BING ZHANG et al: AN OPTIMIZATION MODEL OF CROP’S PLANTING STRUCTURE USING LINEAR . . .
An Optimization Model of Crop’s Planting Structure using Linear Programming
Bing Zhang 1, 2*
1 Research Center of Fluid Machinery Engineering and Technology Jiangsu University Zhenjiang , Jiangsu, China 2 School of Electrical and Photo electronic Engineering ChangZhou Institute of Technology ChangZhou, Jiangsu , China
Abstract — The optimization box of Matlab was used in agricultural planting programming in this paper, and the optimization problem of crop’s planting structure was solved successfully. First we set up a mathematical model, then determined some constraints which affect the programming and lastly solved the problem by function “Fmincon” in Matlab. Results show that this method of optimizing planting structure can help improve profit and increase farmers’ income.
Keywords-linear programming; planting structure; optimzation
I. INTRODUCTION III. OPTIMIZATION PROBLEMS DEFINITION At present, China's agriculture is transforming from traditional agriculture to modern agriculture, but the family The optimization problem is from all possible solutions of independent type agriculture is dominated by the to achieve optimal target selected the most reasonable, traditional management mode, planting crops and how much (maximum or minimum) scheme, that is the optimal is still by the habit determines, the allocation of resources scheme, the optimal scheme is search method for depends on subjective. The farmer to market economy, to optimization problems. By the definition of mathematical optimize the understanding of crop planting structure is not methods are as follows. deep, the limited resources for maximum benefit without A point in n-dimensional Euclidean space E n , complete understanding. From the development trend of f ()x g ()(xi 1,2,, m )hxi()( m 1,, p ) world agriculture, agriculture is not only to ensure sufficient , i , i for a given food production, it is more important to the optimization of n element function, the optimization problem is a general crop planting structure, minimizing the cost, at the same time formulation is in the constraint conditions: under to meet the diversified needs of agricultural human. gi (xi ) 0, 1,2, , m and hxi () 0, i m 1,, p, for Especially important is how to guarantee the sustainable f ()x development of agriculture, how in the limited resource vector function, make the minimal ( or maximal ). conditions, agricultural production efficiency improved step Referred to here f ()x is as the target function, gxi () 0 is by step, is also the planting structure optimization problem, known as the inequality constraints, hxi () 0is called the the linear programming method is used to solve the problem T . equality constraints, x xxx123,,,, xn and is referred Linear programming is a mathematical approach to to as design variables and decision variables. The optimize the management of people, it mainly studies in optimization problem for short is resource allocation, allocation scheme can not only meet the mi nfx ( ) basic requirements of how various aspects, but also can obtain good economic benefit and social benefit, provide st. . gi ( x ) 0, i 1,2, , m (1) service for the scientific decision. hxi i m 1, p II. OPTIMIZATION THEORY To solve the optimization problem of type (1), is the requirement of type (1) for the global optimal solution, but in Optimization theory is a branch of Applied Mathematics, general, we often can find out a local optimal solution of it. is essentially the extreme of function. In twentieth Century 30 at the end of 1980s, due to the rapid development of the IV. GREAT PROBLEMS TRANSFORMATION military and industry, put forward to solve the problem of a The definition of optimization problems is given only series of optimization problems, and using the method of standard for the minimum definition, but the linear differential classical and variation law cannot solve, in many scholars' efforts, gradually developed and formed some new programming model to practical problems is varied, can use mathematical methods, namely the method of optimization. some methods they transformed into equivalent standard. Requirements such as the maximum of the objective
DOI 10.5013/IJSSST.a.17.20.16 16.1 ISSN: 1473-804x online, 1473-8031 print BING ZHANG et al: AN OPTIMIZATION MODEL OF CROP’S PLANTING STRUCTURE USING LINEAR . . .
function zfx () , as long as the target function of the requirements under the conditions of limited resources, determined for each crop planting area, to make the maximum value for the minimum of the objective function maximum profit. can be, i.e. maxz minf ( x ) . TABLE 1 PLANTING INPUT-OUTPUT
V. OPTIMIZATION MODEL ESTABLISHMENT chemical Emplo water ( profit fertilizer, Using fmincon function in MatLab can be very y-ment ton) convenient for solving constrained optimization problems. pesticide ( kg ) The known constraints type (2), the minimal solution of the Grain 10 22 100 200 value function. Vegetable 25 33 150 1000 cx() 0 Tea garden 30 25 250 800 ceq() x 0 Orchard 30 44 200 650 Ax* b Available (2) 553000 690000 3320000 Aeq* x beq resources lb x ub VIII. THE ESTABLISHMENT OF MODEL Among them, x,,bbeqlb , and ub are vector; A and The total profit: Aeq is the matrix; cx() and ceq() x is the return value for INCOME 200* x1234 1000* x 800* x 650* x , the vector function; f ()x is a return value for the scalar Of which: : Grain planting area ; x : vegetable function; cx(), ceqx () and f ()x can be a nonlinear function. x1 2
