Development and evaluation of a simulation model for dairy cattle production systems integrated with forage crop production.
Abstract: Crop-livestock mixed farming systems depend on the efficiency with which nutrients are conserved and recycled. Home-grown forage is used as animal feed and animal excretions are applied to cultivated crop lands as manure. The objective of this study was to develop a mixed farming system model for dairy cattle in Japan. The model consisted of four sub-models: the nutrient requirement model, based on the Japanese Feeding Standards to determine requirements for energy, crude protein, dry matter intake, calcium, phosphorus and vitamin A; the optimum diet formulation model for determining the optimum diets that satisfy nutrient requirements at lowest cost, using linear programming; the herd dynamic model to calculate the numbers of cows in each reproductive cycle; and the whole farm optimization model to evaluate whole farm management from economic and environmental viewpoints and to optimize strategies for the target farm or system. To examine the model's validity, its predictions were compared against best practices for dairy farm management. Sensitivity analyses indicated that higher yielding cows lead to better economic results but higher emvironmental load in dairy cattle systems integrated with forage crop production. (Key Words : Crop-livestock Mixed Farming System, Dairy Cattle, Linear Programming, Farm Management, Simulation Model, Whole Farm)
Article Type: Report
Subject: Dairy cattle (Food and nutrition)
Dairy cattle (Physiological aspects)
Dairy cattle (Genetic aspects)
Crop yields (Models)
Plant-animal interactions (Models)
Manures (Usage)
Agricultural systems (Models)
Linear programming (Methods)
Farm management (Research)
Authors: Kikuhara, K.
Kumagai, H.
Hirooka, H.
Pub Date: 01/01/2009
Publication: Name: Asian - Australasian Journal of Animal Sciences Publisher: Asian - Australasian Association of Animal Production Societies Audience: Academic Format: Magazine/Journal Subject: Agricultural industry; Biological sciences Copyright: COPYRIGHT 2009 Asian - Australasian Association of Animal Production Societies ISSN: 1011-2367
Issue: Date: Jan, 2009 Source Volume: 22 Source Issue: 1
Topic: Event Code: 310 Science & research
Product: Product Code: 0240100 Dairy Cattle; 0240110 Dairy Cows NAICS Code: 11212 Dairy Cattle and Milk Production SIC Code: 0241 Dairy farms
Geographic: Geographic Scope: Japan Geographic Code: 9JAPA Japan
Accession Number: 195919145
Full Text: INTRODUCTION

In Japan, increased inputs of chemical fertilizer and purchased feeds to enhance the economic efficiency of limited amounts of land have intensified dairy production in the past several decades. This trend has created imbalances of nitrogen (N) and phosphorus (P) and thus serious environmental problems. To solve these environmental problems, new laws requiring the proper management of animal excretions and promoting their use as manure were completely implemented in November, 2005.

Recycling of manure nutrients has been the most popular means to address the problem of nutrient imbalance. However, a number of difficulties prevent the effective reuse of N and P in manure: inadequate transportation systems, a shortage of farming area for manure application, and manure's low effectiveness as fertilizer. Consequently, dairy farmers face a new challenge: to simultaneously increase economic efficiency and decrease environmental loads.

A comprehensive approach that integrates dairy production, crop production, feeding and the handling of manure is needed to properly evaluate dairy producer's options for economic and environmental management (Tamminga, 1992; Rotz et al., 1999a). Normative modeling approach at farm level is one way to determine the effects of management measures on the environment (Berentsen and Tiessink, 2003). Many trials have been conducted to support dairy producers in their nutrient and farm management decision-making. Linear programming (LP) has been used to determine least-cost rations and optimal strategies for formulating rations (Henry et al., 1995; Tedeschi et al., 2000). Furthermore, computer simulation with environmental-economic models at the farm level provide a useful tool for integrating knowledge and information to predict production efficiency, environmental impacts, and the effects of management policies on production performance (Berentsen and Giesen, 1995; Berentsen, 1999; Herrero et al., 1999; Rotz et al., 1999a; Thornton and Herrero, 2001; Van Calker et al., 2004).

The objective of this study was to develop an environmental-economic model for integrated dairy systems with crop production in Japan while minimizing feed costs. Optimal farming systems based on nutrient recycling were chosen for whole farm management with least-cost ration calculations.

[FIGURE 1 OMITTED]

MATERIALS AND METHODS

Overview of the present model

An overview of the model structure is illustrated in Figure 1. The model consists of four sub-models: nutrient requirement model, optimum diet formulation model, herd dynamic model, and whole farm optimization model.

The nutrient requirement model was constructed based on the Japanese Feeding Standards for dairy cattle (MAFF, 1999) and used to predict metabolizable energy requirements (ME), crude protein (CP), dry matter intake (DMI), calcium (Ca), phosphorus (P) and vitamin A (VA). In addition, excretions for nitrogen (N) and P were also calculated in this model.

The optimum diet formulation model determined the optimum diet that meets nutrient requirements for the lowest cost using linear programming.

The herd dynamic model calculated the number of cows in each reproductive cycle at equilibrium. In this model, all cows with reproduction failures were assumed to be culled at the end of lactation.

The whole farm optimization model integrated outputs from the first three sub-models and determined the effects of animal performance and management policies on farm behaviors, production efficiencies, and nutrient losses to the environment. The objective function maximized in this sub-model was net profit and the elements were dairy cows, feed production, purchased fertilizer, labor, and surpluses of nitrogen and phosphorus. The production costs of homegrown feed were assumed in this model.

The present model is flexible and can be applied to various dairy cattle production systems integrated with forage crop production in Japan by changing input variables related to dairy and crop production such as genotype, nutrition, management and economic variables of dairy production, and varieties and acreage of forage crops.

Nutrient requirement model

Table 1 shows the values and equations for estimating energy and nutrient requirements based on Japanese Feeding Standards for dairy cattle (MAFF, 1999). Energy requirements of animals and some of the events in animal life were estimated based on growth curves. A growth curve was determined from three animal traits: birth weight (BW), weaning weight (WW), and mature weight (MW) (Table 1). It was also assumed that the growth curve was represented by a straight line from birth (43 kg) to weaning (98 kg) and subsequently from weaning (98 kg) to culling by a Brody curve (Brody, 1945; Kahn, 1982).

The ME requirement for lactation ([ME.sub.l]) was estimated from a lactation curve. The lactation curve for a cow was determined with the integration of biological traits and the parity effect. A continuous function was used to describe milk yield (MY) (kg/d) over a full lactation given by Wood (1967). This function had the form of:

MY = a x [t.sup.b.sub.1] x [e.sup.-et]

where [t.sub.1] is days of lactation and a, b, and c are parameters. Parameters a, b and c respectively determined the level of yield (intercept), the ascending phase to the peak of lactation, and the descending phase to drying up; they were defined by Hirooka (1992) as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

b = 0.208

c = 0.0342

where lacte is lactation period and TMY is the total milk yield at the fifth parity. Total milk yields at different parities were calculated by multiplying coefficients reported by Groen (1988).

It was assumed that a heifer is first inseminated at 18 month after birth, that the lengths of pregnancy and lactation are 280 d and 359 d, respectively, and that the calving interval is 14.1 mo (JDC, 2002).

