 Determination of When to Cull Within a Lactation . . . . . . . . . . . . . . . . . . 51 Generation of Base Herd and Succeeding Generations . . . . . . . . . . . . . . . . . 54 Culling Procedure . . . . . . . . . . . . . . . 61 Comparison of Strategies . . . . . . . . . . . . 67 Analytical Design and Methods . . . . . . . . . 68 RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . 70 Comparison of Strategies . . . . . . . . . . . . 70 Effect of Prices . . . . . . . . . . . . . . . . 88 When to Cull Within the Lactation . . . . . . . 91 Implications for Further Research . . . . . . . 96 LITERATURE CITED . . . . . . . . . . . . . . . . . . . 98 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . 105 iii Table l. 10. 11. 12. 13. 14. 15. LIST OF TABLES Page Present value of income over feed cost (including salvage) . . . . . . . . . . . . . . 70 Effect Of levels of prices on present value of income (including salvage) over feed cost . . . . . . . . . . . . . . . . 71 Average income over feed cost per cow . . . . . 73 Average genetic milk value per cow (lb) . . . . 76 Average fat production per cow (1b) . . . . . . 78 Comparison Of production records of two strategies . . . . . . . . . . . . . . . . 79 Results of two alternative strategies . . . . . 80 Comparison of mean milk production among strategies . . . . . . . . . . . . . . . . . . 81 Average milk production per cow (lb) . . . . . 82 Percentage of voluntary culls . . . . . . . . . 84 Average herd size by strategies . . . . . . . . 86 Average milk production by levels of prices . . . . . . . . . . . . . . . . . . . . 89 Average fat production by levels of prices . . 90 Average gross milk income by levels of prices . . . . . . . . . . . . . . . . . . . . 91 When to cull within the lactation . . . . . . . 94 iv Figure 1.1 1.2 Average Average Average Average Average Average LIST OF FIGURES income over feed cost per cow income over feed cost per cow genetic milk value per cow . genetic milk value per cow milk production per cow . . milk production per cow . . Page 74 74 77 77 83 83 Appendix Table LIST OF APPENDIX TABLES Age correction factors . . . . . . . Part lactation factors . . . . . . . Body weight by age of cows . . . . . Feed requirements for dry period . . Extra hay added to ration of young cows to meet protein needs . . . . . . . . vi Page 106 106 107 107 108 INTRODUCT ION Dairy farmers, as profit maximizers, are constantly striving to expand the income producing ability of their dairy herds. As managers of their business, their direct concern is to enhance the average quality of their herd by removal of the unprofitable producers and as such are faced with two major decisions, which cows to cull and when within the lactation to cull. The objectives of various dairymen may be of differ- ent kinds; for example, the goals of a dairy farmer may be to maximize average milk or fat production or increase the genetic merit of his herd, regardless Of economic consider- ations. For the majority of dairymen, however, it is assumed the major Objective is maximum profit from their dairy herd. Most current systems Of ranking or culling cows within a herd compare the relative merit of cows in question on the basis of their reSpective mature equivalent (M.E.) milk production records. Furthermore, numerous papers have been written regarding the genetic improvement Of dairy herds through selection of both females and sires based on these M.E. records. Few studies, however, have dealt eXplic- itly with the economics of dairy cow replacement policies over time. The present study was initiated to determine the Optimum replacement strategy among several operationally practical systems of culling cows which will maximize income over feed costs. Such a system may subsequently be adapt- able tO standard DHIA operations. Moreover, this study sought to determine the extent to which alternative culling policies deviate from the Optimum as well as to derive the economic loss a dairyman would encounter by using a less than Optimum strategy. Finally, this study sought to indi- cate the change in strategy or economic loss which might result from a change in the price of milk, fat differential, feed, or Operational costs. Yet to compare economic conse- quences of different replacement policies over time, it was necessary to discount future income and costs to the present. Because of the biological nature of a dairy cow, the cyclic aspect of milk production, and the presence Of various stochastic elements, an analysis Of the dairy cow replacement problem calls for a much more complicated model than ordinary replacement theory assumes. To study effectively the long term effects of various culling strategies, it was prOposed to simulate production and reproduction plus certain other stochastic variables of a dairy herd over a period of years. In turn, the data generated from such a simulation would serve as a basis for a comparison of the reSpective strat- egies and related variables. REVIEW OF LITERATURE Replacement theory The recent surge of interest in the economics Of replacement of durable assets arises largely from the con— tinued substitution of capital goods for other inputs in agriculture. Though the theory of replacement of durable capital used in production may be considered part of produc— tion theory in economics, only that part of this theory which deals with production over time is relevant to the replacement problem. For example, the simplest type of replacement problem, such as a dry lot cattle finishing Operation, concerns a short production period where the producer realizes returns only by the sale of the asset. Faris (1960) illustrates this concept in a continuous Opera— tion, in which each lot Of cattle is immediately replaced by a new lot; by this method the Operator strives to maximize his average net revenue over time. Since we simply cannot efficiently manage general equilibrium solutions, economic models dealing with the replacement problem usually are models for sub-Optimization or partial equilibrium. At any time a replacement could be made, we will call this a decision; a sequence of such deci— sions will be called a policy; and the most profitable policy will be called an Optimal policy. Introducing a long production period complicates the problem of determining the Optimum replacement pattern due to both uncertainty and time preference; therefore, we must consider two types of dis- counting. The first type of discounting is due to uncer— tainty of future prices, yields or costs. Burt (1965) has presented a model in which he incorporates such uncertainty but emphasizes that discounting for risk and uncertainty is economic under the assumption that knowledge of future net returns diminishes with time because the variance of net returns increases prOportionally with time. The second type of discounting arises from time preference: a sum of money received or paid at the present time is worth more than the same sum of money at some time in the future; hence, this discounting is primarily a func- tion of opportunity costs (Faris, 1960). Here the supply and demand for loanable funds determines the apprOpriate discount rate. We can eXpress this relationship by the following formula (Paris, 1960): Future Income (1 + i)n Y: where i = the interest rate, n_= the number Of years and X is the discounted future income to present value. In general, the Optimum replacement pattern results from maximizing net revenue over time. Specifically, we select a replacement age to maximize the present value Of the whole future difference between income and outlay streams, where the present value equals the value associated with the existing asset plus the value of all future replace- ments at the time of first replacement, discounted to today (Giaever, 1966). Except for minor modifications with different types of assets, the above principle holds. For example, in the replacement of trees which have long production periods, returns come only from the sale of the asset, whereas assets such as dairy cows or breeding stock are dominated by a flow of revenue over the life of the asset. The biological phenomena of these latter capital items, because of growth and random removal due to death and disease, complicate the replacement problem. For a stand Of timber, Faris (1960) computed the Optimum replacement time as when the marginal net revenue from the present enterprise equals the highest amortized value of anticipated net revenue from the enterprise immedi— ately following. Winder and Trant (1961) refined Faris' equations by defining Opportunity cost Of applying another unit Of input as the marginal factor cost plus the foregone earning of the time required to apply the unit of input. Further refining Faris' equations, Chisholm (1966) emphasized that not only does the money sunk in fixed and variable costs have an Opportunity cost but so does the money tied up in the appreciating asset, the growing trees. We could demonstrate a similar analogy to money tied up in the salvage value of a dairy cow. Using the net present value criterion, a dairyman would maximize the net present value Of all production periods of a cow plus her subsequent replacements, and not, as has been sometimes advocated, choose the single production period having the maximum net present value or simply the lactation with the highest yield. Of several approaches to the problem of replacement of producing animals, White (1959) demonstrated the use of multistage decision making applied to replacement Of laying hens, a method that considers all decision points simulta- neously. Tedford (1964) also used a laying flock to demon- strate equations which maximize net earnings for present and all future replacements. Under conditions of capital rationing, the criterion of "maximum rate Of return" may be more apprOpriate than that of "present value" since a fixed quantity of capital can be compounded at the highest possible rate by maximizing the internal rate of return in the investment (Burt, 1965). With the dairy cow, for example, we must invest in housing and milking equipment as well as the cow, but the amortiza- tion rate of such auxiliary equipment is the internal rate of return which is the unknown being determined. Replacement theory—-dairy cows Few studies have dealt explicitly with the economics Of dairy cow replacement. Jenkins and Halter (1963), how- ever, formulated the problem of dairy cow replacement as a problem of maximization or minimization based on dynamic programming principles and maximization Of present value. Economic factors which they considered in the decision rela- tive to the replacement of the present animal were: (1) market value of the present animal or its possible replace- ment, (2) transaction cost of purchasing an animal, (3) net market value Of the milk production of the present animal or its replacement, and (4) maximum net return in subsequent enterprise periods from replacement Of the present animal. Jenkins and Halter considered certain stochastic factors which influence the dairy cow replacement decision: (1) probability Of an animal failing, that is, involuntary cull or death, (2) probability Of an animal succeeding, and (3) likelihood of finding (or having) a cow in a given lacta— tion. Consequently, the eXpected net returns equals the sum Of the returns from the various outcomes times the probabil- ities associated with the outcomes. Under various prices for cows, feed, beef, and milk, these authors determined the Optimal replacement policies by the model described. When prices were set at 1961 averages, the Optimum policy was to purchase an animal of lactation one, keep her until she completed her sixth lactation, then replace her with another animal of lactation one. Beyond this point, policy was indeterminable. Jenkins and Halter's approach is more an illustration of given principles than an attempt to solve a realistic problem and assumptions of the model render it unrealistic and of doubtful practical value; for instance, they assume the replacement animals will pro— duce at the same butterfat level as the present animals if in the same lactation and assume all cows in the herd pro- duce at herd average. A slightly different approach, presented by Hutton (1965), simulated the eXperience of a dairy herd over a Specified number of years under two alternative basic pol- icies: raise herd replacements or purchase all replacements. After cows are ranked according to projections of net re- turns, they are compared to the heifers which are ranked according to their "eXpected" net returns. Then available heifers from the top Of their array are substituted for cows from the bottom Of their reSpective array. Each dairyman interested in this program answers a 50 item questionnaire regarding such things as intentions of herd eXpansion, feed— ing rates and costs, milk prices eXpected, certain culling practices, rate of involuntary losses, purchase price of cows, and the 305 day Mature Equivalent—Fat Corrected Milk (305-M.E.