Qing WANG, Huaru LIU, Dongpu FENG

School of Civil Engineering and Hydraulic Engineering, Ningxia University, Yinchuan 750021, China

Abstract [Objectives] To analyze and optimize the crop planting structure in Ningxia based on the shortage of water resources and the large proportion of agricultural water consumption in Ningxia. [Methods] The change trend of crop planting area and planting structure in Ningxia in 2004-2018 was analyzed, and a multi-objective optimization model was constructed with the objectives of maximum crop profit and minimum water demand. The STEM method was applied to solve the problem, and the optimization scheme of crop planting in Ningxia was obtained. [Results] In Ningxia in 2004-2018, the planting area showed the characteristics of "increase-decrease-increase"; the area and proportion of cash crops were increasing, and the proportion of grain crops was gradually decreasing, but the proportion of crops with high water consumption was still high. After the planting structure was optimized, the economic benefit was increased by 34.85×108 yuan, and the water demand was reduced by 3.9×108 m3. [Conclusions] Under the premise of ensuring food security, the optimized scheme not only saves water resources but also obtains higher economic benefits. It provides a reference for alleviating water shortage and increasing farmers’ income.

Key words Multi-objective optimization, Planting structure optimization, STEM method

1 Introduction

Because of drought and little rainfall, Ningxia is one of the most water-scarce provinces in China, but its agricultural water consumption accounts for 84.8% of the total water consumption[1]. Especially, crops with high water consumption such as maize and rice have a large planting area, which intensifies the contradiction between supply and demand of water resources. Therefore, optimizing and adjusting the crop planting structure is of great significance to both food security and water resources security of Ningxia.

The optimization of agricultural planting structure is an effective measure to alleviate the contradiction between agricultural water supply and demand and improve the efficiency of water resources utilization[2]. In recent years, some scholars have carried out extensive studies on the optimization of crop planting structure. In view of the current shortage of water resources in the Hetao Irrigation District of Inner Mongolia, Guo Pingetal.[3]applied water footprint to multi-objective optimization of water resources, and used the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method and the coupled fuzzy hierarchy method to evaluate the optimization plan. Their results provided a decision support for local adjustment of planting structure. Deng Lingzhietal.[4]used the C-PAC model to analyze the evolution of planting structure in Guizhou Province in the period of 1949 to 2013, and discussed the optimization strategies of planting structure. Tan Qianetal.[5]established the MRPWU agricultural water resources optimal allocation model for arid and semi-arid regions, and the optimization results show that the MRPWU model can improve the weight uncertainty of the optimization model, and it can save water and improve efficiency through properly reducing the planting area. With the aid of the linear programming model and Lingo software, Zhang Xicheng[6]studied the crop planting structure in the Kaidu-Kongque River Watershed, and the optimized scheme has significant water-saving and benefit effects.

The STEM method is a method for solving multi-objective single-level programming problems, and has good interaction and advantages in dealing with economic and policy optimization[7]. However, this method has little application in the optimization of planting structure. Therefore, in this study, we constructed a multi-objective optimization model for the crop planting situation in Ningxia, and used the STEM method to solve it. Through the optimization scheme of planting structure, it is expected to alleviate the contradiction between supply and demand of water resources in Ningxia, and provide a reference for promoting efficient utilization of water resources and sustainable agricultural development.

2 Materials and methods

2.1 Overview of the research areaNingxia Hui Autonomous Region covers a total area of 66 400 km2. It is located at 35°14′-39°23′ N and 104°17′-107°39′ E. Its terrain is high in the south and low in the north. Ningxia is arid and less rainy, the evaporation intensity is high. Rainfall is mainly concentrated from June to September. The spatial and temporal distribution of water resources is uneven, and the problem of resource water shortage is very prominent.

2.2 Data sourceThe crop irrigation quota used in this study came from theWaterQuotaforRelatedIndustriesinNingxiaHuiAutonomousRegion(2020)[1]. The crop income and cost were selected from the2019NationalAgriculturalProductCostandBenefitDataCompilation[8], and the planting area data were selected from theNingxiaStatisticalYearbook[9].

2.3 Research methodsOn the basis of ensuring the existing farmland area and basic grain planting area, we established a multi-objective optimization model to achieve the maximum economic benefit of crops and the minimum water consumption, and used the STEM method to solve the problem.

2.3.1Determination of decision variables. We took the planting area of 9 main crops in Ningxia as the decision variables, that is, rice, wheat, maize, beans, tubers, oil crops, medicinal crops, vegetables, melons and fruits, expressed asX1-X9, respectively.

2.3.2Determination of objective function. In this study, we took the highest benefit and the lowest water demand as the objective function, as follows:

(1)

(2)

whereAidenotes crop yield, expressed in kg/ha;Bidenotes the net profit, expressed in kg/yuan;Xidenotes the crop planting area, expressed in ha;Cidenotes water demand of crop, expressed in m3/ha.

2.3.3Constraint conditions. (i) Planting area constraint. The average of the total planting area in 2010-2018 was used as the area constraint.

∑Xi≤1 013 100

(3)

(ii) Water consumption constraint.