A cow's daily ME requirement ([ME.sub.(t)]) was expressed as:

ME = [ME.sub.mg] + [ME.sub.p] + [ME.sub.l] (Mcal/day)

where [ME.sub.mg] is the metabolizable energy requirement for maintenance and growth, and [ME.sub.p] and [ME.sub.l] are the metabolizable energy requirements for pregnancy and lactation, respectively. The ME requirement for pregnancy ([ME.sub.p]) was calculated as that at 63 days before calving (MAFF, 1999). The daily DMI, CP, Ca, P and VA requirements were calculated same as the case of ME using these growth and lactation curves as well as the equations (MAFF, 1999) (Table 1). The model simulates daily nutrient requirements on one day time step basis.

Furthermore, excretions for nitrogen (N) and phosphorus (P) were calculated in this model. The daily amount of N in excretions ([N.sub.out(t)]) was calculated from the following equation (Table 1):

[N.sub.out] = ([CP.sub.i]-[NP.sub.g]-[NP.sub.f]-[NP.sub.milk])/6.25

where [CP.sub.i] is CP intake calculated from the optimum diet optimization model (see the next section), [NP.sub.g] is the amount of protein retained in the body shown in Table 1 (Eq(48)), [NP.sub.f] is the amount of protein retained in fetus during pregnancy (Eq(57) in Table 1) and [NP.sub.milk] is the amount of protein in milk during lactation (Eq(59) in Table 1).

The daily amount of P in excretions ([P.sub.out(t)]) was calculated from the following equation (Table 1):

[P.sub.out(t)] = [P.sub.i(t)]-[Pg.sub.(t)]-[Pf.sub.(t)]-[P.sub.milk(t)]

where Pi(t) is P intake calculated from the optimum diet optimization model (see the next section), [P.sub.g(t)] is the amount of P retained in the body (Eq(67) in Table 1), [P.sub.f(t)] is the amount of P retained in fetus during pregnancy (Eqs(68) and (69) in Table 1) and [P.sub.milk(t)] is the amount of P in milk during lactation (Eq(71) in Table 1). The model simulates daily excretions on one day time step basis.

Optimum diet formulation model

Diet compositions for a post-weaning animal were modeled using linear programming (LP) that simultaneously solved nutrient constraint equations and minimized cost of ration. The model can be stated algebraically as follows:

Minimize {[Z.sub.diet] = [c.sub.diet'][x.sub.diet]}

Subject to [A.sub.diet][x.sub.diet] [less than or equal to], =, or [greater than or equal to][b.sub.diet] and [x.sub.diet][greater than or equal to]0

where [Z.sub.diet] is the lowest cost of rations, [x.sub.diet] is the vector of activities, [c.sub.diet] is the vector of costs per unit of activity, [A.sub.diet] is the matrix of technical coefficients, and [b.sub.diet] is the vector of right-hand side values.

The six variables (DMI, ME, CP, Ca, P, and VA) obtained from the nutrient requirement model were used as constraints in this model. The equality and inequality of the constraint, as determined by the nutrient of interest for constructing an optimal ration model, are shown in Table 2. ME intake was set equal to the ME requirement and intake CP, Ca, P, and VA were set to exceed the CP, Ca, P and VA requirements, respectively.

In this model, it was assumed that the prices of homegrown feed were zero, while the prices of purchased feed were set by users. This assumption automatically led to the promotion of the use of home-grown feed instead of purchased feed at daily basis. This assumption reflects the government pollicy on livestock production in Japan, because a decline in the domestic feed supply for livestock has resulted in lower self-sufficiency rate of livestock production and thus Japanese government encourages production and utilization of home-grown feed.

The model assumed that a pre-weaning calf was fed whole milk (4.5 kg) when it weighed less than 45 kg followed by both whole milk (4.5 kg) and dietary feed until it weighed 66 kg (MAFF, 1999). It was assumed that the whole milk would be completely consumed and that dietary feed would compensate for deficiencies against energy requirements. When whole milk supplies exceeded a calf's ME requirements, dietary feed ME was zero.

The feeding cost for the pre-weaning calf in these periods was not solved using LP. Instead it was given by:

when W<45 kg

[Z.sub.diet] = 4.5 x [PRI.sub.milk]

when 45 kg [less than or equal to] W<66 kg

[Z.sub.diet] = 4.5 x [PRI.sub.milk] + ([MEi.sub.(t)] - 4.5 x 0.58)/3.15 x [PRI.sub.creep]

where [PRI.sub.milk] and [PRI.sub.creep] are the prices of whole milk (yen/kg) and creep feed (yen/kg), respectively, and 0.58 and 3.15 are the metabolizable energy contents of whole milk (11.4% dry matter) and creep feed (88% dry matter), respectively (MAFF, 1999).

Herd dynamics model

This model was constructed based on Hirooka et al. (1998). It was assumed that the herd size was stable, all replacement heifers were home grown, heifers were culled when they failed to conceive, and cows that failed to conceive were culled at the end of lactation.

In the model, the growing period (cycle 0, [T.sub.0]) was defined as the interval from birth to the first conception. The growing period of heifers was included in this cycle, because all dairy male calves were sold soon after birth in Japan. The first reproductive cycle (cycle 1, [T.sub.1]) was defined as the interval from the first conception to the end of the first lactation period. For the later reproductive cycle (cycles 2 to n), the length of each reproductive cycle ([T.sub.2][T.sub.n]) was the period from one lactation end to the next lactation end. All cows in the final cycle ([T.sub.n]) were culled at the end of the nth lactation period.

The composition of a cow population was determined by the culling rate ([p.sub.(i)]) of the females (the second and third columns in Table 3). It was assumed that heifers and cows that failed to conceive were culled with the (p(i)) in each reproductive cycle ([T.sub.i]).

For a population with N cows (i.e., herd size is N), the number of females in each reproductive cycle is shown in Table 4, and the herd size N is represented as

N = [N.sub.(0)] + [N.sub.(1)] + ... + [N.sub.(n)] = [n.summation over (t=0)] [N.sub.(1)]

where [N.sub.(0)] and [N.sub.(i)] are the number of females in the growing period and ith reproductive cycle, respectively. Provided that the sex ratio is set as 1:1 and the calf survival rate is set as s, the number of surviving male and female calves produced from cows in the ith reproductive cycle ([N.sub.M(i)] and [NF.sub.(i)]) is calculated as

[N.sub.F(i)] = [N.sub.M(i)] = 0.5s[N.sub.(i)]

When the number of newborn females of [N.sub.0] is used as replacement heifers to maintain a stable herd size, the replacement rate (r) can be obtained as

[N.sub.0] = r [n.summation over (t=1)] [N.sub.f(t)]

r = [N.sub.0] / [n.summation over (t=1)] [N.sub.f(t)]

Therefore, the number of newborn females for sale ([N.sub.SF]) is

[N.sub.SF] = (1 - r) [n.summation over (i=1)] [N.sub.F(i)]

Note that the number of newborn males for sale (NSM) is

[N.sub.SM] = [n.summation over (i=1] [N.sub.M(i)]

The number of animals in each reproductive cycle was adjusted by the length of the cycle as shown in the next section (see calculation of Aveday).