-FCM) record of each cow in the herd. Applying the model to a representative herd, Hutton projected the net returns and production per cow for both the purchase and raise policies in a five year period. Com— puting both the estimated net returns and the variability in returns, he contended the decrease in capital funds more than Offset the generally higher average income under the policy Of purchasing replacements. Assuming milk at $4.60/ cwt for a 30 cow herd, Hutton discounted the present value of the two policies to an average annual rate over a 5 year period of $7,259 and $6,370 for the "raise" and "buy" pol- icies reSpectively. The most intensive study to determine dairy cow replacement policies was developed by Giaever in 1966. Within the framework of Markovian dynamic programming, the resulting derivation Specifies we should replace an asset when rate of income from that asset, plus rate Of increase in salvage value, less rate of outlay equals the interest rate times the sum of salvage value and present value (at time of replacement) of the next asset in the chain. Such a Markov process is a stochastic process in which the prob— ability distribution Of outcomes at any given stage depends only on the actual outcome at the last preceding stage. Based on the parameters derived from the two herds of 700 and 650 cows reSpectively, the Markovian process thus defines the lactation number to replace a cow in a finite production-lactation class under a given set of prices for 10 feed, milk, and culls for each of three calving intervals. Though the process was defined to represent a dairy cow and the chain of her successive replacements, the term "replace- ment" meant any case where one durable capital item, in this instance, a heifer, is substituted for another one, whether output changes or not. Since different stochastic elements enter the re— placement problem, Giaever included three such variables: (a) variation in production both between cows within a herd and between different lactations Of the same cow, or repeat- ability, (b) probability of a given calving interval, and (c) probability of involuntary removal; hence, transition probability equaled the product of these three variables. Based on assumed age-corrected herd averages of 12,000 lb and 11,000 lb 305-FCM from the two herds respectively, the seven production levels were derived as deviations from this base. Giaever assumed in his model that if the decision is to replace, the cow will be sold and replaced with a heifer immediately, while each decision to keep or replace, for simplicity, was made seven months after the last calving. Independently of his Markovian process, Giaever derived a simple decision rule whereby dairymen can deter— mine the Optimal time to replace within a lactation: "if it is decided to replace a cow during the current lactation, it will pay to keep the cow as long as the monthly milk income less feed costs exceeds the monthly interest on ll (salvage plus present value of a heifer including total expected net income over all lactations discounted to the present)" where the interest on (S-+V) equals the Opportu- nity cost of keeping a cow in the herd. Accordingly, to justify keeping a potential cull (another month), her milk income less feed cost must equal or exceed this Opportunity cost. If we cannot solve the replacement problem by the above method, the interest on (S4—V) should approximate "the average per month (milk sales plus beef sales minus feed costs minus replacement costs minus interest on salvage value) per cow for the herd," which says that the opportu- nity cost equals the possible profit from the average of the rest Of the herd. Not surprisingly, results call for more intensive culling if the calving interval is longer, when replacement prices are lower, cull beef prices higher, or when milk prices are higher. The effect of following an extreme sub— Optimal culling policy reduced annual profit per cow by about $6.00 while moderate deviations from the Optimal replacement policy suffered only minor losses. Decision models Various types of formal analytical models have been deve10ped to tackle the problems of managers, yet some prob— lem situations cannot be modeled in this manner. For instance, the dairy farmer, in his replacement problems, 12 faces two principal decisions: which cows to cull and when to cull them. Accordingly, techniques such as "decision theory" arise which attempt to simulate a great part of the rational processes of managers. A manager can utilize rela— tively simple decision models somewhat intuitively but in more complex situations this kind of comparison is beyond the capability of a manager, who must then introduce some decision rule into the formal analysis to substitute for the intuitive evaluation (Hutton, 1965). In general, the decision maker adopts the best or Optimum strategy or ranks the strategies which reflect the given order of consequences for the decision maker as defined by utility, eXpected utility, eXpected loss, or some other appropriate measure (Tedford, 1964). Thus the dairy farmer, as a decision maker, wishes to select the best cull— ing strategy to maximize net income, production per cow, or some other standard he chooses to optimize. Two general types of decision models have been described, namely, game theoretic and probabilistic. Where— as game theoretic models (Tedford, 1964) emphasize decision making in situations of conflict which involve the behavior of the players, probabilistic models stress the decision maker's eXpectations and use of probability measures as eXpressing weights he attaches to possible states of the world. Within the Operation of a dairy herd, for instance, such subjective probability distributions as the price of l3 milk, sex ratio of calves born, chance of involuntary deaths, and the future production of cows and their Offspring, con- front the manager in his decision process. In fact, the biological and environmental nature of livestock require modifications to the common replacement theories which assume fixed output. Simulation Through simulation, one of a growing number of quantitative techniques developed to assist management in decision making, Monte Carlo or other methods generate a stream of behavior which allows management to determine the effect of following alternative policies without actually putting these policies into effect (Babb, 1963). With this method, variables such as sales, production, weather, Or death losses of livestock are subject to probability. By simulation, we can formulate more complex and realistic models than possible by conventional mathematical techniques. Such a technique has been used to study a wide range of problems (Shubik, 1960), including genetics (Fraser, 1962; Gill, 1963) and teaching principles of selection (Heidhues and Henderson, 1961; Everett et al., 1967). Monte Carlo techniques deve10ped by Glickstein et a1. (1962) duplicated the probabilistic nature of milk arrivals of cheese plants in Indiana. With this information, the authors examined 12 different policies or decision rules 14 which affected the amount Of milk purchased, the distribu- tion of milk receipts and prices paid for milk for one year. More directly related to farm managers' activities, Halter and Dean (1965) simulated decision making processes of a large California range feedlot Operation where they compared the mean and variance of net income for each of three models of price eXpectation over a period of 40 years. Optimal organization and managerial policies under the uncertain conditions of low and unstable rainfall Of Israel were inSpected by Zusman and.Amid (1965) through simulation tools. They defined the Optimal decision rules in terms of the present value Of the net return flow and the coefficient Of variation of the income flows. But these authors emphasized that because of the dynamic nature of crOp and livestock farming, any choice among these decision rules and farm organizations should account for the economic performance over a sufficiently long sequence of years. Dairy cattle selection Improving the milk—producing abilities of dairy cattle pOpulations is inherently slow because of low repro— ductive rates, long generation intervals and small heritabil- ities. Deciding which cows to keep forces the breeder to ponder several different characters, i.e., milk, fat percent- age, type and ease of milking. Moreover, natural selection plus the tendency to select for these multiple traits, some 15 of doubtful value, hinder a dairyman's progress. Finding the relative economic value of these characters Often proves difficult because it may vary from region to region or according to market demand. Hazel and Lush (1942) compared the three most common methods of selection for more than one trait: (a) tandem, or a sequence of one trait at a time, (b) total score or all traits simultaneously by some index, and (c) independent culling which establishes a certain level of merit for each trait. They professed total score most efficient and tandem least efficient of the three. Though intensity is maximum when we select strictly on the item under consideration, the degree Of intensity depends entirely on how large a fraction must be saved: with the fraction saved at 0.8, 0.7, and 0.6, the intensi- ties are 0.35, 0.50, and 0.64 respectively (Lush, 1960). When dairymen pay attention to less important traits or sell some higher producing cows for dairy purposes, they reduce the actual intensity of selection. To make selection of dairy cattle or other animals more accurate, we need sound and simple selection indices to place prOper relative weights on each of the traits to eval- uate. Such weights depend on the heritability of the traits, genetic and phenotypic correlations between traits and their economic importance (Lush, 1960; Hazel, 1943). Lush (1960) emphasizes when economic values are changing radically that one cannot afford to follow economic values closely; instead, 16 one would like to select today in accordance with economic values which will prevail 20 years from now. 'But this ream soning, because it is inconsistent with the principle of discounted present value, disregards the Optimum economic path to these goals. By comparing the actual selection practiced among Holstein herds with that which might have been possible, Allaire and Henderson (1966) estimated the efficiency Of intra—herd—year—season—lactation phenotypic selection for M.E. milk as 42, 34, 27, and 25% for the first four lacta— tions reSpectively. From another classification by these authors, the efficiency values of phenotypic selection were 27, 30, and 38% for less than $6,000, $6,000 to $8,000, and over $8,000 income over feed cost per worker reSpectively. One of the few attempts to quantify the selection characters of milk production on a purely net economic basis has been presented by Soller et a1. (1966) who described A.I. sire selection in Israel on the basis of live weight for age (LFA) Of the bull calves as well as the milk production of their daughters. The relative economic value of genetic progress in milk production and of LFA results from compar- ing the increase in gross income as a result of a unit increase in each of the traits, which they found stable under differing economic conditions. 17 Genetic prggress by selection EXpression of the progress achieved in our dairy herd selection programs usually has been based on genetic change in milk Or fat production over time. Possible gains from selection for a trait per unit of time depend on: (1) the selection differential or intensity, which is the dif- ference between the herd or pOpulation mean and the mean of the parents selected from this pOpulation to produce the next generation, (2) heritability Of the trait, and (3) length Of the generation interval (Laben, 1965). The eXpected gain per year in a breeding program for a given trait then equals the selection differential times the heritability divided by the generation interval. Laben (1965) analyzed the records of 12 herds over a 30 year period involving 3,900 cows and found an average in- crease Of 74 lb of FCM per year, an average yearly increase of 0.7%” From these 12 herds, the respective dairymen culled 23% each generation though they could have progressed as far by culling only 4% had they culled for milk yield alone. Everett (1966) found phenotypic trends of 201 i 5.7 lb of milk per year for the A.I. sired population of Mich— igan Holsteins enrOlled in DHIA, while the genetic increase was 2.4%.per year (1953 to 1965) in milk production and 2.6% per year in fat compared to 1.0% and 0.8% genetic increase per year in milk and fat respectively in the naturally sired 18 progeny. Everett et a1. (1967) calculated the genetic and environmental trends from simulated records as 135 and —4 lb milk respectively per year. Replacing 20% of the herd annually with young stock from the tOp 75% of the cows in the herd” 6% Of the herd having been culled for low production, Searle (1961) esti- mated additive genetic superiority after 15 years as 15, 19, and 38 lb of milk fat for the policies of (a) culling low producers, (b) culling low producers and selecting replace~ ments, and (c) culling low producers, selecting replacements using above-average sires, respectively. Van Vleck (1966) has compared the genetic progress eXpected under three different levels of culling. Assuming all herds following the same plan with an assumed 13% invol— untary culling, plan one involves all herds using superior proven A.I. sires (+l,500 lb milk) and females culled to the limit of replacement heifers. Such a plan with a 62% sur- vival rate would progress 13,000 lb M.E. milk in 50 years. Plan two uses tOp A.I. sires (+1,000 1b milk) but heifers are bred to natural service bulls from the top half of the herd. ‘With an Optimum survival rate of 70-76%, genetic progress in 50 years