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,*,a
a Dep. of Crop and Soil Sci., 721 Bradfield Hall, Cornell Univ., Ithaca, NY 14853-1901
b USDA-ARS Pasture Syst. and Watershed Manage. Res. Unit, Bldg. 3702, Curtin Rd., University Park, PA 16802-3702
c Dep. of Agric., Resour., and Managerial Econ., 453 Warren Hall, Cornell Univ., Ithaca, NY 14853-7801
* Corresponding author (eg46{at}cornell.edu)
Received for publication February 23, 2001.
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ABSTRACT |
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 TOPNOTES ABSTRACT INTRODUCTIONMODEL DEVELOPMENTMODEL APPLICATION AND EVALUATIONCONCLUSIONS AND MODEL EVALUATIONREFERENCES |
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Abbreviations: NMP, nutrient management plan • STP, soil-test phosphorus
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INTRODUCTION |
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TOPNOTESABSTRACTINTRODUCTIONMODEL DEVELOPMENTMODEL APPLICATION AND EVALUATIONCONCLUSIONS AND MODEL EVALUATIONREFERENCES |
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A more stringent regulatory environment places an even higher premium on well-organized farm plans for managing nutrients on the farm. Several researchers have studied the relationship between nutrient management and surface water quality (Lanyon, 1994; Bacon et al., 1990), relating nutrient flow from applied manure to soil properties and crop type. Although nitrates are very much a concern on New York dairy farms and current permitting rules are focused on nitrates, P has become an increasingly important concern due to eutrophication of surface waters. Lemunyon and Gilbert (1993) suggested the use of the Phosphorus Site Index (P-Index) to evaluate the risk of P loss to surface waters. Since then, several U.S. states have developed P-Indices as indicators of P pollution potential. Phosphorus Site Indices are empirical indices that assess the risk of environmental P pollution by calculating factors related to fields' potential P export, accounting for transport and source potentials. Field characteristics such as distance to stream, presence of buffer, potential soil erosion, and flood frequency are used to estimate the potential transport of source P. Sources of P are estimated by accounting for total amount of P applied by commercial fertilizers and manure, and risk of pollution also depends on time and method of P application. Operators of large dairy farms with high animal densities can use such indices to confront the management challenges associated with manure handling and utilization. Although the maximization of net farm income is a critically important farming objective, environmental management objectives are also of paramount importance in farm planning and decision-making. Nutrient management plans that incorporate a P-Index can be useful tools for identifying management options that reduce the environmental impact of dairy farms.
Recommendations regarding manure and fertilizer application made by NMPs must be suitable to a wide variety of farming operations and be useful to planners and managers possessing a wide range of knowledge and expertise. Specific recommendations for each planning scenario should be available. The development of decision support systems can assist in the implementation of better management practices on dairy farms. Schmit (1994) characterized a dairy farm as a production system comprised of interdependent components where a change in one of the components can have consequences throughout the entire system. Whole farm–level decision-making with the purpose of finding the optimal balance between production and environmental objectives under a set of constraints can help to resolve seemingly disparate goals. Management decisions can be made or assisted using as a base the solutions obtained through mathematical programming, which can provide a useful economic representation of the whole farm for testing various issues or policy proposals (Hazell and Norton, 1986).
Mathematical programming has been widely used for farm planning and optimization of net profits. Haith and Atkinson (1977) focused on farm-level nutrient management, issuing the optimization of a farm's overall nutrient budget. Tozer and Stokes (2001) used multiple-objective programming to reduce nutrient excretion from dairy cows (Bos taurus) by reducing the excretion of undesirable nutrients and costs of rations. This multiple-objective programming accounts for environmental problems related to nutrient excreted and transported to waters and recommends feeding formulations. Some studies have focused on optimal manure-disposal programs (Coote, 1973; Schmit, 1994; Dodd et al., 1975; McKenna and Clark, 1970), focusing on N or P loading to surficial waters, using several empirical or theoretical models to estimate impacts of legislation or changes in dairy management on water pollution. Hanchar et al. (1998) developed a linear programming model for examining farm profitability under resource constraints and under restrictions to environmental pollution due to P application with manure imposed by use of the P-Index. This was one of the first attempts to include an environmental and management indicator centered on the P-Index in an optimization model. The P-Index was used as a constraint to the farm income optimization process. The results allowed an assessment of the effects of P restrictions on farm profitability.