Whole-farm optimization model

The model was constructed based on the form of a standard linear programming model as follows:

Minimize {[Z.sub.farm] = [c.sub.farm]'[x.sub.farm]}

Subject to [A.sub.farm][x.sub.farm] [less than or equal to], =, or [greater than or equal to][b.sub.farm] and [x.sub.farm][greater than or equal to] 0

where [Z.sub.farm] is maximum return of the whole farm, [x.sub.farm] is the vector of activities and environmental variables, [c.sub.farm] is the vector of gross margins or costs per unit of activity, [A.sub.farm] is the matrix of technical and environmental coefficients and [b.sub.farm] is a vector of technical-environmental right-hand-side (RHS) coefficients. The activities ([x.sub.farm]) are given at the top row in Table 5. The activities include: animal production from dairy cows, heifers, and sale calves; feed production for on-farm use with forage crops available for hay and silage making; purchase and application of different kinds of fertilizer; labor force (working hours); and farm level environmental loads (N and P surpluses). The rows of the matrix (Table 5) represent the type and number of constraints used: land requirements, housing requirement, labor requirement, feeding requirements matching home-grown feed with the sums of animal requirements, fertilizer requirements matching nutrient requirements for crop lands with the available nutrients from manure and purchased chemical fertilizer, and nutrient balances determining the surplus of N and P for calculating their levies. The last row is the objective function of the LP model that is to be maximized. In the objective function, production costs and incomes per unit of activity were summed up, and thereby whole farm outputs were calculated on a yearly basis.

Technical coefficients concerning animal production were calculated on a life-cycle basis, whereas all activities except animal production were obtained on a yearly basis in the model. It was therefore necessary to convert yearly basis technical coefficients from the life-cycle basis. For example, a cow's yearly total intake of roughage j (kg/year/animal) was calculated as follows:

[a.sub.ij] = ([TI.sub.j]/Aveday) x 365

where [TI.sub.j] is the total intake of roughage j of the cow's life cycle, and Aveday is the average period (interval) in each life cycle (day) in a population. [TI.sub.j] was calculated by summing the daily intake of roughage j in each period of the reproductive cycle ([INTj.sub.(i)]) multiplied by the age distribution ([N.sub.(i)]) as:

[TI.sub.j] = [n.summation over (i=0)] ([N.sub.(i)] x [INTj.sub.(i)])

and Aveday was obtained as follows:

Aveday = [n.summation over (i=0)] ([N.sub.(i)] x Ti)

where [N.sub.(i)] and [T.sub.i] are the age distribution of cows and the period of each reproductive cycle, respectively. All the feeding requirements (home-grown and purchased feed), all the animal products (milk and culled animal) and farm-level nutrient excretions for N ([TN.sub.out]) and P ([TP.sub.out]) of the animals were re-calculated by converting from a life-cycle basis to a yearly basis in the same way.

In this model, it was assumed that all excretions (feces and urine) by animals were used to produce manure and were applied to home-grown crop land as organic fertilizer. Since the manure N and P applied to crop land are less effective than chemical fertilizer because of their lower fertilizer-N and P equivalency, the amounts of effective N and P in manure (ETN, ETP) were derived using the efficiency index of manure ([E.sub.N] and [E.sub.P], %) against chemical fertilizer and the emission rate of N as ammonia ([N.sub.loss]) as:

ETN = [TN.sub.out] x (1-[N.sub.loss]) x [E.sub.N]/100

ETP = [TP.sub.out] x [E.sub.P]/100 The present model assumed that the fertilizer requirements of home-grown crops varied from the crop yields and their CP contents. Considering the amount of crop uptake from soil, the fertilizer N and P requirements of home-grown crops were obtained as:

[N.sub.req] = [BN.sub.req] + (DMY-BDMY) x CP/6.25

[P.sub.req] = [BP.sub.req] + (DMY-BDMY) x P

where [N.sub.req] and [P.sub.req] are the N and P requirement (kg/ha), [BN.sub.req] and [BP.sub.req] are the N and P requirements for the annual reference dry matter yield (kg/ha) as basis, DMY is the dry matter yield (kgDM/ha), BDMY is the annual reference dry matter yield as basis, and CP and P are CP and P contents in feed (kg/kgDM) produced from harvested home-grown crop.

From an environmental standpoint, farm-gate balances for N and P were used as indicators of potential N and P losses. N surplus ([N.sub.surp]) and P surplus ([P.sub.surp]) were defined as the N and P differences between exported animal products (milk, calves, and culled cows) from the farm and purchased feed and chemical fertilizer from outside. When the amount of manure applied was less than the fertilizer requirements, the deficiencies were assumed to be met by purchased chemical fertilizer. Equations to estimate N and P contents in animal products are given in Table 6.

In this model, gross margin or cost per unit of activity were given by assuming economic situations in the targeted area. The returns per cattle were calculated with the returns of milk and culled animal minus the costs of purchased feeds, because the costs of home-grown feed are taken into account as separate activities. Milk price in Japan was calculated as:

[M.sub.pri] = 73.0 + ([M.sub.fat]-3.5) x 4.0

where [M.sub.pri] is milk price (yen) per kg and [M.sub.fat] is milk fat content.

RESULTS

Model evaluation

Since a model is based on empirical equations consisting of many experimental results and assumptions, it in itself is just an assumption unless it can prove a generality. Thus, model evaluation is a very important process in modeling studies.

In this study, two situations of typical dairy production systems with crop production in Japan were simulated to validate the whole-farm model. Production systems in both situations were under full confinement operation (i.e., no grazing). A summary of nutrient and mineral contents and the price of each feed used in this simulation are shown in Table 7. These feed ingredients were those typically available to dairy producers in Japan. The information on ingredients and market prices was obtained from the literature (NARO, 2001; MAFF, 2005a). For pre-weaning calves, the prices of whole milk and creep feed were set 82.44 yen/kg and 70.0 yen/kg, respectively (MAFF, 2005a).

Table 8 shows related input variables of the two situations for dairy and crop mixed farming systems in Hokkaido and Honshu areas. The input variables were taken from the management practice guideline (MAFF, 2005b). The values were from data on the top one-third dairy management practices in Hokkaido (Hokkaido situation) and Honshu areas (Honshu situation). According to the guideline, it was assumed that utilization of home-grown feed and purchased roughage for cows was limited to less than 45% and 5% of the ME requirements, respectively (Table 8). In addition, the chemical fertilizer requirements of home-grown feed ([BN.sub.req], [BP.sub.req]) were assumed to be 70 kg N/ha and 31 kg P/ha for pasture and 190 kg N/ha and 87 kg P/ha for maize (JLIA, 1990). The N emission of manure as ammonia was set 25%. The fertilizer equivalency of manure for N and P were assumed to be 30% and 60%, respectively (MAFF and NARO, 2004). The price of purchased chemical fertilizer (0.15 kg N/kg, 0.15 kg P/kg) was 95.34 yen/kg and the labor cost was assumed to be 1,612 yen/hour (MAFF, 2005b). Other fixed costs, such as fixed assets of the farm and the costs of land, barns and machinery, were obtained from statistics (MAFF, 2005c).