would approximate 8,200 lb M.E. milk. Plan three, when all breeders mate their cows to bulls from the tOp half Of the herds, the Optimum survival rate is at 68% with estimated genetic progress 4,000 lb M.E. l9 milk in 50 years. The above author raises the question of whether a dairyman should improve his herd genetically as fast as possible or earn as much money as possible right now. Reasons for disposal Since the average dairy cow produces fewer lactations than her potential, it becomes economically important to examine the reasons for disposal. When farmers sell large numbers of cows for dairy purposes, sterility, and miscel- laneous diseases, they considerably reduce the possible eco- nomic progress through elimination of low producers. But the primary reason for decreasing involuntary losses is to increase the culling rate for low production rather than to increase longevity. Various research studies have listed reasons for disposal of dairy cows. In an extensive study by Seath (1940), total culls were 28.6 and 32.9% respectively of over 8,000 Iowa and 4,000 Kansas cows. In the Beltsville herd where no cows were deliberately culled for low production or type, Parker et a1. (1960) found 41.3% of the Holsteins and 21.3% of the Jerseys were removed as non-breeders. That farmers consider more than one reason for removal Of cows is substantiated by a mail survey Of New York herds in which dairymen listed up to five reasons for diSposing Of each cow (O'Bleness and Van Vleck, 1962). From a total of 12 categories for culling and eight for death, 20 these authors eXpressed the most important reasons for dis- posal as: low production, 27-32% (percentage of total num- ber Of reasons); sterility, 16~19%; udder trouble or mas- titis, 14-20%; and dairy purposes, l4~15%. The proportion culled for low production declined with increasing age but problems of fertility and udder trouble increased with increasing age. Further evidence that cows vary by lacta- tion number or age in both voluntary and involuntary culls was confirmed by Specht and McGilliard (1960) with Michigan DHIA data. Economic conditions may influence rates of removal and reasons for disposal. Asdell (1951) maintained this factor caused the largest year to year variation in the number of cows culled for low production. The price of milk and the cost of cows contributed the greater share of these economic factors. Maintenance of sufficient culling power is dependent upon reduced heifer losses as well as the control of invol- untary culls. From a summary of data on heifers available for replacement, Frick and Henry (1956) suggest that with good commercial management, 335 heifers (similar to estimate of Pelisser, 1965) would enter the milking herd per 1,000 cows. But they stress that net reproduction rate or ratio of animals in two consecutive generations more accurately measures the amount of selection available in heifer calves. 21 Economics of longevity Value of a cow to a herd depends upon her ability to produce and reproduce for many years, both from an economic and breed improvement standpoint. Such longevity should reduce the number, and thereby the cost of herd replacements and subsequently increase the proportion Of mature cows in the herd which produce at near maximum capacity. Several studies have considered the relationship between early production Of a cow and length of time she stays in the herd. This relationship could influence evalua- tion Of lactation records both for sire proofs and culling females. In an analysis of production in 79 Holstein herds, Gaalaas and Plowman (1963) Obtained small but highly signifw icant regression and correlation coefficients of final age on first lactation. Van Vleck (1964) and White and Nichols (1965) agree with these data that high-producing first 1acta~ tion cows produced over a longer life. These results do not substantiate the claim that high producers in the first lac- tation burn themselves out. But if high producers do not burn out or become more susceptible to mastitis and other diseases, they would automatically live longer in the herd because they could survive more culling decisions at those higher productiOn levels. To Obtain a more direct answer to the relationship of economically important characters of longevity, Evans et a1. (1964) calculated the intra—sire phenotype correlation 22 between the first record 2X—305-M.E. milk production and length of productive life in days, actual lifetime milk pro— duction, and actual production per day of productive life as 0.217, 0.285, and 0.497 respectively. The present system now in use in Michigan DHIA reports only current lactations, thus a cow may be subject to culling on the basis of her present lactation. But in an analysis of New York DHIA herds, Van Vleck (1964) noted that the terminal records and to some extent the penultimate lactation records averaged considerably lower than previous records. If the causal factors are non-genetic, we should exclude such records when evaluating either sires or female relatives. If, on the other hand, these factors such as susceptibility to mastitis, feet and leg difficulties do have a genetic origin, we should include these records. Whenever the production ability and hence economic value of the individual cow is hindered by injuries, we can more easily validate our desire to cull on the basis of one lac- tation, especially if the injury or disease causes permanent damage. One would eXpect that, as animals grow older, cull- ing for genetic causes other than yield might become more important, but for yield, on the other hand, the separate culling processes all act on more or less the same genetic variance (Robertson, 1966). 23 Environmental influence Both heredity and environment affect milk and fat yield of dairy cattle but since environment causes a major portion Of variation among production records, the useful— ness of records from all cows for sire evaluation and selec- tion of cows within a herd depends in large part on the possibility of removing or adjusting these environmental effects. Pirchner and Lush (1959) using two methods, found environment to account for 90 and 93.5% reSpectively of the variation among Holstein herds. From A.I. sired Holstein cattle, Van Vleck et al. (1961) calculated the following components of variation in production records: herd, 30%; sire, 6-8%; interactions, 12-l4%; and residual, 50%. A number of eXperiments have been devised to deter- mine which environmental factors affect production measure- ments the most. Of 21 environmental influences tested in 47 herds, Bayley and Heizer (1952) selected nine as most important: number Of days carrying calf, length of preced— ing dry period, length of lactation, pounds of TDN fed per 1,000 pounds body weight, herd size, age at calving, and selection rating. Further, though body weight accounted for 11.9% of the variation, Lee et al. (1961) calculated three other environmental factors (breed, stage of gestation, and season Of calving) that had significant effects on FCM pro— duction. Moreover, Erb and Ashworth (1961) found the age of the cow affected FCM production twice as much as body weight 24 but the influence of weight was not significant if age and breed effects were removed. Deciding which cows to cull involves deciding what records to use and how to use them most efficiently to mea— sure the profit Or producing ability of each cow; thus we might decide on single records or multiples combined in various ways. Deaton and McGilliard (1964) indicated that the first record gives essentially as reliable an estimate of a cow's breeding value measured by the daughter's perfor— mance as does an apprOpriately weighted combination of multi- ple records. Results from analysis of Holstein records (Barr and Van Vleck, 1963) suggest "repeatability" in the range of 0.40 to 0.45 but first lactations were most unlike all others phenotypically and genetically. The degree Of accuracy of correction factors which standardize production records may in part rely on the bias due to interaction of the environment and the level of pro- duction. Lush and Shrode (1950) indicate that under prac- tical conditions, relationships between yield and age cannot be estimated without bias. Since culling removes lower pro- ducers at young ages, if only repeated records are used to derive correction factors, such factors overestimate the producing ability of very young cows. Hickman and Henderson (1955) derived a negative correlation between the level of first-lactation production and increase from first tosecond lactation (comparable to Hickman, 1962), which indicates an 25 interaction between level of herd production and relation- ship between yield and age. To compare accurately the milk records of different cows for culling purposes, we may want to consider the dif— ferences in reproductive performance affecting the respec- tive records. Investigations of such relationships should account for the influence of herd, year, season, age and length Of the previous dry period. Smith and Legates (1962) found intra-herd-year-season phenotypic correlations (0.05 to 0.08) between 90-day production and days open were not significant, suggesting level of production had very little influence on this measure Of fertility. Furthermore, length of the previous dry period accounted for less than 0.1% of the variation in 305—day milk production, while days Open during the lactation accounted for 6.6 and 4.2% of the variation in yield for first and all lactations respectively. Yet the ratios developed by Sargent et al. (1967) seem to justify a correction for fat percentage when incomplete records are extended. When we compare cows of varying lactation lengths for culling or ranking purposes, we may wish to consider the relative merits of the lactation lengths. Though Frieze and Corley (1962) stratified 81,226 Holstein records into five different duration groups up to 365 days, they noted no important trends in the distribution of length of lactation over three levels of 2X herds. Neither did significant 26 differences exist in the estimates of 305 vs 365-day records, but they did not study the difference in production between 305 and 365—day records per day of life or differences in long run economic return. Tucker and Legates (1965), from an analysis of Holstein HIR data consisting of 121,935 lactations, found a significant difference between the variance within the dif- ferent months Of the year, fall values being large. Simi— larly, from a study of 108,000 observations Of Canadian Holstein records, Gravir (1966) noted the effect of season of freshening (fall or Spring) has a marked effect on the yield-age relationship for animals of all ages irrespective of lactation number. Part lactations Because herdsmen must frequently decide which cows to cull before a cow completes her lactation, part records occupy an important position in dairy cattle selection--both for culling cows from the herd and for sire selection. Fur— thermore, since they will have cows in various stages of lactation, dairymen must know not only the relative accuracy of various parts of the lactation in predicting the whole but must know the most economical point in the lactation to cull both the voluntary and involuntary culls. Several workers have attacked various phases of this problem. To learn the extent to which farmers actually cull before the end of a lactation, Maxley (1966) sampled l8 27 Holstein herds which had been on test for ten years. Not only did these dairymen cull 67% of the cows before the end of their lactation, but of those culled after 10 months lac- tation, they sold 60% for dairy. Estimates in this study Of the genetic correlations between cumulative parts of the lac- tation for milk were essentially unity (Madden et al., 1955 obtained over 0.9). Consequently, selecting on the cumula- tive part record would improve production nearly as much as selecting on the complete record itself. When Van Vleck and Henderson (1961) compared regres- sion vs ratio factors to determine relationships of part lactation to the whole, they found six and seven cumulative months had a correlation with total yield of 0.93 and 0.95 respectively while corresponding multiple correlations were 0.94 and 0.96. The more practical way, eSpecially for cen- tral processing centers, is to extend cumulative monthly test—day records. Effect of body weight on selection The primary purpose of selection by dairymen should be to maximize the profit of their cows by methods which weigh the relative economic importance of all traits con- cerned. What role body size or weight plays in relation to milk production in such dairy cattle selection has been sub- ject to much controversy. Presumably milk represents income, a positive value, whereas body weight reflects maintenance 28 and should be charged against the cow. Despite this rela- tionship, dairymen generally discriminate against smaller animals which produce on a par with their larger herd mates. Further complications arise in assessing relationships of size to production because environmental conditions which are conducive to large size also contribute to higher milk production (Mason et al., 1957, Clark and Touchberry, 1962). Lush and Shrode (1950) state that presently used age correction factors tend to favor early-maturing individuals. Whereas McDaniel and Legates (1963) found a positive linear regression of milk yield on weight independent of age, results