Swine finishing produces a large contribution of manure to nearby surface water and ground water in Jiulong upstream watershed, south Fujian Province, China. It is urgent to find a comprehensive, cost-effective way, not only to solve the manure pollution problem, but also to utilize the nutrients of manure for local farming. Gekou, a small hoggery village in the dense swine-farming core area of the upstream watershed, was selected as the study area. Mixed integer programming models based on uncertain interval numbers were employed to generate optimal whole farm plans for specialized hoggery. Emphasis was placed on discerning the most profitable ways to formulate hog feed rations, manure collection, manure storage, and manure application to achieve the maximum profit and the minimum pollution emission. Analyses were concentrated on ammonia emissions, excess total nitrogen and excess total phosphorus from manure operations, not only as nutrients applied to croplands, but also as pollutants to be minimized in compliance with environmental criteria. Three different hog feed rations, two alternative ways of collecting hog manure, and two alternative storage methods were combined with five alternatives for field application of manure to provide different combinations of hog feeding and manure-handling to be evaluated in the mixed integer programming models. Results indicated tradeoffs between economic goals and environmental goals, the latter being achieved only at some expense to farm net returns. The kaleyard and fishpond are recommended alternatives for field application of manure compared to three other alternatives.

Introduction

Manure from swine farms, a considerable source of agricultural pollution, brings extreme damage to the environment in Jiulong River watershed, Southeast China. Increasing public concerns about environmental protection are obliging farmers to be more careful about how manure is handled in order to reduce, or at least minimize, the environmental damage.

The objective of this study was to develop a decision-making aid for assessing and optimizing alternative manure-handling systems. The mixed integer programming (MIP) model, as a system optimization tool, is designed to evaluate and integrate the technical, environmental and economic impacts of alternative manure systems for swine farm operations. With the help of the MIP model we can get an optimal combination of farming practices that includes feed ration, collection of manure and land utilization in compliance with economic and environmental criteria.

Processes of swine finishing manure

The study area

The Jiulong River watershed is the second largest in Fujian Province, in the southeast of China. Livestock farming was rapidly increased in this watershed over the past twenty years. Pollution of surface water and ground water has been high because of manure emission. The Gekou swine finishing field, a small village in the upstream region, was chosen as the case study area. The total acreage of the test area is 0.69 km2, which includes forestry (62.20%), bamboo groove (5.71%), grape orchard (5.46%), paddy field (3.74%), kaleyard (1.30%), jujube orchard (4.15%), fishponds (1.42%), aerobic ponds (0.99%), and other uses (including villages, feedlots, road, etc. 15.03%). The locality of the study area and study hog farm is shown on Figure 1.

Alternatives related to pollutant emission

There are four processes that have effects on the level of polluted emissions, the feed process, manure collection, manure storage and manure application. Each process involves several alternative practices. The handling system is formed from the arrangement of these alternatives.

Three variant choices of the corn–soybean meal rations were offered as alternatives. The first is a common ration, corn-soybean feed only. The second variant includes synthetic lysine, one of the essential amino acids in the pig's diet. The added lysine can replace some of the crude protein in the ration and hence reduce nitrogen emissions in swine manure. The third variant combines exogenous phytase with the basic corn–soybean meal ration. The added phytase can reduce phosphorus requirements, and hence phosphorus emissions in swine manure. Each additive has been shown to increase feed efficiency in swine (De Lange, 1999).

Manure handling can be categorized into collection and storage processes. In this study, it was assumed that all manure would be handled in time, and that both processes should have two alternatives. The two manure collection alternatives are the collection by manual work through which solid and liquid manure can be sorted out respectively; and the collection by wash faucet, which always collects manure in liquid form. Two manure storage alternatives are storage in a rectangular, above-ground, open-topped earthen pit, and storage in a rectangular, above-ground, covered concrete tank. Both kinds of storage have a capacity sufficient for holding manure from 12 months' production (Stonehouse et al., 2002).

The manure is applied after anaerobic processing. Considering diverse cultivating on a farm, five manure application alternatives will be combined in the study area simultaneously, including flow into an aerobic pond, transferring into fishponds as a nutrient supply for a fishery, and manuring of crop fields, kaleyard, and orchard. Waste sewage from the field after manure application would be discharged into a nearby water body in compliance with emission control regulations.

Environmental impact and economical cost of alternatives

Each alternative has pre-determined operating costs (fuel, machinery repairs, labor), ownership costs (amortized capital outlays for machinery, equipment, building components), and with ammonia (NH4), total nitrogen (TN), and total phosphorus (TP) loss rates or pollution rates. For each of the three feed alternatives, two manure collection alternatives, two manure storage alternatives and five manure application alternatives, operating costs and depreciation of fixed assets become additive across alternatives.

The total capacity in this site is 11 000 swine per 180-day cycle. Two cycles per year were assumed. Sources of revenue include sales of finished swine, crops, fish, fruits, vegetables and even marsh gas. Costs were incurred for feeds, labor, and amortization of livestock housing capital outlays, which also incurred for land needs and for construction of ponds. To simplify the calculation of the increasing manure output as the swine grow from 10 kg to 100 kg, it was assumed that each swine averaged 0.45 m3 per100 d (Stonehouse et al., 2002).

The mixed integer programming model and formulation

The model

The MIP model is based on an interval number optimization because real situations are always under uncertainty. Binary variables have active levels bounded at the upper level of one and the lower level of zero, so that such variables are either included fully in the basic feasible solution or excluded entirely (Boland et al., 1998; Fleming et al., 1998; Huang et al., 2001). The function of MIP is:

formula
formula
formula
where A± {R± }m× n represents the matrix of technique coefficients, with mean intensity of pollution emission applying different practices per unit; B±{R±}m× 1, represents the environmental capacity of polluted emission; C± {R±}n represents profit coefficients of each alternative; X± {R± }n× 1, represents controllable decision variables of every alternative; f± represents the objective function (f±, C±, X±, A±, B± are interval numbers).