The fixed milk prices were set in Hokkaido and Honshu, respectively. The prices of male and female calves were both set as 38,458 yen/animal and that of culled cows was set as 1,508 yen per 10 kg body weight (MAFF, 2005a). The annual yield of maize and pasture (timothy and alfalfa) were assumed to be 13,770 kg DM/ha and 5,740 kg DM/ha in Hokkaido and 12,393 kg DM/ha and 6,020 kg DM/ha in Honshu (JLIA, 1990).

Figure 2 and 3 illustrate the predicted daily ME intake and DM intakes of home-grown feed by maintenance and growth, pregnancy and lactation stages for a cow in Hokkaiso. The results show increased ME intake and dry matter intake of home-grown feed during late pregnancy and lactation stages. Distributions of females in each reproductive cycle are shown in the 4th and 5th columns in Table 3 for Hokkaido and Honshu, respectively.

Comparisons between values in the management practice guideline for the two situations and predictions from the present model are given in Table 9. There was small discrepancy in the number of cows and production costs except labor cost in both Hokkaido and Honshu situations. In contrast, large differences of labor costs were found for both situations. This result may reflect the difference in the calculation way of labor cost: the management practice guidelines assume that full-time employees with higher payment would be hired, whereas the present model calculates labor cost by summing the labor cost per hour taken from standard management practices in statistics. Without the difference in labor costs, the model predictions for revenues, total costs and net profits in both Hokkaido and Honshu agreed well with the values given in the management practice guideline. This result indicated that the present model would be applicable to actual situations for dairy and crop mixed farming systems in Japan.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

N surplus was higher in Honshu than in Hokkaido. This may be mainly because of the difference of production intensities in the situations; the animal intensity in Honshu is more than that in Hokkaido. The animal intensity difference between the two areas is reported in Tsuiki and Harada (1996). Considerably higher P surplus was obtained in the situations. The unexpected result may be reflected from utilization of fixed chemical fertilizer with higher P content (0.15 kg N/kg, 0.15 kg P/kg). P control by the chemical fertilizer would make it possible to reduce the P surplus.

[FIGURE 5 OMITTED]

Sensitivity analysis

Sensitivity analyses allow us to examine the impacts of changing values of susceptible variables of the integrated system on economic variables (revenue, total cost, and net profit) as well as environmental variables (N and P surpluses). In this study, changes of [+ or -]5% and [+ or -]10% with respect to the assumed value of milk yield (MY) were examined in Hokkaido. In this section, only sensitivity results for Hokkaido situation were shown, because the similar results were obtained for Honshu situation.

Figure 4 and 5 show the effects of milk yield on economic (revenue, total cost, net profit) and environmental variables (N and P surpluses), respectively. Changes in MY were made at a time while all other variables were kept constant.

The results in Figure 4 showed that each of these economic variables was sensitive to changes in MY. The high sensitivities of revenue and total cost were obtained, since milk sales provided the highest income in the situation. An increase in MY led to a rise in the revenue due to a rise in milk sales. To fulfill the higher nutritional requirements of the animal caused by higher milk production, the model compensated for the quality and quantity of the diet by increasing the amounts of purchased feed, which increased total cost. The increment in revenue was higher than that in total cost, providing a positive net profit for the farm. Economically, these results indicated that farmers should raise higher-performance cows in this situation.

N and P surplus were slightly sensitive to changes in MY (Figure 5). Increasing MY caused rises in both the input and output of N and P. These were expected because more purchased feed was utilized and more milk was sold. However, the higher nutrient inputs from the purchased feed led to increased amount of excretions for use as manure. Consequently more organic fertilizer (manure) was utilized to complement the chemical fertilizer. That is, a rise in the purchased feed requirement reduced the chemical fertilizer requirement when the total fertilizer requirement was constant. P surplus was less sensitive than N surplus. The low sensitivity of P may be resulted from excess P fertilization by the utilization of purchased chemical fertilizer with high P content (0.15 kg N/kg, 0.15 kg P/kg). Environmentally, these results indicated that the nitrogen load on the environment was substantially increased by improving MY of cows in this situation.

DISCUSSION

The objective of this study was to develop a bioeconomic simulation model for Japanese dairy production systems with forage crop production. The present model includes not only bio-economic factors but also environmental factors, and thus provides a useful tool for evaluating and comparing the environmental impacts as well as the economic performance of alternative systems. For animal and crop producers, it is important to quantify the trade-off between profitability and environmental loads derived from production and to evaluate the effects of recycling nutrients on the profitability of the whole farm. Janssen and Van Ittersum (2007) reviewed studies using bio-economic farm models and pointed out that such models may permit us to consider many activities, restrictions, and new production techniques simultaneously while also allowing us to examine the effects of changing parameters through sensitivity analysis. Those authors also noted that a bio-economic farm model can be defined as a model that supports farmers' resource management decisions by describing current and alternative production possibilities in terms of required inputs to achieve certain outputs and associated externalities.

In Europe and the USA, bio-economic farm models that include economic and environmental factors have been developed to evaluate dairy and forage crop mixed farming systems at the whole-farm level. These models were used to determine the optimum cropping system for both manure nutrients and crop nutrients (Henry et al., 1995), to evaluate the impacts of institutional, technical and price changes on the farm plan as well as the impacts of nutrient losses on the environment while maximizing farm profitability (Berentsen and Giesen, 1995), and to analyze the effects of environmental policy and management measures on the economic and ecological sustainability of dairy farms (Steverink et al., 1994; Koenen et al., 2000; Berentsen, 2003; Berentsen and Tiessink, 2003; Berntsen et al., 2003; Van Calker et al., 2004). Rotz et al. (1999a) developed a simulation model for dairy and forage crop mixed farming systems that integrates many biological and physical processes on a dairy farm. The model revised by Rotz and Coiner (2006) has been applied to evaluate economic and environmental feasibility of a dairy farm with changing the management (Rotz et al., 1999b; Soder and Rotz, 2001; Rotz et al., 2002; Rotz et al., 2005; Ghebremichael et al., 2007).

In Asian countries, the integration of crop and animal production is well developed and most on ruminant livestock are found on such mixed farming systems (Devendra and Thomas, 2002). Devendra (2007) reviewed improved crop-animal integration systems in Asia and advocated that system approach is required to interpret the contribution of the many components in mixed farming systems that identified through detailed analysis of the need and constraints. In our companion paper (Kikuhara and Hirooka, 2008), the model described here is applied to evaluate integrations systems between forage rice and dairy cattle production in Japan.

The model in the present study was used to find an optimum combination of feed resources that minimize daily feed cost and to predict the effects of alternative management decisions on farm profitability and the environment within the existing framework. The results of sensitivity analyses showed that many variables affect the optimal farming system, indicating the complexity of dairy and crop mixed farming systems. The economic and environmental variables were sensitive to the change in milk yield. Increased milk yield caused total sales and cost, and thereby higher net profit. Further, higher milk yield also raised the amounts of N and P surpluses (Figure 5). These results were in good agreement with those in Rotz et al. (1999b). These sensitivity analyses allow us to assess how changes in the values of susceptible variables (both economic and environmental variables) affect certain whole-farm outputs.