by Miller and McGilliard (1956) indicate influence of weight on production is largely the product of differ- ences among herds and that large heifers have little or no economic advantage in their first lactation if calving is delayed to obtain additional weight. Moreover, Clark and Touchberry (1962) noticed that increases in yield associated with increases in weight among cows of the same age and herd suggest heavier cows possess little if any superiority in production efficiency. On the other hand, when cows are culled on produc- tion regardless Of size, small cows which remain in a herd after culling produce more efficiently than large ones (Clark and Touchberry, 1962). Harville and Henderson (1966) indicated the assumed traits for which we select are breed- ing value for milk or milk fat production but that in prac- tice dairymen should be trying to breed cows which will 29 return maximum profit. A positive genetic correlation between body size and production means that selection for production will result in large cows with increased growth and maintenance costs. Though these authors found body weight a slightly more important source of the intraherd variation in actual first lactation, incorporation Of body weight into a selection index for predicting breeding value for Holstein milk production increased the accuracy less than 1%. Further, these authors believe if the economic value or lack of body size relative to economic value of milk production were known and included in an index, these overall indices should more efficiently estimate the breed- ing value for monetary profit. To compare two or more cows for selection purposes, a dairyman may need to adjust or correct for cows of differ- ent ages or weights to accurately estimate income over feed cost. From first lactation Holstein data, Clark and Touch~ berry (1962) indicated that for a constant age, milk produc- tion increased 134 lb and fat 7.8 lb for each 100 lb in— crease in body weight. Their comparable genetic correla- tions between body weight and production ranged from near zero in the first lactation to -0.53 in the second. McDaniel and Legates (1965) emphasize the relative values of body weight and production rather than their absolute values deserve importance in determining prOper selection emphasis to apply to each trait. For example, 30 if feed costs and milk prices were both low (hay @ $25/T; concentrate @ $56/T; milk @ $3.50/cwt) or both high, return over feed costs from about 225 1b Of milk would Offset the cost of 100 lb of maintenance for one year. Combining medium priced milk ($4.75/cwt) however, with high feed costs would raise the requirement to 300 lb of milk. Relationships of feed costs to profit If dairymen eXpect to cull their cows on the basis of income over feed costs, they must first accurately deter— mine feed consumption. Furthermore, the relationship between feed consumption, the input, and milk production, the output, must be known for varying levels and months of the lactation. Conversely, if the higher producing cows of a herd convert feed more efficiently than the lower yielding cows, we can select cows on the basis of milk production or gross income from milk. Attempts to measure the economics, relationships, and cause of variation between feed intake and milk output have been approached from several directions. Following pioneer methodological studies estimating milk production functions by Jensen et a1. (1942) and by Heady (1951), McDaniel et a1. (1961) indicated that the therms Of net energy consumed was the most important environmental factor of those studied influencing changes in production over a seven year period. Coffey and Toussaint (1963) compared net 31 returns over feed cost for "Optimum rations" with most profitable "stomach capacity rations" at several feed:milk price ratios. Their results suggest (1) there is a fairly wide range of feeding over which returns are not affected much, (2) hay-grain isoquants are essentially linear, (3) Optimum rations lie near the stomach—capacity limit for most prices of hay, grain and milk, and (4) significant differ— ences in returns exist between rations. Contrarily, Hoover et al. (1967) provide evidence indicating nonlinearity of the milk production function and decreasing marginal rates Of substitution of grain for hay. These researchers further stressed that the definition of 4% FCM as an energy transformation has no direct relation to the price of milk assumed in the analysis. From 1,014 herd-month observations, Matherne (1965) deve10ped a regression equation to estimate income over feed cost from independent variables: days in milk and therms ENE from each of concentrates, silage, hay and pasture. From another report, Green (1966) confirmed that the feeding program significantly affected the level of milk production and income over feed cost. He found the program that furnished the most energy per 100 lb body weight yielded most milk and income over feed cost whereas regression of income over feed cost was linear. Of the changes in income over feed cost, 45% were noted as levels of production increased. 32 Measurement Of feed intake of individual cows to compare income over feed cost is further complicated because cows vary widely in their appetite and consequently feed intake. Even after Johnson et a1. (1966) corrected for FCM yield, body weight, weight changes, grain intake, age, body condition, and stage of lactation or gestation, they could account for only about one—half of the variation in forage DM intake but stage Of lactation appeared the most important. Fixed costs The role of fixed costs in replacement theory has been approached from several points of view. In the long run, to progress financially in the business, dairymen must cover their fixed costs, though trouble arises when we attempt to correctly Specify all cost elements in a replace- ment problem. Since depreciation costs are that portion of orig- inal cost Of buildings and equipment charged to each year of use, total depreciation chargeable to the milking herd equals the sum of depreciation for all items used by the milking herd: buildings, milk house, feed storage and facilities, paving, milking machine and bulk tank (Schultis et al., 1963). If feed, however, is charged at farm cost, feed storage is not charged to the milking herd but to the crOpping enterprise. 33 As referred to previously, Burt (1965) Specified that the present value per cow investment in auxiliary cap- ital (housing and milking equipment) is added to the cost of the cow; hence, it is this total investment that must earn a rate of return as applied to the replacement decision. Chisholm (1966) asserts there is general agreement that fixed and variable costs which are actually incurred should be compounded at an appropriate interest rate to permit comm parison of costs and returns occurring at different points in time. Since sunk dollars establish no minimum marginal return that must be met other than salvage value, Breimyer (1966) emphasizes that when these fixed costs are disre- garded in making decisions as to variable inputs, a bias, usually upward, enters into the decisions on use of those inputs. EXP ER IMENTAL PROC EDURE General Procedure and Derivation of Parameters To study how various strategies of culling dairy cows affect such factors as income over feed cost and aver— age production per cow over time, it is first necessary to establish parameters of such a cattle population which con- form tO the variables under study. One possible method to examine these factors is Simulation. Not only will computer models allow us to look at the effect over an intermediate run of 2 to 3 years but also over the longer run of 10 to 20 years when future generations of those cows selected to remain in the herd come into production. In contrast to actual current production records, by Simulation procedure, we can fix certain variables not under study, while those variables subject to uncertainty we can vary randomly. Therefore, this study treated certain elements as stochastic while others were held constant. The stochastic factors were: (a) variation in milk production and milkfat percent— age between cows and between lactations of the same cow, (b) chance Of a calf being a heifer or bull, (c) chance of invol- untary death or removal Of cows and youngstock, and (d) chance of month of the year Of involuntary removal and death. 34 35 To prepare for the Simulation, the first procedure established parameters from known research in regard to such data as milk production and its variation, probability dis- tribution of involuntary culls, milk prices, and costs of feed and other inputs. After computing or deriving the parameters necessary for the study, a herd of 80 cows plus their OffSpring was generated by use of CDC 3600 computer. Their production and reproductive performance was then simulated over a period of 15 years. Strategies and prices studied Six different culling strategies were examined; that is, the cows were ranked yearly on each "extended" 305 day record according to a determined strategy which was constant throughout the 15 years of the trial. The bottom cows of the rank were then culled until the herd equalled approx— imately 80 cows at the end of each year. The following strategies or criteria for culling or ranking the cows were used: 1. Mature Equivalent (M.E.) milk (305 days). 2. Mature Equivalent gross income from milk. 3. Actual milk (305 days). 4. Actual gross milk sales (305 days). 5. Actual income over feed costs (365 days). 6. Present value Of eXpected gross income of cow and her subsequent replacements. 36 Under each strategy 24 = 16 different trials or com- binations of prices were employed with 2 replications per trial totaling 16 x 2 x 6 = 192 replications. The following prices used as parameters represent approximate low and high values respectively on Southern Michigan dairy farms in the 1960's: Low High a. Base milk price (cwt) $ 4.25 $ 5.25 b. Fat differential .07 .08 c. Price of feed (ton) Grain 60.00 70.00 Hay 20.00 25.00 Silage 7.00 8.00 d. Operational costs/cow/month 21.92 25.38 The price of milk in the above table represents approximate manufacturing and Class I price minus hauling charges respectively, whereas the fat differentials Of $0.07 and $0.08 for adjustment of price of milk per 0.1 change from 3.5 test represents two alternatives used in milk mar— kets in Michigan. The alternative feed prices Simply repre- sent a low and high for on—farm costs for Southern Michigan dairy farms. A cull price of $l6/cwt used throughout all replications approximates the average yearly prices received in southern Michigan country markets from 1958 through 1966. Though not charged against the cows per se, Operat- ing costs from the above table functioned as parameters to help determine the profitable point to cull a cow within her lactation. These Operational costs were calculated as fol— lows: From 266 "Southern Michigan Dairy farms" utilizing 37 the Telfarm record keeping system in 1966, 72 farms were selected which had 60 or more cows per herd. From a ranking of these farms on the basis of improvement investment per cow, the records of the top one—third (23) farms were clas— sified as "high" Operating costs while the records of the bottom third (23) represented "low." From an average of the 23 farms in each group the following costs were derived as a pro-rated share (in parenthesis) Of the entire farm business charged to the dairy herd (Hepp and Brown, 1967): Charge per cow per year L93 High 1. Power & machinery eXpense (30%) $ 33.86 $ 37.78 2. Improvement costs (80%) 30.41 44.63 3. Livestock eXpense (100%) 30.19 33.57 4. Utilities (90%) 9.20 11.49 5. Taxes (31.24% & 36.19%) 5.11 7.20 6. Interest paid (31.24% & 36.19%) 10.93 15.86 7. Interest on owned invest- ment (31.24% & 36.19%) 21.11 31.87 8. Other eXpenseS (30%) 1.37 1.35 Total $142.18 $183.75 Charge per cow per month $ 11.85 $ 15.31 Labor @ $1.50/hr, 70 hr per cow per year 8.75 8.75 Interest on salvage value 1.32 1.32 Total operational costs/month $ 21.92 $ 25.38 38 It is not surprising these Operational costs of $21.92 and $25.38 should fall in the range of the $22.21 per month Opportunity cost from the example of Giaever (1966) in determining the point to cull within the lactation. To com- pute the above interest charges allocatable to the cow herd the following figures are relevant: Leaflet Improvement invest./cow (80%) $ 322 $ 568 Machinery invest./cow (30%) 272 360 Livestock invest./cow (100%) 373 373 Total farm invest./cow $2282 $4285 i.e., (0.80 x 322 + 0.30 x 272 + 373)/2282 = 31.24%. Hence, taxes and interest were allocated from the sum of the live- stock investment, 30% of the machinery investment and 80% of the improvement investment as a proportion of the total farm investment or 31.24% for the low and 36.19% for the high farms. Feed consumption Profitable Operation of a dairy herd involves both the income and costs of each cow in the herd as well as overhead costs charged to the dairy herd. To determine which cows in the herd return the most profit and which a dairyman should cull then becomes a matter of determining which incomes and which costs vary between cows. Of the several incomes, milk sales vary the most between cows, while potential sale as dairy or salvage ranks a poor second. 