Economic analysis of manure handling and management related to water quality impacts is not new. In a small watershed in central New York, where dairy farming was the main activity, Schaffer et al. (1989) quantified the losses of soil and nutrients and analyzed the system with respect to economic and environmental impacts of controlling nutrient losses in the watershed. These authors also used linear programming to optimize returns and income related to manure-handling systems.
Rotz et al. (1989) developed the DAFOSYM model, which simulates the growth, harvest, storage, and utilization of alfalfa (Medicago sativa L.) and corn (Zea mays L.) on a dairy farm over a 25-yr period. Borton et al. (1995) expanded this model by including submodels for manure production, collection, storage, and application to cropland. These integrated models provided a tool for evaluating and comparing the long-term performance and economics of several manure systems for dairy farms. Although useful for long-term evaluation of farm systems, this modeling tool was not developed for helping with on-farm manure allocation decisions. It accounts mainly for cost and labor variables but does not include an assessment of environmental pollution potential based on P-Index.
Levins et al. (1996) developed the Manure Applicator Planner (MAP), which is a computer software used to help develop manure application plans. The software uses linear programming for determining the most cost-effective manure application method and rates for each field. Concerned with water quality issues related to manure management, this proposed tool includes constraints that limit excess nutrient application. Although nutrient application can be limited, no environmental indicator is used for assessing potential pollution.
The objectives of this study are to (i) develop a multiple-criteria programming approach for environmental and economic optimization of on-farm manure allocation, (ii) test the results of the automated approach against plans developed manually by planners to determine the need for a tool of this kind, and (iii) assess the usefulness of the tool for general farm planning. The model intends to optimize manure allocation in time and space to meet crop nutrient requirements, minimize costs, and lower environmental pollution risks using the P-Index as an indicator of P pollution potential.
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MODEL DEVELOPMENT |
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TOPNOTESABSTRACTINTRODUCTIONMODEL DEVELOPMENTMODEL APPLICATION AND EVALUATIONCONCLUSIONS AND MODEL EVALUATIONREFERENCES |
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The objectives to be optimized by this model are average P-Index weighted by area; standard deviation of these P-Index values; and cost of commercial fertilization and of manure handling, storage, and application. The P-Index is used as an indicator of potential pollution caused by P losses to stream waters and is weighted by area. The standard deviation of the P-Index is optimized to prevent the model from recommending massive applications of manure in only a few fields. Cost evaluation is part of the objective function because costs should be minimized if the farm is to be viable in the long run. In all three cases, minimal values for these objectives are optimal. The P-Index used in developing this model is the New York P-Index (Bryant et al., 2000), but the model can be adapted for use with any of the P-Indices developed after Lemunyon and Gilbert (1993).
The P-Indices (PI) are calculated for each field after estimating a P source factor (PSFf) and a P transport factor (PTFf) by:
 | [1] |
The P-Index source factor estimates the amount of P subject to transport from each field, accounting for the soil-test P (STP), P added by manure applications, and P added by fertilizer applications. In accounting for P added by manure or fertilizer, factors considered are rate, method, and time of P application. The P-Index transport factor accounts for risk of P in each field being transported to water bodies and considers distance to water bodies, drainage, and flooding frequency.
Although the variables related to the transport factor can be modified by implementing conservation management practices, for the purpose of this study, they are calculated for each field and are considered constants. The management variables associated with the source factor are the main variables that may be varied to affect the risk of P loss. Therefore, activities that can be varied to affect optimization objectives are manure application on fields, differentiated by different application methods and timing on arable land throughout the year; application of commercial fertilizers, also differentiated by different application methods and timing; and presence or absence of manure storage facilities, which affect the flexibility with respect to timing of manure applications. All of these activities are management variables in the New York P-Index and commonly occur in P-Indices developed by other U.S. states.
The model requires the specification of a set of input variables or parameters for each planning situation and associated management factors that are used to structure the optimization process. Input variables affecting the objective functions are length of planning horizon, number of cows in the dairy herd, proportion of manure produced on the farm that can be collected, distance from manure storage facilities to individual fields, field's STP values, P-Index transport factor for each field, cost of manure storage, cost of equipment operation used for manure spreading, labor requirements, cost of labor, cost of machinery and equipment operation at the barn or treatment plant, cost of fertilizers, and cost of fertilizer application.