There are two important characteristics of the present model. The first is applicability. The present model appears to be easily changed to accommodate other dairy and forage crop production circumstances in Japan by changing input variables assumed in the study. This is because the biological relationships and assumptions used in the model are general. In this respect, the model is flexible and can be used to contribute to insights obtained by carrying out proper calculations and publishing the findings for mixed farming systems in wide-ranging production circumstances. The model allows us to modify even the structure (i.e., equations) of the model and to replicate assessments for a vast range of spatial conditions and farm practices. For example, the users may change from the feeding standards for Japanese dairy cattle (MAFF, 1999) to other feeding standards, allowing them to transfer the model between different locations and farms in the USA (NRC, 2001) and the UK (AFRC, 1993) without changing the basic framework of the model. Jansen and Van Ittersum (2007) point out that an easily transferable bio-economic farm model will enable a group of researchers to work jointly by allowing the re-use of results of simulations across farm types and locations.

The second important characteristic is that the model was developed using both of system simulation (Dent and Blackie, 1979) and linear programming which are typically adopted methodologies to construct models for agricultural systems; system simulation is used to predict nutrient requirements and herd dynamics and linear programming is used for diet optimization and whole farm optimization. In general, system simulation consists of modeling the strategies and biological processes of agricultural systems and simulating between these processes. The methodology has been widely used to simulate animal properties in animal science fields (Sanders and Cartwright, 1979ab; Groen, 1988; Hirooka et al., 1998; Rotz et al., 1999a; Rotz and Coiner, 2006). On the other hand, linear programming has been extensively used to investigate livestock production systems at farm level. The methodology offers the potential to identify optimal systems and many models at farm have been constructed using this methodology (Berentsen and Giesen, 1995; Van Calker et al., 2004). In addition, the present model is unique in that the linear programming is utilized twice in the optimum diet formulation model on a daily basis and the whole-farm optimization model on a yearly basis. Despite the uniqueness, it should be noticed that optimization in each sub-model dose not always provide optimal at the whole farm level; in this model, use of home-grown feed is maximized by setting prices of zero in the optimum diet formulation model, but production costs for home-grown feed are only taken account in the whole farm optimization model. The present model put emphasis on encouragement of utilizing home-grown feed in order to enhance self-sufficiency of feed production advocated by Japanese government.

In this study, a normative approach was adopted, because the model's objective was to find optimal solutions and alternatives to the problems for mixed farming systems. As pointed out by Janssen and Van Ittersum (2007), however, there is a gap between normative-derived advice given to a farmer and the farmer's actual situation. To overcome this problem, positive approaches, which try to model the farmer's actual behavior by studying farm responses and trying to understand them, should be adopted and incorporated into the simulation process with the model. However, this kind of argument is beyond the scope of this study.

Finally, no simulation models can demonstrate a real system completely. Consequently, models should be continuously improved by incorporating updated knowledge and information. Perhaps with further improvement through verification and validation of the model, a more refined and sophisticated model can be developed and thereafter updated.

ACKNOWLEDGMENTS

This work was supported in part by a Grant-in-aid (Integrated research for developing Japanese-style forage feeding system to increase forage self-support ratio) from the Ministry of Agriculture, Forestry, and Fisheries of Japan (JFS-08-26006-2).

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K. Kikuhara, H. Kumagai and H. Hirooka *

Laboratory of Animal Husbandry Resources, Graduate School of Agriculture Kyoto University, 606-8502 Kyoto, Japan

* Corresponding Author: H. Hirooka. Tel: +81-75-753-6363, Fax: +81-75-753-6373, E-mail: hirooka@kais.kyoto-u.ac.jp Received February 8, 2008; Accepted September 13, 2008
Table 1. Values * for life cycle of dairy cattle and
equations * to estimate energy and nutrient requirements
quoted from Japanese Feeding Standard for Dairy Cattle

Eq.   Variable         Constraint

1     mo
2     t
3     Tp
4     prete
5     lacte
6     MY
7     [M.sub.fat]
8     FCM
9     W
10    DG
11    BW
12    WW
13    MW
14    DMI
15    ME
16    CP
17    P
18    Ca
19    VA
20    CPi
21    Pi
22    W                <3 month age
23    W                <20 month age
24    W                >20 month age
25    DG               <3 month age
26    DG               <20 month age
27    DG               >20 month age
28    [DMI.sub.mg]     W<45
29    [DMI.sub.mg]     45 [less than or equal to] W<66
30    [DMI.sub.mg]     before 1st calving
31    [DMI.sub.mg]     after 1st calving
32    [DMI.sub.p]      9-4 weeks before calving
33    [DMI.sub.p]      3-0 weeks before calving
34    [DMI.sub.l]
35    [ME.sub.mg]      W<66
36    [ME.sub.mg]      66 [less than or equal to] W<120
37    [ME.sub.mg]      before 1st calving
38    [ME.sub.mg]      after 1st calving
39    [ME.sub.mg]      dry cow
40    [ME.sub.p]       9-4 weeks before calving
41    [ME.sub.p]       3-0 weeks before calving
42    [ME.sub.l]
43    FN               W<66
44    FN               W [greater than or equal to] 66
45    UN
46    SP
47    [NP.sub.m]
48    [NP.sub.g]
49    EP               45 [less than or equal to] W<66
50    EP               66 [less than or equal to] W<120
51    EP               W [greater than or equal to] 120
52    [CP.sub.mg]      before 1st calving
53    [CP.sub.mg]      after 1st calving
54    PP
55    DCPR             9-4 weeks before calving
56    DCPR             3-0 weeks before calving
57    [NP.sub.f]       9-0 weeks before calving
58    [CP.sub.p]
59    [NP.sub.milk]
60    [CP.sub.l]
61    [N.sub.out]
62    [P.sub.mg]       W<90
63    [P.sub.mg]       90 [less than or equal to] W<250
64    [P.sub.mg]       250 [less than or equal to] W<400
65    [P.sub.mg]       before 1st calving
66    [P.sub.mg]       after 1st calving
67    [P.sub.g]
68    [P.sub.f]        9-4 weeks before calving
69    [P.sub.f]        3-0 weeks before calving
70    [P.sub.p]
71    [P.sub.milk]
72    [P.sub.l]
73    [P.sub.out]
74    [Ca.sub.mg]      W<90
75    [Ca.sub.mg]      90 [less than or equal to] W<250
76    [Ca.sub.mg]      250 [less than or equal to] W<400
77    [Ca.sub.mg]      before 1st calving
78    [Ca.sub.mg]      after 1st calving
79    [Ca.sub.p]       9-4 weeks before calving
80    [Ca.sub.p]       3-0 weeks before calving
81    [Ca.sub.l]
82    [VA.sub.mg]
83    [VA.sub.p]
84    [VA.sub.l]