39 Conversely, by far the greatest difference in costs between cows is in their feed intake. This difference results largely from such variables as milk production, body size, stage of lactation, age, and individual appetite. But under farm conditions, the individual dairyman has no practical method to measure the appetite differences between cows; consequently he must rely on the other variables mentioned to help determine differences in feed consumption. For this Simulation program, the higher requirements for Total Digestible Nutrients (TDN) established by Morrison (1959) according to body weight, milk production, pregnancy, and growth were the criteria for feed consumption and requirements. TDN requirements per pound of milk below thef 3.0% test listed by Morrison were linearly extrapolated down to 2.0% test. An additional 15% was charged for waste due to refusal by the cow, shrinkage, rodents and Spillage. Accordingly, such waste was charged on a prorated basis because these are the actual costs incurred for the feed. All cows in milk were fed 40 1b corn silage per day, grain was fed 1 lb per 3 lb milk, and the balance alfalfa hay to meet TDN requirements. The limiting factor at all levels Of production for all ages except 2 and 3 year Old cows was TDN. To preserve model simplicity, additional hay was fed to these animals at certain levels of milk produc- tion to meet protein requirements. These added amounts are given in Appendix Table 5. Grain was assumed to contain 12% 4O digestible protein (D.P.) and 75% TDN; alfalfa hay 10.9% D.P. and 50.7% TDN; corn silage 1.3% D.P. and 19.8% TDN. For the 10 month lactation for cows which remained in the herd, feed requirements simply equaled 305 times the daily requirement. During the 60 day dry period cows consumed 40 lb Silage per day plus enough hay to meet TDN require- ments (see Appendix Table 4). Generation and use of random numbers Sequences of numbers generated by an arithmetical process in a computer can be used as random numbers for simulation problems. Though they fulfill many criteria for randomness, such numbers are often called pseudorandom Since they are generated by a deterministic process and hence are not actually random. The computer system available for this study, the CONTROL DATA 3600 located at Michigan State Uni- versity, is a general purpose digital computing system with large storage capacity. A library program, RANF, which generates a sequence of over 68 billion numbers before re- peating, was available for generation of these uniformly distributed pseudo-random numbers. To avoid separate trials on runs of this simulation program from starting at the same point in the sequence, RANFSET(TIMEF) was called which started the sequence according to the time on the com- puter clock. All random numbers called in floating point consequently lie 0< ri mean 6, variance 1.0 and (E5 uniform) - 6.0 pro- vided N(0,l) random deviates. Subsequently, several samples of random deviates were generated which conformed closely to the standard normal distribution. Random numbers again were used to determine the involuntary culls and deaths. A random number was multi- plied by 100, producing a number in the range of 0 to 99.999, which by the addition of 1 yielded a number in the range of l to 100.999. This number was then truncated to integer value resulting in a number which has the range of l to 100. Such a number was drawn each year for each animal. With cows 5 years Of age or Older, for instance, a "l" signified 42 death, while a number ranging from 2 to 15 inclusive signi- fied an involuntary cull. The chance of culls by age were as follows: Chance of Chance of Agg death involuntary cull 5 .01 .14 3 & 4 .01 .08 2 .01 .05 yearlings .17 ... calves .17 ... This simulation program maintained distinction between death and involuntary culls in the milking herd in order to credit the culls with a salvage value but since the yearlings and calves did not enter into a return or cost, all deaths and culls for these animals for all causes includ- ing stillborn calves and sterility Of yearlings were treated as death or Simply elimination from the herd. The above probabilities of death and involuntary culls for milking cows were computed from data derived by Dayton (1966) from 30,308 complete Holstein records made from 1957 to 1962 of A.I. OffSpring in Michigan DHIA. Involuntary culls are here defined as cows removed for all reasons except dairy and low production. Probability of calf and yearling losses, on the other hand, approximate the distribution of such losses of simulated herds in the undergraduate breeding course described by Everett (1966). The chance of a cow having a calf of a given sex was also considered a stochastic variable so it too was determined 43 by random numbers. Since the distribution of the random numbers has a mean of 0.5, by adding 1.5 to a random number then truncating to an integer value, either a "l" or "2" is obtained at random. Thus arbitrarily, a "l" designated a heifer while a "2" designated a bull calf resulting in a probability Of 0.5 or a calf being a heifer. Probability Of a cow dying in any given month of the year once she drew a "l" signifying death was assumed to be 1/12. Similarly, but contrary to intuitive eXpectation, the probability of an involuntary cull in any given month of the lactation or dry period was also considered 1/12 once the random process has determined a cow as an involuntary cull (Aulerich, 1966). Therefore, since the specific month of removal is a stochastic process, this event was Similarly determined by the random number generator. Age correction factors For simplicity of design and to eliminate any weight- age interaction, all cows of a given age were assumed to weigh the same. From the regression equation deve10ped by McDaniel and Legates (1965) from heart girth measurements of 1595 Holsteins, the respective weights were determined by the equation: /\ Y = 757 + 20.91M - 0.2036M2 + 0.00066M3 /\ where Y'is the predicted body weight and M is age in months. The resulting weights by ages are listed in Appendix Table 3 and refer to age at freshening. Such body weights helped determine both feed consumption and salvage value. The basic program in simulation of the base herd and subsequently the Offspring called for generation Of the mature equivalent (M.E.) milk production. Therefore, to convert the M.E. to actual milk production for certain cull— ing strategies and to determine actual milk income, correc- tion factors are needed. In such a reverse process, the reciprocal Of the standard USDA age correction factors were utilized (McDaniel et al., 1967). Since the model implied no seasonal effect, a weighted average of two seasons based on the number of cows used to determine the regional (includ- ing Michigan) Holstein age correlation factors were used. Resulting correction factors and their reciprocal are listed in Appendix Table 1. Similarly, under the assumptions of the model, the 305 day complete records were simulated for each cow. In reality, 305 day records can be predicted from the extension of partial records with a reasonable degree of accuracy. Madden et al. (1959) obtained correlations of 0.90 and 0.95 between 3 and 4 months cumulative records reSpectively and 305 days production of cows under 3 years and 0.85 and 0.90 for the corresponding figures of cows over 3 years Old, (Similar to Van Vleck and Henderson, 1961, and Van Vleck, 1964). But since the potential 305 day record of each cow served as the base, it was necessary to compute a partial 45 record from the whole by the reciprocal of the extension factor to determine any incomplete actual milk production records of involuntary culls and to help determine the most profitable month to remove the voluntary culls. For sake of simplicity, the model assumed identical lactation curves for any given 305 day milk production record. Though this method (rather than generating each month's production independently) introduces some error in monthly variation of the lactation curve, little error will be implied in the mean of the lacta- tion curve for a given 305 day production. The reciprocal correction factors carried to the nearest 4 places employed to estimate these partial records were derived from data Of 15,330 Michigan Holstein records < 36 months Old and 32,986 Z_36 months Old (Aulerich, 1966) using the weighted average according to numbers of cows in each of the two seasons and divided into their respective age groups. These correction factors are listed in Appendix Table 2. Present value strategy The sixth strategy examined, based on the present discounted value Of eXpected gross income of a cow and her subsequent replacements, employed a simple set of correction or adjustment factors according to the age of the cows. That is, to rank a herd Of cows and adjust for the different ages, You mulitply each cow's current gross milk income by 46 the apprOpriate correction factor. Such a procedure is based on the principle that a sum of money at present is worth more than the same sum in the future (Giaever, 1966; Faris, 1960). This discounting furnishes a method of trans- ferring a stream of future income to a single number called the "present value" of the future stream. From this approach each cow and her subsequent replacements can be thought of as a stanchion or space in the herd. Thus, with a 15 year planning horizon, the income stream develops from the eXpected relative production of each cow until the year Of her eXpected involuntary loss or death plus the eXpected production of her future replacements over their lifetime. TO determine these corrections factors, a two dimen- sional array was made of each age group (2, 3, ... 12) times the 15 year planning horizon. By the standard M.E. age cor- rection factors for milk production used by DHIA, the rela- tive expected production for each year was listed; for example, for a 2 year Old with a relative value of 1.0, her 7 year Old value, 5 years hence, would simply equal the cor- rection factor of 1.28 times 1.0 or 1.28 while, say her expected 5 year Old production would equal the reciprocal age correction factor (0.971) times 1.28. The potential length of life for each cow was deter- mined from Pearl's formula (1930) for life eXpectancy, in this case, based on the rate of involuntary culls used in this study: 47 e = 1/2 1X + lx+l + 1X+2 ... X 1 x where lx is the number of cows living in year x, lx+l the number living in year x + 1 etc. The resulting life eXpec— tancies were truncated to the nearest one—half year result- ing in the following eXpectations: Agg Life Expectancy 2 7.0 years 3 6.5 years 4 6.0 years 5-8 5.5 years 9-12 5.0 years Two year olds coming into the array in the second and following generations were given a genetic value equal to a 2% gain per year from the genetic value of the cow she is replacing, hence assuming that each year's crop of heifers will produce 2% above the previous year's crOp. For discounting calculations, the year's values following on the half year basis were pro-rated according to the respective values in the cells. The final year that each animal was eXpected to produce, a relative salvage value Of 0.5 was added to the milk value. This procedure assumes that the salvage income will approximate one-half of the income over feed cost for that year. Each cell was then divided by its reSpective discount rate which was as follows: lzggg Discount 2 1.03 3-15 (1.03)(l.06)n_2 48 where p_= year and the first year was considered the year of production to be compared and the second year the first year of future income. A discount rate of 3%.was used the second year on the assumption that milk checks would be received monthly SO a monthly discount rate is effective. Then the respective discounted values were added to obtain the total present value and subsequently reduced to a value of 1.00 assigned to the present value of the 7 year old cow. By multiplying these adjustment values times the corresponding gross income values, the prOper weight should be given each animal relative to her present value and all her subsequent replacements in a 15 year planning horizon. Such a planning horizon was simply truncated at the end of 15 years but this does not imply the herd would be sold at that time. By relating to gross milk income rather than milk production, allowances are made for the relative eco- nomic value of milk and fat. These correction or adjustment factors were then adjusted 10% Of the difference between this new value toward the standard M.E. milk age correction factors to allow for a discounted genetic value Of the Offspring of these reSpective cows on the assumption that half of the calves will be heifers and that heritability is about 25% and therefore only 12.5%.of the transmitting ability of a cow can be realized and roughly some Of this will be discounted, SO an approximate value of 10% of the transmitting ability can be 49 allowed toward the discounted producing ability of the animal in question. The resulting adjustment factors and their method of derivation are unique but the component parts consist simply of the concepts of milk production converted to income, standard age correction factors, life eXpectancy, eXpected genetic progress and standard discounting principles. These factors are as follows: Agg_ P.V. Factor Ag§_ P.V. Factor 2 1.201 8 1.004 3 1.127 9 1.030 4 1.056 10 1.052 5 1.016 11 1.066 6 1.004 12 1.115 7 1.000 General assumptions For simplicity, since computer time and storage capacity are finite, and to determine relevant effects of the given strategies and prices, certain variables were held constant. Accordingly, several assumptions in addition to those eXplained elsewhere are in order: 1. All cows freshen on September 1 and milk for 10 months unless removed by death, involuntary cull or voluntary cull; calendar year in turn commences September 1. 