planting area; x3 : Tea cultivation area ; x4 : Orchard VI. EMPIRICAL ANALYSIS planting area; INCOME ：The total profit. Zhenjiang City Jingkou District belongs to the The conditions of constrained resource: subtropical monsoon climate, the annual average (1) Land restrictions: the total planting area is 22137 mu, temperature of 15.5 degrees C, frost free period of 237.2 i.e. xxxx1234 22137 days, 2057.2 hours of sunshine hours, rainfall of 1070 mm. (2)Labor restrictions: growing three crops of labor and can Located in the South Bank of the Yangtze River not exceed the allowable value of 553000 works, downstream, the ancient canal to the East, latitude 32 i.e.10*xxxx1234 25* 30* 30 * 553000 degrees 10'-32 degrees 15', longitude 119 degrees 26'-119 (3) The water restrictions: growing three crops in the water degrees 38'. A hilly area and the Yangtze River alluvial and can not exceed the allowable value of 690000 tons, plain area, the terrain is high in southeast, northwest during i.e. 22*xx123 33* 25* xx 44* 4 690000 low, intermediate and zone along the flat terrain, slope hilly (4) Fertilizer, pesticide restrictions: growing three crops with region interspersed, grain, vegetable fields, tea plantations, a fertilizer and medicine and can not exceed the allowable value of total area of 22137 mu of orchard planting. 3320000 work, i.e.100*xx1234 150* 250* x 200* x 3320000 VII. PUT FORWARD PROBLEMS (5) The non NULL constraint, i.e. xxxx1234,,, 0 Jingkou zone climate and geographical environment In summary, our problem is in the (1) ~ (5) of the constraint are suitable for these four crops, how to optimize plant conditions, to work out the optimal x ,,,xxx ,in order to structure, an important constraint condition is limited 1234 make the maximum. Therefore, the mathematical model of the available resources. To make the maximum total profit, problem is as follows: hand hope planted high profit crops; but on the other hand, maxINCOME max(200 * x1234 1000* x 800* x 650* x ) high profit crops resources needed is much also, bringing xx costs, that could reduce the total profit. So the essence of As a constraint: optimizing planting structure is in a resource constrained xxxx123422137 conditions, the constrained optimization problem to seek the 10*xxxx1234 25* 30* 30* 553000 maximum profit, the available MATLAB optimization toolbox to solve. 22*xx123 33* 25* xx 44* 4 690000 (3) Because of the influence of crop economic profit by 100*xx 150* 250* x 200* x 3320000 policy, market, natural conditions of the larger, in different 12 3 4 time and different crop resources also have the difference, xxxx1234,,, 0 the data in the table is obtained in a simple research foundation, and the purpose is to clarify a planting structure To solve the model optimization method for obtaining the maximum profit. Data In accordance with the standard form, the original problem is show that the number of each type of crops per acre required transformed into: resources and profits and resources available, the
DOI 10.5013/IJSSST.a.17.20.16 16.2 ISSN: 1473-804x online, 1473-8031 print BING ZHANG et al: AN OPTIMIZATION MODEL OF CROP’S PLANTING STRUCTURE USING LINEAR . . .
Through the comparison of planting structure can be minf (xxxxx ) min( 200*1234 1000* 800* 650* ) xx found using linear programming to determine the most fully Ax* b rational use of existing resources, and making profits have greatly improved. As a constraint: Aeq* x beq (4) lb x ub X CONCLUSIONS Among them: Linear programming energy distribution for energy, 10 25 30 30 553000 make the optimal choice when empty, in the energy supply is becoming increasingly tense situation becomes more and A 22 33 25 44 b 690000 more important. There are many methods to solve the linear 100 150 250 200 3320000 Aeq 1111 , , , programming model of MATLAB, compared with other x 22137 methods, it has high calculation speed, modeling is 1 0 relatively easy, rich features such as scalability, but also can x2 0 22137 x ub avoid some tedious programming. According to the Jiangsu lb x3 0 22137 area climate characteristics and plant species, mathematical beq 22137 x 22137 model is established by linear programming method of 4 , 0 , (5) Using the MATLAB optimization to solve the constrained Jingkou District of Zhenjiang City, planting a detailed optimization function in fmincon toolbox, the results are as location, quantitative research, finally choose a planting follows: structure scheme, this scheme makes full use of local advantages of water, heat and other resources. But in xx122704, 18086, xx 34 1347, 0 , the total profit of practical application should consider many factors, such as 19704000. the change of the market, change the cost and profit; the IX PREDICTED VALUE COMPARISON WITH THE premise to ensure the ecological balance of the grain and TRUE VALUE grain under the protection of planting structure optimization At present, Jingkou District with cropland area of 15456 mu, etc.. vegetable area of 6281 acres, 100 acres of tea plantations, 500 ACKNOWLEDGMENTS acres of orchards, according to table 1 provides the resource consumption and profit, can calculate the total resources of four This article was funded by Project of China crop consumption, compared with the optimized results, the results Postdoctoral Science Foundation. Authors are grateful to in figure 1. Before optimization of the profit is 9777200 Yuan, Huang Wensheng, Bao Yujun for their help in data after optimization of the profit is 19704000 Yuan. collection. Jun Sun is also acknowledged for helping with data collections.
REFERENCES [1] Feisi science and technology R & D center. “MATLAB 6.5 auxiliary optimization calculation and design”, Beijing: Publishing House of electronics industry, 2003. [2] Bureau of agricultural economics at Jingkou Jingkou District Agriculture Jingkou rural profile. Http://www.jknw.com/htm/rzny.asp. [3] Zhiyong Zhang. “Proficient in MATLAB5.3 edition”, Beijing: Beihang University press, 2001. [4] Dong Xu, Zheng Wu. “Based on the MATLAB6.X system analysis and design”, Xi'an: Xi'an Electronic and Science University press, 2002. Fig. 1 Comparison of resource consumption before and after optimization. [5] Shangming Ma, Chengjun Xie. “Planting structure optimization and adjustment of benefit evaluation analysis”, Ningxia forestry science and Technology, vol. 2, No. 05, pp. 47-51, 2000.
DOI 10.5013/IJSSST.a.17.20.16 16.3 ISSN: 1473-804x online, 1473-8031 print