Eq.   Variable         Equation or value

1     mo               30.4 days (length of a month)
2     t                days of age
3     Tp               days in pregnancy
4     prete            280 days (pregnancy period)
5     lacte            359 days (lactation period)
6     MY               milk yield
7     [M.sub.fat]      fat content in milk
8     FCM              (15.0 x [M.sub.fat]/100.0+0.4) x MY
9     W                live weight
10    DG               live weight gain
11    BW               43 kg (birth weight)
12    WW               98 kg (weaning weight)
13    MW               690 kg (mature weight)
14    DMI              [DMI.sub.mg]+[DMI.sub.p]+[DMI.sub.l]
15    ME               [ME.sub.mg]+[ME.sub.p]+[ME.sub.l]
16    CP               [CP.sub.mg]+[CP.sub.p]+[CP.sub.l]
17    P                [P.sub.mg]+[P.sub.p]+[P.sub.l]
18    Ca               [Ca.sub.mg]+[Ca.sub.p]+[Ca.sub.ll
19    VA               [VA.sub.mg]+[VA.sub.p]+[VA.sub.l]
20    CPi              CP intake
21    Pi               P intake
22    W                BW+(WW-BW) x ((t/mo)/3)
23    W                22.5 x ((t/mo-3)+WW
24    W                MW x (1-0.98268 x [exp.sup.(-0.0587258 x
                         (t/mo))])
25    DG               (WW-BW)/(3 x mo)
26    DG               22.5/mo
27    DG               0.058725 x (MW-W)/mo
28    [DMI.sub.mg]     4.5 x 0.12
29    [DMI.sub.mg]     4.5 x 0.12+((0.1183x [W.sup.0.75]+0.1205 x
                         DG x [W.sup.0.75])-4.5x 0.58)/3.15
30    [DMI.sub.mg]     0.49137+0.01768 x W+0.91754 x DG
31    [DMI.sub.mg]     1.5+0.01 x W
32    [DMI.sub.p]      5.13/2.28
33    [DMI.sub.p]      6.85/2.42
34    [DMI.sub.l]      2.98120+0.00905 x W+0.41055 x FCM
35    [ME.sub.mg]      (0.1152 x [W.sup.0.75]+0.1205 x DGx
                         [W.sup.0.75]) x 1.1
36    [ME.sub.mg]      (0.1152 x [W.sup.0.75]+0.1293x DG x
                         [W.sup.0.75]) x 1.1
37    [ME.sub.mg]      (0.1152 x [W.sup.0.75]+0.1355x DG x
                         [W.sup.0.75])x 1.07
38    [ME.sub.mg]      0.1163 x [W.sup.0.75]
39    [ME.sub.mg]      0.1163 x [W.sup.0.75] x 1.1
40    [ME.sub.p]       ((416.2 x [exp.sup.(0.0174 x prete)]/35.2
                         xBW-416.2 x [exp.sup.(0.0174 x prete-63))]/
                         35.2 x BW)/63/0.123) x 0.9/1,000.0
41    [DME.sub.p]      ((416.2 x [exp.sup.(0.0174 x prete)]/
                        35.2 x BW-416.2 x [exp.sup.(0.0174 x
                        prete-63))]/35.2 x BW)/63/0.123) x
                        1.2/1,000.0
42    [DME.sub.l]      ((0.0913 x [M.sub.fat]+
                         0.3678)x MY)/0.62
43    FN               2.0 x DMI
44    FN               4.8 x DMI
45    UN               0.44 x [W.sup.0.5]
46    SP               0.2 x [W.sup.0.6]
47    [NP.sub.m]       FN x 6.25+UN x 6.25+SP
48    NPg              10.0 x DG x 23.5505 x [W.sup.-0.0645]
49    EP               0.75
50    EP               0.63
51    EP               0.51
52    [CP.sub.mg]      ([NP.sub.m]+[NP.sub.g])/EP
53    [CP.sub.mg]      2.71 x [W.sup.0.75]/0.60
54    PP               (1.486 x [10.0.sup.-4] x [prete.sup.3] -4.247
                         x [10.0.sup.-2] x [prete.sup.2]-3.173
                         x prete-0.328) x (-0.323 x [10.0.sup.-6]
                         x [prete.sup.3]+3.000 x [10.0.sup.-4]
                         x [prete.sup.2]-9.430 x [10.0.sup.-2]
                         x prete+11.263) x 6.25-(1.486
                         x [10.0.sup.-4] x [(prete-63).sup.3]-4.247
                         x [10.0.sup.-2] x [(prete-63).sup.2]+3.173
                         x (prete-63)-0.328 x (-0.323x [10.0.sup.-6]
                         x [(prete-63).sup.3]+3.000 x [10.0.sup.-4]
                         x [(prete-63).sup.2]-9.430 x [10.0.sup.-2]
                         x (prete-63)+11.263) x 6.25
55    DCPR             (PP x BW/38.5/63) x 0.9/0.6+(4.8 x 5.13/2.28)
                         x 6.25
56    DCPR             (PP x BW/38.5/63) x 1.2/0.6+(4.8 x 6.85/2.42)
                         x 6.25
57    [NP.sub.f]       ((1.486 x [10.0.sup.-4] x [Tp.sup.3]-4.247
                         x [10.0.sup.-2] x [Tp.sup.2]-3.173
                         x Tp-0.328) x (3 x (-0.323) x [10.0.sup.-6]
                         x [Tp.sup.2]+2 x 3.000 x [10.0.sup.-4]
                         x Tp-9.430 x [10.0.sup.-2]) +(3 x 1.486
                         x [10.0.sup.-4] x [Tp.sup.2]-2 x 4.247
                         x [10.0.sup.-2] x Tp-3.173) x (-0.323
                         x [10.0.sup.-6] x [Tp.sup.3]+3.000
                         x [10.0.sup.-4] x [Tp.sup.2]-9.430
                         x [10.0.sup.-2] x Tp+11.263)) x 6.25
58    [CP.sub.p]       DCPR/0.60
59    [NP.sub.milk]    1,000 x MY x (1.9+0.4 x [M.sub.fat])/100.0
60    [CP.sub.l]       (26.6+5.3 x [M.sub.fat]) x MY/0.65
61    [N.sub.out]      (CPi-[NP.sub.g]-[NP.sub.f]-[NP.sub.milk])/6.25
62    [P.sub.mg]       0.0156 x W+10.7 x DG
63    [P.sub.mg]       0.884+0.0500 x W+4.86x DG
64    [P.sub.mg]       7.2+0.0215 x W+6.02 x DG
65    [P.sub.mg]       13.5+0.00207 x W+8.29+DG
66    [P.sub.mg]       0.0143 x W/0.5
67    [P.sub.g]        DG x (1.2+(4.635 x [MW.sup.0.22])
                         x [W.sup.-0.22])
68    [P.sub.f]        (0.0047 x 1.23 x W) x 0.9
69    [P.sub.f]        (0.0047 x 1.23 x W) x 1.2
70    [P.sub.p]        [P.sub.f]/0.5
71    [P.sub.milk]     0.90 x FCM
72    [P.sub.l]        [P.sub.m]/0.5
73    [P.sub.out]      Pi-[P.sub.g]-[P.sub.f]-[P.sub.milk]
74    [Ca.sub.mg]      0.0213 x W+20.9 x DG
75    [Ca.sub.mg]      8.00+0.0367 x W+8.48DG
76    [Ca.sub.mg]      13.4+0.0184 x W+7.17 x DG
77    [Ca.sub.mg]      25.4+0.00092 x W+3.61 x DG
78    [Ca.sub.mg]      0.0154 x W/0.38
79    [Ca.sub.p]       (0.0078 x 1.23 x W/0.38) x 0.9
80    [Ca.sub.p]       (0.0078 x 1.23 x W/0.38) x 1.2
81    [Ca.sub.l]       (1.20 x FCM)/0.38
82    [VA.sub.mg]      0.0424 x W
83    [VA.sub.p]       0.0336 x W x 0.9
84    [VA.sub.l]       1.2 x MY