2. All heifers freshen at 2 years of age and if they remain in the herd maintain a calving interval of 12 months. 50 All cows of a given weight and milk production will eat the same amount of feed. All deaths, involuntary and voluntary culls take place at the end of the month, where respective months are determined by methods described above. Cows are ranked once per year on their "potential" 305 day record but this does not imply cows Should be ranked only once per year nor simply that they are ranked at the end of their lactation. A dairy cow's 305 day record can be accurately estimated from a 3 or 4 month part record (Madden et al., 1959). Time of paying for feed and time for receiving milk income were assumed identical in that there is no difference in discounting the two accounts; in fact, within a given year, no discounting of feed or milk is assumed when computing income over feed cost; but of course over the 15 year period average income (including salvage) over feed cost per cow is dis— counted by the respective years to equate all trials to a common present value. All replacements are raised, and it is assumed the dairyman has no restrictions on capital, labor or building to raise the replacements. 51 Determination of When to Cull Within a Lactation After he has determined which cows Of his herd to cull, the next major decision facing the dairyman is to decide the most profitable point within the lactation to cull these cows. This point will depend on the value of cull beef and value of milk and the costs of production including feed, labor, livestock eXpense and interest on investment. These in turn are dependent on the weight of the cow, her level of milk production within the lactation, and related prices. At most levels Of production and prices, it will not pay to keep a potential cull until she is dry or due to dry up. By that time, if she is within 60 days of calving, in order to capitalize on her peak producing period in the fol- lowing lactation, it would pay to keep her until she freshens again. More importantly, a cow nearly dry is losing money for her owner, for under most conditions, She is not paying for her feed, labor and fixed costs. In fact, carrying a potential cull beyond the point where MC = MR will reduce the average net revenue for the herd. If a dairy herd is to profit in the long run, each cow must pay her share Of not only her variable costs but her fixed costs. It can be argued that the proportional share of both interest paid and interest on investment allocated to the milking herd must somehow arise from the 52 milking herd, each cow to pay her share if possible. Of course, a dairyman has no direct control over death losses and certain involuntary losses in regard to paying these interest costs. Though this simulation program specified involuntary losses occurred randomly as to month of lacta- tion, it is conceivable that under actual conditions, a farmer could Sell shy breeders at the most profitable time within their lactation. Thus, to determine the most profitable point to cull within a lactation, a cow must cover her share of feed costs, the interest and taxes mentioned above, labor,and interest on salvage value, plus other eXpenseS Of livestock, machinery, and building allocated to the milking herd (consistent with fixed cost allocation prOposed by Chisholm, 1966; Burt, 1965; and Breimyer, 1966). Since all cows milked for 10 months in this simula- tion program, it was necessary to consider the possibility that potential cull cows from high level herds may still return a profit in their 10th month. This is especially probable when high milk prices fuse with low feed and Opera- tional costs. From the potential 305 day actual production, where months of a lactation were defined as 30.5 days, the simulation model computed milk production and milk Sales for the 10th month then compared these sales with the sum of the feed costs plus Operational costs. Feed costs for the 10th month were Similar to the other 9 months except that 53 allowances of the 10th month were increased for pregnancy. Grain was fed according to production, 1 lb grain:3 lb milk; silage 40 lb per day; and enough alfalfa hay to meet TDN and protein requirements. If milk sales of the cow to be culled exceeded feed costs plus operational costs, She was culled at the end of the 10th month; if not, the potential milk sales allocated to the 9th month were compared to the potential feed costs of this month. Likewise, if the milk sales were greater than these two items, the cow was culled at the end of the 9th month. The program then computed total milk sales, total feed costs and salvage value and added this to the respective herd totals according to the month she left the herd. The Operational costs were not charged to the cows as such in this program, but used only as a parameter to help determine the most profitable point within the lactation to remove each voluntary cull. If the milk sales for the 9th month were less than the feed costs plus Operational costs, the computer program compared the 8th and earlier months in sequence in a Similar manner, all cows being culled at the end of the month. Such a procedure can be applied to actual dairy herd conditions under the assumption that one can predict the whole lacta- tion or any of its reSpective parts from 90 or 120 days production. Under the conditions of constant milk prices and feed and Operational costs in this simulation program, 54 the actual point Of breaking even for profit or month in this case, can be determined with more accuracy. Generation of Base Herd and Succeeding Generations Base herd Forming Of a base dairy herd or genetic system for simulation procedure involves the establishment Of certain parameters or characteristics needed to identify the herd. Such procedures have been demonstrated by Heidhues and Henderson (1961) and Everett et al. (1967). In this case variance for both milk and fat percentage and their correla- tion were chosen as the relevant characteristics. The vari— ances of milk production used to generate the base herd were obtained from the same bases used in an undergraduate dairy cattle breeding course at Michigan State University which represented the approximate variation found in the Holstein pOpulation of Michigan (Everett, 1966; Everett et al., 1967). Since the present study involved a single herd under constant yearly herd environment, the variances between herd and between year were eliminated, but the residual or tempor— ary environmental variance representing variation between lactations of the same cow was retained. The genetic and permanent environment on the other hand were constant throughout each cow's life, which automatically accounts for some, if not all the repeatibility of milk production. 55 Therefore, the following variance components for milk were used: Milk Variance Std. Dev. Total (lb) 4,100,000 ... Genetic 1,210,000 1100 Permanent envir. 640,000 800 Residual (temp. envir.) 2,250,000 1500 The fat percentages and correlations of milk with fat percent were taken from data by Butcher et al. (1967) from records Of Holstein cows in the North Carolina Institu- tional Breeding Association and are as follows: Fat pgrcentage Variance Total .0862 Genetic .0537 Environmental .0325 From a genetic correlation of -0.61 i 0.13 and an environmental correlation of 0.16 between milk and fat per— cent (Butcher et al., 1967), the reSpective genetic and environmental coefficients were derived using 14,000 lb milk, 3.63% test as approximate Michigan DHIA Holstein M.E. average. Mature Equivalent milk production of base pOpula- tion then equals: = . . + .. YMij Pm + g1 + p1 r13 14,000 + 91 Dev.(llOO) + g Dev.(800) + 5 Dev. (1500) where j in this case is the base year or lactation YM is the jth M.E. milk record of ith cow, ij r.. 13 is is is is of the the the the jth 56 pOpulation mean for milk (M.E.) additive genetic effect of ith cow, permanent environmental effect Of ith cow, residual or temporary environmental effect record of ith cow. Fat percentage of base pOpulation equals: Yr. 13 where e.. l] _ t — Pt + bl(pm + gi) + gi + b2(rij) + e. 3.63 13' = 0'00013(Pm + gi) + N Dev.(0.18) + 0.000017(rij) + N_Dev.(0.18) is the 1th test of the ith cow, is the pOpulation mean test, is regression coefficient for correlation of test with genetic milk, is genetic chance effect of test Of ith cow, is regression coefficient for correlation of temporary environmental portion of test with residual (temporary envir.) portion of milk, is environmental chance effect of test of jth record of ith cow. That portion of the variation in test associated with perma- nent environment was only 0.01 so was considered as zero. Though none of the culling strategies was based on the "true" genetic value of each cow, this value was pre- served internally in the computer so that at any given year 57 or generation, the true genetic value of each animal living in the herd could be examined. To assess more accurately the effect Of the culling strategies on a female pOpulation under the fixed prices, the breeding value of the Sires were assumed equal and held constant over all strategies and prices for any given year. From a breeding value of 15,000 lb milk for the base year, the sire value advanced 130 lb of milk each year; thus the calves born in year two were sired by bulls with the 15,000 lb breeding value. This procedure was identical for all trials, that is, all strategies and prices. This genetic value and gain per year was assumed to represent the rela— tive value Of the best Holstein bulls used in A.I. studs. Likewise, the breeding value Of sire fat test was started at the base year at 3.63 - 0.00013(1000) = 3.5% and was de- creased each year by 0.00013(l30) or the identical regres- sion coefficient used in the cow population, thus consistent with the negative correlation of milk and fat test. Second and following generations The genetic ability of an offspring results from averaging the genetic ability of both parents and adding a chance deviate. Mendelian segregation in the parents fol- lowed by recombination in the zygote results in half of the additive genetic variation in an Offspring accounted for by the parents and half being random. This random part has a 58 standard deviation of approximately 800, therefore the vari- ation due to chance is added to the genetic ability of each individual by multiplying a random normal deviate by 800. Specifically, the milk production of the second and following generations were derived as follows: YM.. = 1/2 vm + 1/2 Vm + gdi + pi + rij 13 s d = 1/2 Vm + 1/2 vm + 3 Dev. (800) + 3 Dev. (800) s d + 5 Dev. (1500) where YM is jth M.E. milk record Of ith cow, V is breeding value of sire for milk, V is breeding value Of dam for milk, gd. is genetic chance effect of milk of ith cow, pi is permanent environment effect of milk for ith cow, rij is residual effect of 1th record of ith cow. The first three terms of the above equation define the genetic ability and the first four the producing ability of the animal in question. Thus the genetic and permanent environment effect are determined at birth and the residual determined independently for each lactation. The fat percentage Of the Second and following gener- ations were derived as follows: 59 YTij = 1/2 Vts + 1/2 th + bl(gdi) + gti + b2(rij) + eij 1/2 V t + 1/2 V - 0.00013(gdi) + g Dev.(0.129) S td + 0.000017(rij) + p Dev.(0.18) where Y is the 1th fat test Of the ith cow, V is breeding value of sire for test, V is breeding value Of dam for test, b is regression coefficient for regression of test on genetic chance Of milk, is remaining genetic chance effect Of test of ith cow, b is regression coefficient for correlation Of tempo- rary environmental portion of test with residual (temporary environmental) portion of milk, i' is environmental chance effect of test of jth record 3 of ith cow. For model simplicity, fat test did not vary by stage of lac- tation. The regression coefficients used in the above equa- tions were determined as follows from correlations derived by Butcher et al. (1967). For the base population the compo- nents Of variance of fat test of a single record were postu- lated to be: 2_ 2 2 0't ‘Ugt+0et or total test variance = genetic variance of test + environmen- tal variance of test 60 where 0.0862 = 0.0537 + CTZt therefore: (j-gt = 0.0862 — 0.0537 = 0.0325 and bl = correlation of genetic test with genetic mllk (Ugt/ 09,“) = -0.61( Jb.0537/1,210,000) = -0.00013 and b2 = correlation of environmental test with environmental milk ( O-et/ Gem) = 0.l6(\/0.325/2,890,000) 0.000017 The genetic portion of the variance of test can be further divided into a portion correlated with the genetic milk and a portion due to genetic chance. Thus: 2 _ 2 2 where 0.0537 = (-0.00013)2(1,210,000) +crgt. therefore: crgt, 0.0341 cr t' \/0.0341 = 0.18 9 Likewise, the environmental portion of test can be further divided into a portion correlated with permanent environment effect of milk, a portion correlated with the residual or temporary environmental portion of milk plus a random envi- ronmental effect. Thus: 61 2 _ 2 2 2 Get—Iboem+0et where 0.0325 (0.000017)2(2,890,000) +cr:t. therefore: CTZ 0.0316 et' (jét, — \/0.03l6 = 0.18. For the second and following generations, the addi- tional coefficients and multipliers for test were deriVed as follows from correlations of Butcher et al. (1967): 2 _ 2 2 2 (Tgt - 1/405 + 1/40d + V209,. 