M

(4)

whereWis the minimum value of agricultural water consumption in the past ten years.

(iii) Constraint of planting area of grain crops. In order to ensure food security, grain crops must reach a certain proportion. Through the analysis of the planting area of grain crops in the past two decades, we determined the proportion of the largest and smallest areas of food.

(5)

(ix) Non-negative constraint.

Xi>0

(6)

(v) Rice planting area constraint.

Considering the 14thFive-Year Plan and local conditions in Ningxia, we determined the rice planting area to be 14 000 ha in this study.

2.3.4Solution based on STEM method. The STEM method solves the multi-objective optimization model through multi-parameter optimization step by step calculation, and uses trial calculation and iterative calculation to solve the multi-objective optimization model. The method has the characteristics of strong global optimization ability and good convergence. The specific process is as follows:

Assume there is a linearity withkobjectives:

(7)

whereR={X/AX≤b，X≥0},Aism×nmatrix,Cisk×nmatrix.

The calculation steps to solve are as follows:

Step 1: solve the solutions ofksingle-objective linear programming problems separately.

(8)

(9)

(10)

Step 2: calculate the weighting coefficient.

(11)

(12)

After normalization, we obtained the weight coefficient:

(13)

Step 3: construct a linear programming problem and solve it.

(14)

Assuming that the obtained solution isx(1), then the correspondingkobjective value isc1x(1)c2x(2), …,ckx(k). Ifx(1)is the ideal solution of the decision maker, its correspondingkobjective values arec1x(1),c2x(1), …,ckx(1). At this time, the decision maker compares the objective value of , if the decision maker is satisfied, he can stop calculation; if the difference is too far, he should consider appropriate corrections. If the decision maker considers to be lenient on thejthobjective, that is, make a little concession, reduce or increase aΔcj, and change the constraint setRto

(15)

Let the weight coefficient of thejthobjective π=0, which means reducing the requirements of this objective. Then solve the following problems:

(16)

Repeat the steps until the results are satisfied.

3 Results and analysis

3.1 Planting area and structure analysisFrom Fig.1, it can be seen that the total planting area of crops in Ningxia shows a trend of "increase-decrease-increase". By the end of 2018, the planting area and proportion of maize in grain crops had been increasing rapidly, while the planting area and proportion of wheat, tubers and beans had dropped significantly, and the fluctuation of rice planting area had increased slightly. Among cash crops, compared with 2004, the planting area and proportion of oil crops decreased significantly, while medicinal crops increased by 5 times; vegetables, melons and fruits and feed increased by 2.6, 3.4 and 1.8 times, respectively. From the change of planting structure, it is found that both the planting area and proportion of cash crops were increasing, while the proportion of grain was gradually decreasing. This is conducive to increasing farmers’ economic income and forming a diversified planting pattern, but the proportion of crops such as rice and maize with high water consumption was still relatively high.

Fig.1 Changes in crop planting area and structure in Ningxia in 2004-2018

3.2 Optimization of planting structureThrough solving the model, we obtained the optimization scheme of planting structure in Ningxia, and compared and analyzed the current situation of annual average planting area in Ningxia. After the planting structure is optimized, the economic benefit was increased by 34.85×108yuan, the water demand was reduced by 3.9×108m3, and the net output value was increased by 31.46×108yuan. Specifically, the rice planting area decreased by 64 818 ha, water demand decreased by 8.07×108m3; wheat planting area decreased by 67 688.6 ha, water demand decreased by 3.15×108m3; maize planting area increased by 119 411.5 ha; tubers planting area decreased by 81 555.2 ha, water demand decreased by 1.96×108m3, net output value decreased by 0.78×108yuan; the vegetable planting area increased by 70 582.5 ha, the water demand increased by 3.18×108m3, and the net output value increased by 23.15×108yuan; the fruit planting area increased by 32 689.5 ha, the water demand increased by 1.37×108m3, and the net output value increased by 13.82×108yuan. The adjustment of oil crops, beans and medicinal crops was not significant. Although vegetable and fruit cultivation consumed a lot of water, the economic benefits were very high, which is conducive to increasing the economic income of local people.

Table 2 Comparison of current situation and optimized scheme of planting structure in Ningxia

4 Conclusions

In this study, we analyzed the changes of crop planting area and structure in Ningxia in 2004-2018, established a multi-objective optimization model, and solved it by STEM method, finally arrived at the following conclusions. (i) There was no obvious trend in the total planting area of grain crops, and each grain crop varied greatly. The total planting area of rice showed a stable trend, while wheat and beans showed a downward trend. Maize and tubers planting area showed an increasing trend. The total planting area of cash crops was on the rise. Among the cash crops, oil crops decreased slightly; the planting area and proportion of medicinal crops melons, fruits and vegetables increased greatly. (ii) The optimized planting scheme was consistent with the overall planning of Ningxia. The optimized planting structure reduced crops with high water consumption and low economic benefits, and increased crops with high economic benefits. In addition, the optimized planting scheme not only saved water resources, but also improved economic benefits, and the planting area of each crop was also in line with the future agricultural development direction of Ningxia.