Eq.   Variable           Unit

1     mo
2     t
3     Tp
4     prete
5     lacte
6     MY                kg/d
7     [M.sub.fat]         %
8     FCM               kg/d
9     W                  kg
10    DG                kg/d
11    BW
12    WW
13    MW
14    DMI               kg/d
15    ME               Mcal/d
16    CP                 g/d
17    P                  g/d
18    Ca                 g/d
19    VA                 g/d
20    CPi                g/d
21    Pi                 g/d
22    W                  kg
23    W                  kg
24    W                  kg
25    DG                kg/d
26    DG                kg/d
27    DG                kg/d
28    [DMI.sub.mg]      kg/d
29    [DMI.sub.mg]      kg/d
30    [DMI.sub.mg]      kg/d
31    [DMI.sub.mg]      kg/d
32    [DMI.sub.p]       kg/d
33    [DMI.sub.p]       kg/d
34    [DMI.sub.l]       kg/d
35    [ME.sub.mg]      Mcal/d
36    [ME.sub.mg]      Mcal/d
37    [ME.sub.mg]      Mcal/d
38    [ME.sub.mg]      Mcal/d
39    [ME.sub.mg]      Mcal/d
40    [ME.sub.p]       Mcal/d
41    [ME.sub.p]       Mcal/d
42    [ME.sub.l]       Mcal/d
43    FN                 g/d
44    FN                 g/d
45    UN                 g/d
46    SP                 g/d
47    [NP.sub.m]         g/d
48    NPg                g/d
49    EP
50    EP
51    EP
52    [CP.sub.mg]        g/d
53    [CP.sub.mg]        g/d
54    PP                 g
55    DCPR               g/d
56    DCPR               g/d
57    [NP.sub.f]         g/d
58    [CP.sub.p]         g/d
59    [NP.sub.milk]      g/d
60    [CP.sub.l]         g/d
61    [N.sub.out]        g/d
62    [P.sub.mg]         g/d
63    [P.sub.mg]         g/d
64    [P.sub.mg]         g/d
65    [P.sub.mg]         g/d
66    [P.sub.mg]         g/d
67    [P.sub.g]          g/d
68    [P.sub.f]          g/d
69    [P.sub.f]          g/d
70    [P.sub.p]          g/d
71    [P.sub.milk]       g/d
72    [P.sub.l]          g/d
73    [P.sub.out]        g/d
74    [Ca.sub.mg]        g/d
75    [Ca.sub.mg]        g/d
76    [Ca.sub.mg]        g/d
77    [Ca.sub.mg]        g/d
78    [Ca.sub.mg]        g/d
79    [Ca.sub.p]         g/d
80    [Ca.sub.p]         g/d
81    [Ca.sub.l]         g/d
82    [VA.sub.mg]      1,000 IU/d
83    [VA.sub.p]       1,000 IU/d
84    [VA.sub.l]       1,000 IU/d

* Detailed information on these values and equations are given in JDC
(2002) and MAFF (1999).

Table 2. Equations of constraints for constructing optimal
ration model

Constraint

Dry matter intake (DMI)  [summation][a.sub.ij][X.sub.j] [less than
                           or equal to] [DMI.sub.mg]+[DMI.sub.p]+
                           [DMI.sub.l]
Metabolizable energy     [summation][a.sub.ij][X.sub.j] [less than
 requirement (ME)          or equal to] [DME.sub.mg]+ [DME.sub.p]+
                           [DME.sub.l]
Crude protein            [summation][a.sub.ij][X.sub.j] [greater
  requirement (CP)         than or equal to] [CP.sub.mg]+
                           [CP.sub.p]+[CP.sub.l]
Calcium                  [summation][a.sub.ij][X.sub.j] [greater
  requirement (Ca)         than or equal to] [Ca.sub.mg]+
                           [Ca.sub.p]+[Ca.sub.l]
Phosphate                [summation][a.sub.ij][X.sub.j] [greater
  requirement (P)          than or equal to] [P.sub.mg]+
                           [P.sub.p]+[P.sub.l]
Vitamin A                [summation][a.sub.ij][x.sub.j]
  requirement (VA)         [greater than or equal to] [VA.sub.mg]+
                           [VA.sub.p]+[VA.sub.l]

Table 3. Culling rate * ([p.sub.(i)]) (%) and simulated herd
composition (%)

Reproductive   Culling rate         Herd composition
  cycle        Hokkaido   Honshu    Hokkaido   Honshu

0                 --        --         25        27
1                 17        19         25        27
2                 29        33         20        22
3                 31        39         14        15
4                 39        46         10         9
5                 43        47          6        --
6                 52        53         --        --
7                 55        53         --        --
8                 56        71         --        --

* Detailed information is reported in LIAJ (2005).

Table 4. Definition of the number of female cattle in each cycle

Cycle   Period ([T.sub.i])                          Number of
                                                    females
                                                    ([N.sub.(i)])

0       Birth--1st conception                       [N.sub.(0)]
1       1st conception--1st lactation end           [N.sub.(1)]
2       1st lactation end--2nd lactation end        [N.sub.(2)]
3       2nd lactation end--3rd lactation end        [N.sub.(3)]
:       :                                           :
n-1     n-2th lactation end--n-1th lactation end    [N.sub.(n-1)]

n       n-1th lactation end--nth lactation end      [N.sub.(n)]

Cycle   Expression

0       [N.sub.0]
1       [N.sub.0](1-[p.sub.(0)])
2       [N.sub.0](1-[p.sub.(0)])(1-[p.sub.(1)])
3       [N.sub.0](1-[p.sub.(0)])(1-[p.sub.(1)])
          (1-[p.sub.(2)])
:       :
n-1     [N.sub.0](1-[p.sub.(0)])(1-[p.sub.(1)])
          (1-[p.sub.(2)]) - (1-p(n-2))
n       [N.sub.0](1-[p.sub.(0)])(1-[p.sub.(1)])
          (1-[p.sub.(2)]) - (1-p(n-2))(1-p(n-1))

Table 5. Structure of whole-farm LP-model

                                 Activities

                         Animal              Home-grown
Constraint             production          feed production

Land                                              1
  requirements
Housing                     1
  requirements

Labor               [a.sub.ij.sup.a]      [a.sub.ij.sup.a]
  requirements
Feeding             [a.sub.ij.sup.a]      [a.sub.ij.sup.a]
  requirements
Fertilizing         [a.sub.ij.sup.a]      [a.sub.ij.sup.a]
  requirements
  (Nitrogen)
Fertilizing         [a.sub.ij.sup.a]      [a.sub.ij.sup.a]
  requirements
  (Phosphorus)
Farm-level          [a.sub.ij.sup.a]
  nutrient
  balance
(Nitrogen)
Farm-level          [a.sub.ij.sup.a]
  nutrient
  balance
  (Phosphate)
Financial             Gross margin           Cost per ha
  coefficients