2 2 _ _ 2 2 therefore. CTgt' l/ZCTgt bl(l/2CTgm) 1/2(0.054) - (—0.00013)2(605.000) 0.0166 C12 «0.0166 = 0.129. Culling Procedure First_year The basic procedure in any simulation process involv- ing generation and projection of events over time must start with a given population, herd, firm, or the unit on which you base the simulation. Therefore, to generate an 80 cow dairy herd and accompanying young stock with known mean and variance of milk production involves the use of the random number generator as described previously. The base herd was composed of the following age distribution: 62 Age No. of animals 6 8 5 10 4 l6 3 22 2 24 l 26 calves 38 Total 144 In the first or base year, after the computer pro- gram generated the M.E. milk production and test for each of the cows in milk along with the genetic and permanent envi- ronment milk production potential Of the young stock, the number and identity Of deaths and involuntary culls and their month of removal were derived from the random number process described above; however, no cows were culled volun- tarily the first year. Then the actual 305-day milk produc- tion of each cow was computed by the reciprocal factor times the generated M.E. milk production. Milk sales for each cow were then determined according to the given price Of milk, fat differential and reSpective test Of each cow where the fat differential was added or subtracted for each tenth point in test‘: 3.5%. If the simulation program removed a cow involun- tarily before she completed her lactation (one of first 9 months), her milk production and milk sales were adjusted according to the proper ratio factor to convert whole lac— tations to their respective cumulative parts. 63 Feed costs were then computed for each cow according to her body weight and milk production. The 11th and 12th month consisting of 30 days each were considered as dry months where feed consumption was 40 lb silage per day plus enough hay to meet TDN requirements for maintenance and pregnancy according to Morrison's (1959) higher standards. For cows which died or were sold before the end of the 11th month, feed costs were reduced proportionately. Likewise, if a cow was sold in the 12th month She was charged a full year's feed costs. Yearly herd totals of actual milk production, feed costs, income over feed costs, number Of culls, etc. were then recorded for the milking herd and average per cow com- puted where average number of cows equals total cow months divided by 12. Second and following years To start the second year of the simulated herd, the age Of each animal advanced one year and her weight advanced according to her respective age. Since all cows were assumed to begin their lactation on the first of the year, all calves were born at that time. To generate the Off- Spring Of each cow and determine its sex, the random number generator was again utilized as described previously. If a bull calf was born, it simply was ignored Since their rec— ords were not utilized for any purpose. AS the heifers were 64 born, their genetic and permanent environment portion of their potential milk production which then equals their "producing ability" plus their genetic portion of milk test was generated as described in the previous section. For the milk cows, their "potential" M.E. milk pro— duction was generated each lactation by: (M.E. milk)i = (producing ability)i + N Dev.(1500) where the last term is the residual (Ri) or temporary envi- ronment effect, yet "producing ability" of ith cow generated at birth is constant throughout her life. Thus, the model generated a new temporary environment each lactation for each cow where the normal deviate (N_Dev.) N(0,1) created from the random number generator is unique for each lacta- tion of each cow. Each cow's test was determined by: (Test)i = (genetic test)i + 0.000017(Ri) + N Dev.(0.18) where the second term of the above equation is the correlation of residual milk production of ith cow with test and the last term a chance portion Of the environmental test (0.18 is the standard deviation of the environmental test). Again, N Dev. is unique for each lactation Of each cow and is distinct from the N Dev. in the milk equation. The next step was to "estimate" the number of invol- untary culls among the milking cows. This was assumed tO be consistent with reality in that from past experience, a dairyman can estimate the number of involuntary culls with 65 some intuitive probability distribution. For this problem in year 2, the estimated number was set at 8% of the herd but for the remaining years estimated number equaled average number of involuntary culls of past 2 years. The number Of cows available then for voluntary culls equals: (number Of cows in the herd) minus (estimate of involuntary culls) minus 80. This definition assumes a dairyman would have a chance to milk all his two year olds at least two to three months before he determined which of his cows to cull voluntarily and thus would at some times of the year have flexibility to maintain some cow number above the basic herd size of 80. From a total Of say, 95 cows that have been in the herd at one time during a twelve month period, not all cows will be in the herd at any given time. For this simulated herd, however, for model simplicity, all cows which are ever in the herd during the year will produce milk at least the first month of the lactation year. After determining how many cows to cull, the com- puter ranked the cows from high to low based on the current year's records according to one of the Six culling strategies, while each respective strategy was constant for any given run of 14 years beyond the base year. Then the number of volun- tary culls Specified were culled from the bottom of this rank. Based on the principle of marginal returns where each month's income and eXpenses are considered as the marginal increments, the actual month to remove the voluntary culls 66 was determined by the point which would yield the highest total net income over feed and Operating costs for the lac- tation, as eXplained previously on page 52. The true number of involuntary culls and their month of removal was then determined by the random number gener- ator so that at the end Of the year, there Should remain approximately 80 milk cows. It is logical this step should succeed ranking, since when a dairyman ranks his cows he does not know exactly which potential voluntary culls or which potential survivors he may cull fOr involuntary rea— sons. For instance, from an extension of a three month record, a cow a farmer plans to cull for low production in the seventh month Of her lactation, he possibly may cull for disease in the fifth month. For this simulation problem, if a cow pegged to be a voluntary cull was also drawn to be culled involuntarily, her month of involuntary cull was then drawn randomly in the usual procedure and she was subse- quently culled on the first of the two Specified months. From the voluntary and involuntary culls, the milk production, sales and feed costs were computed according to month of removal. Then total herd production, milk and salvage sales, feed costs and income over feed costs for all cows were summarized and average per cow computed for the year. For the third and succeeding years up to 15 years of simulation, the procedure was identical with that of the 67 second year; that is, the animals were advanced one year in age, a new cr0p of calves was generated, M.E. milk produc- tion generated, actual milk and income over feed cost com- puted, then voluntary and involuntary culls determined and yearly income and costs summarized. For each set of fixed prices and strategy, two replications were run; that is, for each replication, a new base herd was generated but with the same mean and variance of milk production and fat test. Likewise, for each new strategy or new set of prices, a new base herd was generated and simulated over the 15 year horizon. Comparison of Strategies Multiperiod production, or production over a period of years, i.e., 15, is characterized by factors Of produc- tion employed during one time period which influence levels of output during subsequent time periods. Specifically, different culling strategies may have diverse effects on income at various points in time. It is further assumed that there exists a market for money at which money can be borrowed or lent at a given rate of interest. By using this compounded rate of interest, not only can outlays or income incurred during different time periods be made comparable by discounting them to one and the same time period, but for this problem, such a procedure can reduce each strategy to a 68 single value relative to its future income stream discounted to the present. Therefore, the basic criterion used to compare each strategy under all combinations of prices was the "present values of income over feed cost per cow over the 15 year horizon." This total figure was then averaged by Hutton's (1966) method to obtain a more conceptual figure. Thus: 15 Present value of income I/FCi + Salvi over feed cost per cow = i-l 15 i=1 (l.03)(1.06) where I/FCi = income over feed cost per cow for year i. Analytical Design and Methods To compare the effects of the six strategies and the effect of various levels Of fixed prices upon the results generated by the simulation program, a 6 x 25 complete fac- torial design as described by Steel and Torrie (1960) was utilized. Six strategies times two levels of each of four prices times two replications each yielded 192 replications. Logical mutually orthogonal contrasts were predetermined before the data were generated to compare the strategies under various categories. Since the major criterion Of com- parison was income over feed cost, the culling strategy based on income over feed cost was compared with the average of the other five; present value, because it was unique, was 69 compared against the average Of strategies 1 to 4; the aver- age Of 1 and 2, the M.E. strategies was compared against strategies 3 and 4, those based on actual milk and gross income. The remaining contrasts compared 1 vs 2 and 3 vs 4, or milk compared to gross income within each group. If there were no significant interactions between strategies and prices, if there was significant differences between strategies, and if orthogonal contrasts were not utilized, Duncan's new multiple range test described by Steel and Torrie (1960) was used to test for Significant differences between all combinations of the ranked values. If interactions existed, we can assume the impor- tance Of each strategy or price is affected by the partic- ular combinations of prices in effect in those replications. On all values but the discounted income over feed cost including salvage, a simple average Of the 15 years was used as the basis to test for Significant difference among strat- egies and prices for: income over feed cost without salvage, gross income, milk production, fat production, genetic milk value, herd size, average month of culling, and culling rate. Computer time for the main program or simulation of the data was approximately one minute per replication or 192 minutes. RESULTS AND DISCUSSION Comparison of Strategies The present value Of income over feed cost per cow averaged over the 15 year horizon, used as the major crite- rion to compare strategies, showed no significant differ- ences between the six culling strategies examined. From Table l, the overall mean was $295.85 while the mean value for culling strategies based on M.E. milk, M.E. gross income, actual milk, actual gross income, income over feed cost, and present value was $295.68, $296.70, $294.91, $296.21, $295.72, and $295.87 respectively. TABLE 1. Present value of income over feed cost (including salvage) Present value Of income Strategy over feed costa l. M.E. milk $295.68 2. M.E. gross income 296.70 3. Actual milk 294.91 4. Actual gross income 0 296.21 5. Income over feed cost 295.72 6. Present value 295.87 Overall Mean $295.85 aNo significant difference between strategies. 