Objective Function
The objective function consists of a set of measures of the distance that the optimal solution is from the ideal point (i.e., the minimum value) for each of three subfunctions to be minimized: the mean P-Index across fields weighted by area [Z1(x)]; the standard deviation of the P-Index [Z2(x)]; and the total cost of manure handling, storage, and fertilization [Z3(x)]. As used by Alocilja (1998), a distance function [dS(x)], which is the difference between the objective function and its ideal relative minimum value (ZSmin), may be written as:
 | [2] |
These distance functions are normalized by the introduction of undesirable points ZSmax, which are the maximum values for each of the subfunctions. The expression for a normalized distance function is given as (Alocilja, 1998):
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Each of the subfunctions can be weighted such that optimization may be tailored for meeting the purpose of the planning process. The sum of the weighted distances gives a composite distance function Z:
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The solution is obtained by solving for Z in the nonlinear programming Eq. [4], which is the objective function to be minimized.
Manure Management Constraint
Part of the total manure produced by all cows on the farm is collected, and part is not. The proportion of manure produced that can be collected is mainly that part excreted in the barn, and that manure has to be managed. For each time period, the total manure collected can be estimated by:
 | [5] |
Mcolt = manure produced and collected during time period t (m3)
a = animal types 1 to i (animal types include milking cows, dry cows, heifers, and calves)
t = time periods 1 to k
Nt = number of cows on the farm during time period t
Mprodat = manure produced by one cow during time period t by animal type a (m3 d-1)
Tt = length of the time period t (days)
pt = proportion of manure produced that is collected on the farm duringtime period t
The manure available for field application in each time period (Mavt) is the sum of the total manure collected during the time period (Mcolt) plus the manure that was in storage at the end of the previous time period [MS(t-1)]:
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Total manure applied on the farm yearly must be equal to the total manure collected on the farm:
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The total manure applied during a time period (Mat) is the sum of the total manure applied during that time period in each field using any application method (Mafm):
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Total manure in storage at the end of each time period (MSt) is the difference between the manure available in the current time period and the total manure applied in this time period:
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Manure storage facilities, if available, must be at the same capacity at the end of the entire planning period (MSt=k) as they were at the beginning of that period (MSt=0):
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The total volume of manure in storage during each time period should be less than or equal to the maximum storage capacity (MSC) (m3):
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Manure application may not be allowed in some combinations of fields and time periods because crop growth stage would prevent it; therefore, a matrix is used to regulate permissible application conditions (Haith and Atkinson, 1977):
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Additionally, some application methods can be inappropriate for some time periods. For example, it may not be possible to incorporate manure during winter periods when the ground is frozen. These combinations should be restricted using a similar procedure:
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Nutrient Requirements for Crops Constraint
Crop, crop sequence, and soil nutrient status determine nutrient needs on the farm. For modeling purposes, one requirement is that all crop nutrients necessary for the crop or crop sequence to be grown during the time being evaluated must be met and must come either from the manure applied or from commercial fertilizers. However, not all nutrients added by manure application during the year should be considered available for crop usage. Part of the manure will be added after the time when crops need it. Therefore, only the amount of nutrients in the manure applied from the time when the soil samples were taken until the planting period is considered. If that amount is not enough to meet crop nutrient recommendations, fertilizers must be applied. When N requirements are not met by manure allocations, commercial fertilizer application satisfies the balance of the requirement as follows:
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In the optimization process, commercial fertilizer application is minimized because of the costs associated with purchase and application. However, some purchase may be necessary because satisfying total N requirement with manure may be limited by the companion objective to lower the mean and variance of the P-Index. Although the need for this model arises out of the commonly occurring situation in which P is present or is being applied in excess of crop needs, the model does account for the total amount of P applied and compares that to the amount of P needed to meet crop recommendations. Potassium is treated similarly to N and P. Additionally, maximum amounts of allowable nutrients to be applied in each field can be specified as a constraint.