                               Activities

                       Purchase of
Constraint             fertilizer           Working hours

Land
  requirements
Housing
  requirements

Labor                                            -1
  requirements
Feeding
  requirements
Fertilizing         [a.sub.ij.sup.a]
  requirements
  (Nitrogen)
Fertilizing         [a.sub.ij.sup.a]
  requirements
  (Phosphorus)
Farm-level          [a.sub.ij.sup.a]
  nutrient
  balance
(Nitrogen)
Farm-level          [a.sub.ij.sup.a]
  nutrient
  balance
  (Phosphate)
Financial              Cost per ha           Cost per ha
  coefficients

                                 Activities

Constraint              Surplus N             Surplus P

Land
  requirements
Housing
  requirements

Labor
  requirements
Feeding
  requirements
Fertilizing
  requirements
  (Nitrogen)
Fertilizing
  requirements
  (Phosphorus)
Farm-level                 -1
  nutrient
  balance
(Nitrogen)
Farm-level                                       -1
  nutrient
  balance
  (Phosphate)
Financial               Cost per              Cost per
  coefficients             unit                 unit

                             Right-hand
Constraint                      side

Land                  [less than or equal to] Available
  requirements                    hectares
Housing               [less than or equal to] Available
  requirements                 cow place
Labor
  requirements                      =0
Feeding
  requirements          [less than or equal to] 0
Fertilizing
  requirements          [greater than or equal to] 0
  (Nitrogen)
Fertilizing
  requirements          [greater than or equal to] 0
  (Phosphorus)
Farm-level
  nutrient
  balance                           =0
(Nitrogen)
Farm-level
  nutrient
  balance                           =0
  (Phosphate)
Financial
  coefficients

* [a.sub.ij] is the technical coefficient that
relates activity i to constraint j.

Table 6. Equations * to estimate nitrogen and phosphorus contents
in animal production

Equation    Variable    Constraint       Equation and value

1           N[O.sub.1]  --               YBMY x [M.sub.pro]
                                           /6.38
2           P[O.sub.1]  --               YBMY x [M.sub.p]
3           N[O.sub.2]  --               EBP/6.25
4           P[O.sub.2]  W<56 kg          7.23W+21
5           P[O.sub.2]  56 kg100 kg         10.6W-0.00663
                                           [W.sup.2]-399

Equation      Unit

1              kg

2              g
3              kg
4              g
5              g
6              g

N[O.sub.1] is the amount of N in the yearly basis milk yield;
P[O.sub.1] is the amount of P in the yearly basis milk
yield; N[O.sub.2] is the amount of N in cattle body;
P[O.sub.2] is the amount of P in cattle body.

YBMY is the yearly basis milk yield; [M.sub.pro] and
[M.sub.P] are protein and P contents in milk; 6.38
is the nitrogen-protein conversion coefficient.

EBP = Empty body protein; EBW = Empty body weight;

SBW = Shrunk body weight; W = Body weight (W).

EBP = 0.2358EBW-0.00013EB[W.sup.2]-2.418; EBW =
0.891SBW; SBW = 0.94W

* These equations are given in ARC (1980) and NRC (2001).

Table 7. Dry matter (DM), metabolizable energy (ME),
crude protein (CP), calcium (Ca), phosphorus (P),
and vitamin A (VA) contained in each feed applied
to the structuring of optimal ration

                             Purchase feed

Ingredient           Corn      Barley      Bran     Beet pulp

DM (kg/kg)           0.87       0.88       0.87        0.87
ME (Mcal/kg)         3.09       2.84       2.41        2.44
CP (g/kg)           80        106        157         109
Ca (g/kg)            0.26       0.62       1.13        5.11
P (g/kg)             2.68       3.35       9.57        0.78
VA (1,000 IU/kg)     0.00       0.00       0.00        0.00
Prices (yen/kg)     39.18      44.74      32.17       49.58

                             Purchase feed

                   Soybean    Mineral    Alfalfa
Ingredient           cake      block     hay cube

DM (kg/kg)           0.88       0.10       0.89
ME (Mcal/kg)         2.95       0.00       1.79
CP (g/kg)          461          0        147
Ca (g/kg)            2.91      22.00      11.86
P (g/kg)             6.18      10.00       2.58
VA (1,000 IU/kg)     0.00       0.00      11.60
Prices (yen/kg)     68.90      42.50      51.04

                             Home-grown feed

                   Timothy    Alfalfa     Maize
Ingredient          silage     silage     silage

DM (kg/kg)           0.30       0.24       0.26
ME (Mcal/kg)         0.73       0.49       0.64
CP (g/kg)           46         39         21
Ca (g/kg)            1.47       4.04       0.74
P (g/kg)             0.90       0.65       0.71
VA (1,000 IU/kg)     4.80       3.87       4.43
Prices (yen/kg)      0.00       0.00       0.00

Table 8. Input variables for two situations (Hokkaido
and Honshu areas)

                                           Situation
Items
                                    Hokkaido      Honshu

Maximum allowance of                    5            4
  culling (parity)
Milk yield (kg/cow/year)            8,600        8,400
Milk price (yen/kg)                    73.6         89.1
Labor requirement for                  66          104
  feeding (hour/cow)
Available hectares (ha)
  Pasture                              51.1       12.9
  Maize                                12.8        5.5
Labor requirement for
  home-grown feed (hour/ha)
  Pasture                              21.2       42
  Maize                                35.2       51.5
Yield of home-grown feed
    (kg DM/ha)
  Pasture                           5,740      6,020
  Maize                            13,770     12,393
Home-grown feed production
  cost (a) (yen/ha)
  Pasture
    Timothy                        77,715     77,715
    Alfalfa                        55,577     55,577
  Maize                           161,670    151,775
Utilization of purchased               --    5% of MEicow
   roughage (Alfalfa hay cube)
Restriction for home-grown             --    [less than or
   feed utilization                            equal to] 45%
                                               of MEicow
Fixed cost (yen/cow)              164,093    157,956

Home-grown feed production cost is calculated as
feed production cost minus fertilizer cost, labor
cost, fixed cost, and land cost MAFF (2005c).

Table 9. Comparison between management guidelines and
predictions from farm-LP model

                                      Hokkaido

                            Management        Model
Items                        guideline     predictions

Number of cow                      8,800             89
Labor requirement (hour)           6,800          7,480
Labor cost (yen)              13,500,000      8,833,857
Feed cost (yen)               17,200,000     17,599,729
Revenue (yen)                 52,500,000     51,558,670
Total cost (yen)              45,000,000     41,217,320
Net profit (yen)               7,500,000     10,341,350
N surplus (kg/ha)                    --              76
P surplus (kg/ha)                    --              65

                                       Honshu

                            Management        Model
Items                        guideline     predictions

Number of cow                         40             43
Labor requirement (hour)           5,640          5,378
Labor cost (yen)               8,300,000      5,444,842
Feed cost (yen)               10,500,000      9,653,892
Revenue (yen)                 31,000,000     28,921,160
Total cost (yen)              25,000,000     22,013,330
Net profit (yen)               6,000,000      6,907,830
N surplus (kg/ha)                --                 159
P surplus (kg/ha)                --                  87
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