70 71 From this data, we can surmize that the choice of one of these strategies by a dairyman is not critical in the generation of income. Results from the 6 x 25 complete fac- torial design related to the above income values showed no Significant interaction between strategies and levels of prices used in this study. Consequently, a change in prices does not indicate a change in strategy to maximize income over feed cost. This income was affected by the levels of milk price, feed cost, and Operational cost (P .01). Values with the same superscript indicate no Sig- b 74 425 400 375 350 325 425 400 " 375 I- 350 J l I I ll L l l 1 A 2 3 4 5 6 7 8 9 10 ll 12 l3 l4 Strategy — M.E. Milk "-" Act. Mi'k a l l l l 1 1 l 3 4 5 6 7 8 9.10 H l2 l3 14 Years Fig. 1.1 Average income over feed cost oer cow. Strategy — Act. Gross —-- Income/EC. ---- Pres. Value I A Years Fig. 1.2 Average Income over feed cost per cow. 15 75 Secondly, thOugh the genetic milk value may be highest at the end of 15 years when culling on M.E. milk as demonstrated in Table 4 and Figures 2.1 and 2.2, the profit may be little different than that realized by culling on actual milk, actual gross, or actual income over feed cost. Even in the 15th year when the difference in genetic value was the greatest, the differences in returns over feed cost were minor, due in part to the presence of young animals in the herd which did not produce at their mature value. Thirdly, strategies which rank higher in milk pro- duction also tend to rank lower in fat and vice versa. Average fat production per cow listed by years and strat- egies in Table 5 was different (P<:.01) among strategies though the magnitude of the differences are not great. The strategy with the highest fat production was actual gross with 505.6 lb while the lowest was with M.E. milk at 500.8 lb. Fourthly, the time Of culling within the lactation is Similar among strategies, which subsequently affects total herd production. An example may show why we obtain similar milk production and income over feed cost under the two culling strategies Of either M.E. milk or actual milk. If we compare the records of two cows, one a three year old, the other seven years Old, and the consequences of culling one of them under the two strategies, we can see how the advantages of each strategy balance each other.. From Table 6 76 TABLE 4. Average genetic milk value per cow (lb)d Strategies Actual M.E. M.E. Actual Actual Inc. OVer Present Year Milk Gross Milk Gross Feed Cost Value 1 13,988 14,029 14,028 13,991 13,985 14,000 2 14,075 14,087 14,099 14,066 14,025 14,069 3 14,199 14,192 14,197 14,148 14,105 14,166 4 14,400 14,406 14,394 14,303 14,264 14,376 5 14,638 14,583 14,558 14,477 14,404 14,558 6 14,845 14,756 14,745 14,646 14,568 14,740 7 15,055 14,938 14,911 14,802 14,735 14,892 8 15,237 15,104 15,086 14,957 14,900 15,047 9 15,402 15,254 15,227 15,110 15,029 15,219 10 15,581 15,393 15,397 15,250 15,177 15,382 11 15,753 15,559 15,561 15,392 15,336 15,526 12 15,923 15,700 15,714 15,524 15,469 15,662 13 16,078 15,860 15,882 15,672 15,617 15,804 14 16,231 15,989 16,022 15,810 15,751 15,941 15 16,376 16,136 16,139 15,963 15,888 16,085 Ave. 15,188a 15,065 15,064b 14,941C 14,884c 15,031 ab cValues with the same superscript indicate no signif- icant difference (P> .01). dComputed as average genetic value Of the cows remain- ing in the herd at the end of each year. 77 100 I. In. 160 I 155 I- 150 h 145 I- Strategy — M.E. Milk I --- M.E. Gross 14o ’ -'-' ‘6'. Mi'k I 1 4 e A A 1 J 1 '4 A 1 l A 3456.789101112131415 Years - Fig. 2.1 Average genetic milk value per cow. I00 Lbs. ‘60 ..I".’.F 155 b 150 I- 145 Strategy — Act. Orou --- Inc OMOIF.C. 140 V ---- Pres. Value L A 1 l 1 I 1 l I 1 e A l 1 i 1234.56789101112131415 Your: Fig. 2.2 Average genetic milk value per cow. 78 TABLE 5. Average fat production per cow (1b) Strategies Actual M.E. M.E. Actual Actual Inc. Over Present Year Milk Gross Milk Gross Feed Cost Value 1 450 449 448 449 449 448 2 466 471 465 467 468 471 3 486 489 486 487 482 486 4 491 492 492 492 495 495 5 496 497 498 502 500 498 6 499 503 505 506 505 503 7 503 i 505 508 509 507 506 8 507 506 510 512 512 513 9 509 512 511 517 514 509 10 513 , 511 514 517 517 514 11 515 515 517 523 519 519 12 516 519 517 521 524 518 13 517 521 517 526 526 523 14 518 520 523 529 525 525 15 523 523 525 528 530 527 Ave. 500.8 502.2 502.6 505.6 504.8 503.6 “9' 3.49% 3.53% 3.50% 3.54% 3.54% 3.52% Test Ave. Test 3.35% 3.40% 3.37% 3.43% 3.44% 3.41% Yr. 15 79 TABLE 6. Comparison of production records of two strategies Production Record Cow Actual 305-day M.E. 3 yr. old 12,000 lb 14,160 lb 7 yr. old 13,000 lb 13,000 lb are listed the predicted 305-day actual and adjusted age corrected M.E. production of these two cows computed from say, a 60 or 90 day record. The 3 year old at 12,000 lb would have an M.E. record of 14,160 while the 7 year old at 13,000 lb actual would have an M.E. of 13,000 lb milk. A comparison of the results of culling under the two strategies is presented in Table 7. Assuming we want to cull one of these cows, under actual milk the 3 year old would be culled, while under the M.E. milk strategy, the 7 year old would be the one culled. Yet either cow would be culled at the most profitable time to cull within their respective lactations. Under a given price structure then, each would be culled at the approximate same level of pro- duction although at different points in their lactations. If their total production to date before culling was say, 8,000 lb milk, then the remaining cow would produce at her predicted actual 305—day production; thus when culling is based on actual milk production, total production for the 80 TABLE 7. Results of two alternative strategies Culling Strategy Cow Actual Milk M.E. Milk 3 year old 8,000 lb 12,000 lb 7 year old 13,000 lb 8,000 lb Total for year 21,000 lb 20,000 lb two cows would yield 8,000 lb for the 3 year old plus 13,000 lb for the 7 year old or 21,000 lb milk, while under the M.E. strategy, production would total 20,000 lb. However, we are sacrificing some future producing ability and some genetic value by removing the 3 year old. Average milk production per cow was affected (P< .01) by the strategy used. No interaction between strategies and prices was significant from the factorial design. Since the means were significantly different, orthogonal contrasts were utilized to test the more logical comparisons. They are listed in Table 8. 81 TABLE 8. Comparison of mean milk production among strategies Strategy Mean Milk‘ Orthogonal Contrasts 1. M.E. milk 14,357 lb 5 vs 1,2,3,4,6** 2. M.E. gross income 14,266 6 vs 1,2,3,4 3. Actual milk 14,374 1,2 vs 3,4 4. Actual gross income 14,301 1 vs 2** 5. Income over F.C. 14,247 3 vs 4** 6. Present value 14,288 **Significant (p< .01) . The strategy based on income over feed cost was lower (P‘<.01) in average milk production than the average of the other five; M.E. milk at 14,357 lb was higher (P< .01) than M.E. gross at 14,266 lb milk per cow while the culling strategy based on actual milk (14,374 lb) was higher (P<:.01) than the one based on actual gross with 14,301 lb. From Table 9 and Figures 3.1 and 3.2, average milk production under the strategy of actual milk was higher than under M.E. milk up through the 10th year when M.E. strategy gained a slight advantage. Average gross income per cow per year for the 15 year span did not differ significantly by strategies. These ranged from a high of $682.72 under the strategy of actual gross to a low of $679.52 per cow under M.E. gross. 82 TABLE 9. Average milk production per cow (1b) Strategies Actual M.E. M.E. Actual Actual Inc. Over Present Year Milk Gross Milk Gross Feed Cost Value 1 12,441 12,417 12,373 12,403 12,403 12,354 2 12,861 13,026 12,876 12,894 12,926 12,981 3 13,441 13,495 13,458 13,442 13,328 13,463 4 13,659 13,693 13,726 13,653 13,704 13,739 5 13,915 13,878 13,950 13,997 13,910 13,898 6 14,113 14,088 14,264 14,130 14,058 14,079 7 14,316 14,248 14,408 14,314 14,206 14,255 8 14,519 14,370 14,552 14,461 14,388 14,498 9 14,649 14,603 14,674 14,653 14,528 14,526 10 14,882 14,636 14,846 14,746 14,676 14,724 11 15,043 14,809 15,046 14,937 14,806 14,917 12 15,163 15,001 15,125 14,995 15,023 14,958 13 15,303 15,143 15,231 15,205 15,140. 15,197 14 15,432 15,201 15,503 15,325 15,221 15,299 15 15,625 15,381 15,587 15,392 15,386 15,464 Ave. 14,357 14,266 14,374 14,301 14,247 14,288 83 1000 the. I- .a ,4 .’.I "’v’ ‘5 p .’. ”” p .’. ’,” .I' I”’ 0” '4 h .’.:” ’ I I b / Strategy ‘3 ' /’ —Me'e M‘Ik --- M.l. Groe e -.- Ag’eM5'k g l A 1 L L n A A 1 1 A e 12 34 5 7 5 9101112131415 Years ' Fig. 3.1 Average milk production oer con. 1000 the. 15 ' I 14 - b '3’ Strategy — Act. Groee ---|neamell.€. -°-- Free. Value , A A 1 1 1 41 1 1 j A A A l 2 3 4 5 6 7 5 9 10 11 12 13 14 15 Years Fig. 3.2 Average milk production per con. 84 The mean percentage of voluntary culls also varied (P<<.01) by strategies. The mean rate of culling computed as the percentage of the herd at the beginning of the year which were subsequently removed voluntarily was 29.7%. The difference in percentage of voluntary culls among strategies is listed in Table 10. The culling rate of 30.93%.under the strategy of M.E. gross was significantly higher than those under actual milk (28.66%) or income over feed cost (28.93%) while M.E. milk strategy at 30.58% voluntary culls was sig- nificantly higher than actual milk. TABLE 10. Percentage of voluntary culls Strategy Culling Rate (96). M.E. milk 30.58ac ab M.E. gross 30.93a a Actual milk 28.66b C Actual gross 29.43ab be Income over F.C. 28.98bc C Present value 29.61ab abc Level of sig. .01 .05 ab CValues with the same superscript indicate no significant difference. 85 Since all strategies culled on the basis of avail- able replacements, the only eXplanation for these differ- ences is that under the strategy of actual milk, actual gross income and income over feed cost, there would tend to be a higher proportion of the younger cows culled voluntar- ily than for strategies based on some mature equivalent fac- tor. But these younger cows have a lower involuntary removal rate; thus the herd will tend to average a higher age under culling on actual records because a higher propore tion of younger cows will be culled voluntarily. Conse- quently, more cows will be culled voluntarily under the M.E. strategies than under the actual strategies. The culling rate, however, in any herd will depend on both the available replacements and rate of involuntary culls. Though the base herd size was set at 80 cows and the approximate size of the herd at the end of the year was 80, the average herd size as defined by total cow months divided by 12 resulted in an average herd size of 98.8 for all replications. There was a difference (P<:.01) among strat- egies in herd size as listed in Table 11. Both the culling strategies based on M.E. milk (99.453) and the one based on M.E. gross income (99.447) had larger (P< .05) average herd size than any of the other strategies. 86 TABLE 11. Average herd size by strategies Strategy Average Herd Size M.E. milk 99.453a M.E. gross 99.447a Actual milk 98.397b Actual gross 98.597b Income over F.C. 98.359b Present value 98.562b ab Values with the same superscript indicate no significant difference (P>>.05) Mean age of voluntary culls was not recorded but we could assume a herd culled on the basis of actual milk pro- duction would lose a higher proportion of young cows than one culled on some basis of mature equivalent. Both herd size and culling rate are thus affected by this age relation— ship. One would wonder why culling rate is higher under the M.E. strategies yet herd size is larger. Since younger cows have a somewhat lower lactation curve, when culling at the most profitable month, the younger cows would on the average be culled earlier in their lactation than older cows, thus reducing the number of cow months and subsequently herd size. From the factorial design, however, in analysis of average month culled there is a four way interaction of strategies with milk prices, Operational costs, and feed prices. 87 The assumed discount rate of 6% compounded and applied to the income over feed cost (including salvage) indicates a dairyman can either earn that much interest with the money he possesses or he can borrow at that rate to eXpand his business. The 15 year planning horizon does not imply the farmer will diSperse his herd at the end of the 15 years or that potential income of year 16 is sacrificed to maximize early revenue, but it simply means truncating at the end of 15 years. Yet a farmer planning to diSperse his herd, say in one or two years, may wish to discount at a different rate or he may even choose to cull his less profit- able cows on a different strategy. Conversely, beyond 15 years, planning and goals lead to more uncertainty; thus different planning horizons may indicate various discount rates. Farmers whose herds deviate markedly from the invol- untary losses of either cows or young stock assumed in this study may find comparison of strategies different than these results indicate. For instance, a dairyman who has high death losses among his calves and consequently has fewer replacements, would have a higher percentage of mature cows than a farmer with few calf losses. Since the strategies based on M.E. production or income tend to cause a higher proportion of older cows culled than under actual strategies, this difference could cause a change in profit among strat- egies. 88 Simple strategies such as those based on actual milk, or actual gross income should appeal to most dairymen in that they are easy to use and understand and need no Special adjustment factors. Such strategies he can apply from sim- plified DHIA reports or simply from milk weight records. If dairymen know they would not sacrifice profit by using such strategies, they may wish to employ these simpler culling policies. Importantly as well, errors in age adjustment factors which admittedly differ from herd to herd and region to region are eliminated when using actual records. Effect of Prices Average milk income over feed cost over the total of 15 years was analyzed in a complete factorial design. Results show there was a three way interaction (P_ 15,250 I I 175 1b For lactations leSS than 10 months Age Production (per mo.) Extra Hay (per mo.) 2 Z 610, < 915 18 1b 2 915, < 1220 30 lb 2_1220, < 1525 ' 40 1b 2 1525 ‘ 48 1b 3 Z_915, < 1220 12 1b Z_1220, < 1525 24 1b 2 1525 30 lb ‘ HICHIan STATE UNIV. LIBRARIES illilHillWilliWIWilli”HIIIWIWINillHINHI 31293104244177