Labor Requirements and Cost Calculation
Labor requirements for handling and applying manure are determined by the method and location of manure application and can be calculated by (adapted from Coote, 1973):
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Lmht = labor used for manure handling during time period t (h)
Lmb = labor requirements for in-barn manure handling (h m-3)
Maft = manure applied on field f during time period t (m3 ha-1)
Lmt = labor requirement for transporting manure from barn to fields during time period t (h m-3 km-1)
Df = distance of application from the barn to field f (km)
Lamm = labor necessary for applying manure using method m (h m-3)
The labor required for manure handling is tracked for the sole purpose of calculating labor costs. No labor constraints, such as availability, have been included in this model. Although a complete accounting for manure-handling costs might include annual depreciation allowances for equipment and facilities, the model only takes into account costs that pertain to the storage, transportation, and application of manure. These are the fixed and variable costs of storage and the costs of labor and tractor operation. The costs of handling and applying manure are calculated by (adapted from Coote, 1973):
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Cost of fertilization to meet crop recommendations using commercial fertilizers includes both fertilizer and application costs, which are calculated by Eq. [17] and [18]:
 | [18] |
Costs of manure storage (CS) are calculated by:
 | [19] |
Solving the objective function under these constraints will generate recommendations for manure allocation for each field and time period, recommendations for fertilizer application, and calculation of cost and labor associated with these recommendations. The recommendations will be accompanied by an estimate of the P pollution potential, as estimated by the P-Index, and by an indication of the variability of these P-Indices among fields.
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MODEL APPLICATION AND EVALUATION |
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TOPNOTESABSTRACTINTRODUCTIONMODEL DEVELOPMENTMODEL APPLICATION AND EVALUATIONCONCLUSIONS AND MODEL EVALUATIONREFERENCES |
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The P pollution potential was evaluated according to the most recent draft of the New York State Phosphorus Site Index, which is still in development (Bryant et al., 2000). This index is determined for each field and has two main components: a P source factor (PSFf) and a P transport factor (PTFf). The variables related to PTFf are physical characteristics of the field that were predetermined. The PTFf variables were treated as constants, whereas the variables associated with nutrient management in the PSFf are those subject to optimization. The PSFf can be calculated using Eq. [20] to [23]. The values for PSFf result from the addition of three functions related to STP, P fertilizer application, and organic P applications, respectively. The STP factor (PSTf) is calculated by Eq. [21]. The multiplication of factors for P application rate, time of application, and method of application solve the functions related to P application for individual applications. The values for each of these factors are defined in the P-Index and specified in the next paragraphs among the description of variables.
 | [20] |
PFRf = P fertilizer rate factor for field f
PFMf = P fertilizer method factor on field f and is defined in the New York P-Index as: 0.2 if fertilizer is injected or subsurface-banded 0.7 if fertilizer is broadcasted and incorporated 0.8 if fertilizer is surface-applied 1.0 if fertilizer is surface-applied on frozen, snow-covered or saturated ground
PFTt = P fertilizer timing factor, which is defined in the New York P-Index as: 0.4 if fertilizer is applied May through August 0.7 if fertilizer is applied September through October 0.9 if fertilizer is applied November through January 1.0 if fertilizer is applied February through April
PMRftm = organic P application rate factor for field f during time period t using method m
PMMm = organic P method factor for method m, which has the same values as PFMf
PMTt = organic P timing factor, which may have the same values as PFTt
 | [21] |
 | [22] |
 | [23] |
Nutrients available for crop use derived from manure applications during the current crop year are counted as being those supplied by manure application between soil testing in October and the planting period in May. When the amount of nutrients supplied by manure application is not enough to supply recommended crop requirements according to Cornell Recommends (Cornell Coop. Ext., 1999), commercial fertilizers supply the remaining nutrients. Fertilizers are applied in May (P fertilizer timing factor is 0.4) by broadcasting and incorporation in cornfields and by surface application in pastures (P fertilizer application method factors are 0.2 and 0.8, respectively, for these two methods of application). No restrictions were made with respect to the total amount of manure application; rather, it was preferred that all manure produced on the farm be managed within the farm, without export of manure. Due to crop growth characteristics, manure could not be applied to cornfields during June through September.
An economic characterization of the farm was not available, so representative values for New York State were used and are shown in Table 2. Respective sources of information are reported; values presented without a source were not available in published literature and were defined by consulting several local extension agents.