The processing of solutions to models (1) to (3) can be described as the following procedures. K1 former ordinal interval numbers of N in objective function are assumed negative, while K2 interval numbers are positive. C±j ≥ 0 (j = 1, 2, . . ., K1), and C±j < 0 (j = K1+1, K1+2, . . ., N). Then, the procedure of solving the upper maximum objective value is defined as,

formula
formula
where Sign represents signal function, equal to 1 when its independent variables are positive, equal to −1 when its independent variables are negative, or equal to 0 when its independent variables are zero. The values of x+j(j = 1, 2, . . ., K1), xj(j = K1+1, K1+2, . . ., N) and their associated objective upper maximum value f+ are calculated through the procedure of solving models (4)—(5). Furthermore, the value of xj (j = 1, 2, . . ., K1), x+j(j = K1+1,K1+ 2, . . ., N) and their correlated objective lower maximum value f are also worked out in the same way.

Formulation

We let x1, x2, x3 represent respectively alternatives of feed ration, x4, x5 represent alternatives of manure collection, x6, x7 represent two alternatives of manure storage, and x8, x9, x10, x11, x12 represent fixed acreages of land for manure application in a fixed land.

The objective function is determined while considering total profit of the whole farm, including the sale of swine, fish, fruit, crops, vegetables and methane with the costs of operating livestock farming and land agronomic cultivation.

formula
where Z = total profit; P = the number of swine; f0 = revenue per swine; c0 = depreciation of fixed assets; fi = revenue of each alternative method; and ci = cost of each alternative method.

The constraints focus on binary integer variables from x1 to x7, as

formula
For selecting only one of three alternatives of feed ration, only one of two alternatives of manure collection, and only one of two alternatives of manure storage, defined as
formula
Emissions of TN, TP, NH3 during each alternative of handling and application are limited under a permission amount (PERM)j in compliance with environmental quality criteria, defined as
formula
where aij, is the loss amount of each nutrient or pollutant per unit; PERMj = the permitted amount of each nutrient or pollutant (TN, TP, or NH3). The total available land area is 623.07 acres except for forest land, and the total applied area should be over 467.30 acres, defined as
formula
Each application of manure should be over 20.0 acres, Assuming cultivating diversely on a farm, five manure application alternatives will be evaluated in the study area simultaneously, as
formula

Data for parameters in MIP

A set of emissions of nutrients or pollutants from a swine farm was modeled according to actual case situations by using field sampling and lab analysis. Secondary data sources relied upon market prices. The permission amount of pollutant emission was determined on the basis of the integrated emission criteria of pollutants from hog farming (State Environmental Protection Administration of China, 2001).

Results

Optimal interval numbers of variables were ascertained after calculation of the models (6) to (11) using computer language (Lingo 4.0). The upper values are: x1 = 1, x2 = 0, x3 = 0, x4 = 0, x5 = 1, x6 = 0, x7 = 1, x8 = 20.00 acres, x9 = 102.10 acres, x10 = 20.00 acres, x11 = 20.00 acres, x12 = 308.75 acres. The upper objective value, was Z = 7 788 635 ¥/a− 1. Therefore, an optimal combination of farming practices would include corn-soybean ration, collection of manure by wash faucet, storage in an open-topped earthen pit, an aerobic pond of 20.00 acres, a fishpond of 102.10 acres, crop fields of 20.00 acres, an orchard of 20.00 acres, and a kaleyard of 308.75 acres.

The lower values can be described as x1 = 1, x2 = 0, x3 = 0, x4 = 1, x5 = 0, x6 = 0, x7 = 1, x8 = 20.00 acres, x9 = 51.02 acres, x10 = 20.00 acres, x11 = 115.28 acres, x12 = 261.00 acres. The objective value under this scenario is, Z = 5 232 524 ¥/a. This included a combination of corn-soybean ration, collection of manure by manure work, storage in an open-topped earthen pit, an aerobic pond of 20.00 acres, a fishpond of 51.02 acres, crop fields of 20.00 acres, an orchard of 115.28 acres, and a kaleyard of 261.00 acres.

Discussion

These results can be viewed alternatively by focusing on the optimal solutions under the comprehensive economics and environmental criteria. (1) Synthetic lysine ration and exogenous phytase ration has much more cost than corn-soybean ration, but these two rations can reduce TN or TP emissions in swine manure; (2) Different collection methods have different cost-effectives for compliance with economic and environmental criteria; (3) Storage in a covered concrete tank will comply with both environmental and technical demands; (4) Kaleyards and fishponds are preferentially recommended when applying the manure on limited land; and (5) as well as these economic-environmental tradeoffs, some differences in selected feed/manure-handling components were evident among the solutions to meet environmental criteria.

Conclusion and suggestion

There are multiple ways for livestock producers to feed their swine or handle livestock manure both form an economic and society-wide environmental protection perspective. Mixed integer programming models based on interval numbers under uncertainty are very useful because they identify the best way to feed livestock or manure operation systems.

The results indicate that the current land use patterns in the Gekou hoggery village need to be improved. To achieve a reasonable and applicable solution, the decision maker can integrate the findings of the model with his experience and other relevant information. Using the generated program as a tool can guarantee a maximized economic output within the limits of pollution controls.

Acknowledgements

Most of the work in this paper was supported financially by the Key Scientific Project of the Ten-Year Plan of Fujian Province of China (No. 2002H009).

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