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Table 3 shows the recommended manure allocation, in terms of quantity of manure to apply monthly in each field, and the resulting P-Index in each field based on the annual application rates recommended in the NMP. The annual application rates were kept as recommended (Table 1). However, because the NMP does not specify monthly manure application rates, the optimization model was used for optimizing monthly manure applications considering the broad time periods suggested by the planner. This resulting scenario was assumed as the current practice and produced a mean P-Index weighted by field area of 64, with a standard deviation of the P-Index of 32 units. The cost of manure allocation according to this NMP was $146570.00.
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Some fields with low STP and low P transport factor (PTFf), which were planned to receive smaller amounts of manure in the original NMP, are receiving more manure in the optimized scenario without excessive elevation of the P-Index, as is the case of Fields 40 and 41. In the optimization results, fields such as 48 and 49, which have low STP but high transport potential, received less manure than in the original NMP, keeping the P-Index lower in comparison with the original NMP. Fields 12 and 13, which already had a high STP and high transport potential, did not receive any manure in the optimized scenario. According to the optimized recommendation, Fields 40, 41, 26, 30, and 8, which are located closer to the barns and have low STP, are receiving larger amounts of manure than other fields due to lower transportation costs.
In the scenario where manure allocation was optimized in both time and space, all nutrient crop requirements were satisfied, and fertilizer application (22 kg N ha-1) was recommended on Fields 12 and 13. Manure applications, which contain P, were not recommended on these and other fields having high STP and a high P-Index transport factor. Otherwise, manure applications supplied all of the nutrients required for the corn or pastures. Compared with crop requirements (Cornell Coop. Ext., 1999), application of excess of nutrients is occurring because the model was not restricted by a maximum nutrient status. Rather, the model was set to allocate the total amount of manure available to the fields that would result in the smallest increase in risk of P pollution. Maximum nutrient applications could be imposed for each field, but this procedure might result in total applications being smaller than the total manure available, thereby requiring that manure be exported from the farm.
As the three subfunctions of the composite objective function received the same weight, none of the individual subfunctions reached its minimum. Changes in the importance among these subfunctions would produce different results. For example, with slightly heavier weighting of the economic subfunction, costs could be made equal to or lower than the costs associated with the original NMP, and some slightly higher mean P-Index and/or higher variability of the P-Index would result.
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CONCLUSIONS AND MODEL EVALUATION |
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TOPNOTESABSTRACTINTRODUCTIONMODEL DEVELOPMENTMODEL APPLICATION AND EVALUATIONCONCLUSIONS AND MODEL EVALUATIONREFERENCES |
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Including the standard deviation of the P-Index required that the model be nonlinear, bringing with it the disadvantage of being harder to solve. However, including the standard deviation of the P-Index was necessary to avoid the recommendation of very high application rates of manure in small fields with low transport potential, as would happen if only the weighted mean of the P-Index were to be considered. Given the complexity of the process of solving nonlinear mathematical equations, there are several local optima, and the commercially available solver engines cannot define a single global optimum. Therefore, their use requires input from the planner in the form of suggesting possible solutions as starting points to find better solutions. For this reason, this particular model is not user friendly and would not serve individual producers and planners well in its present form. Although the approach is valid and a tool of this kind is needed, this specific model is better used as a research tool.
Some suggestions for possible variations in implementing the model are to include labor restrictions and tailor the economic parameters for each farm and region. Labor availability, its cost, and seasonality of labor use are important issues on dairy farms. Therefore, including labor availability as a constraint in the model would likely result in a more realistic scenario for a specific farm.
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ACKNOWLEDGMENTS |
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NOTES |
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TOPNOTESABSTRACTINTRODUCTIONMODEL DEVELOPMENTMODEL APPLICATION AND EVALUATIONCONCLUSIONS AND MODEL EVALUATIONREFERENCES |
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sponsored by CAPES (Brazilian Federal Agency for Post-Graduate Education) 
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REFERENCES |
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TOPNOTESABSTRACTINTRODUCTIONMODEL DEVELOPMENTMODEL APPLICATION AND EVALUATIONCONCLUSIONS AND MODEL EVALUATIONREFERENCES |
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This article has been cited by other articles:
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  E. Giasson, R. B. Bryant, and N. L. Bills Optimization of Phosphorus Index and Costs of Manure Management on a New York Dairy Farm Agron. J., July 1, 2003; 95(4): 987 - 993. [Abstract] [Full Text] [PDF]
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