Analysis of Efficiency Differences and Research on Moderate Operational Scale of New Agricultural Business Entities in Northeast China

Abstract

Various new agricultural business entities in China are important business organizations to improve agricultural production and management efficiency, and to promote the professional and large-scale development of agriculture. Exploring the efficiency differences of different business entities and the importance of moderate management scale in promoting the modernization of agriculture development has important practical significance. Based on the theory and method of system engineering, this study takes the main grain production areas of Northeast China as an example, and analyzes the efficiency differences of various new agricultural business entities by using the survey data of agricultural business entities and data envelopment analysis. Moreover, it applies the DEA-GA-BP prediction model and the entropy method (gray correlation analysis method) to study the moderate scale of agricultural business entities. The results show that there are certain efficiency differences among new agricultural business entities, among which the family farm has the highest average cross-efficiency value, and the best operational scale of the family farm is when the land cultivation area input is 9015~10,000 mu. The most optimal ranges of its production input factors are obtained, but the performance of the technical efficiency of family farms needs to be improved. Based on this, it is proposed that the focus of the construction of new agricultural business entities should be on family farms, with the best ratio of production factors for reference, constantly optimizing the allocation structure of production factors on family farms and strengthening the effective application of advanced production technologies on family farms.

1. Introduction

In order to achieve modernized agricultural development and comprehensive revitalization of the countryside, China has seen the diversification of new agricultural business entities such as family farms, large rural professional households, and agricultural cooperatives under a strong policy push. Exploring the operational efficiency and moderate business scale of different new agricultural business entities to promote their healthy development has become an inevitable requirement for the sustainable development of Chinese agriculture. The study of operational efficiency can reflect the full use of resources by new agricultural business entities while maintaining output levels. The relationship between net income per unit area and farmland area alone does not fully reflect the operation level [1], which can be more fully reflected by scale efficiency and technical efficiency. However, technical efficiency rises and then falls as the size of the farmland increases [2]. Under certain technical conditions, the scale of agricultural farmland management is always moderate, which enables the optimal allocation of the input factors of production and the maximum economic profit generated by the agricultural farmland. This scale is the moderate operational scale of agricultural farmland management [3,4,5]. Operational efficiency and moderate operational scale interact in agricultural production. Therefore, the main objective of this paper is to find out the best new agricultural business entities for dry farmland crops in the main grain-producing regions of Northeast China, as well as the moderate operational scale of operation of the business entities, through the analysis of operational efficiency.

The efficiency of agricultural business entities is one of the most important indicators of the comprehensive production capacity of agriculture, and the larger the scale of an agricultural business, the better. Moderate operational scale of agricultural businesses is a goal to avoid the blind expansion of farmland scale. Accordingly, while ensuring the efficiency of the scale of agricultural business entities, exploring the moderate operational scale of operations has become an important issue for scholars to study.

In the analysis of the efficiency of agricultural business entities, scholars have mostly applied DEA models based on input-output indicators for evaluation and have conducted in-depth and extensive analyses of the influencing factors of each input. For example, Giang and others applied parametric and non-parametric DEA models to study the agricultural operational efficiency of 60 provinces in Vietnam and found that the average allocative, technical, and economic efficiency values were relatively low [6]. Marvin and others argued that both high and low grain production efficiency are largely influenced by natural disasters [7]. In contrast, Lunik and others found that high seed costs were the main factor affecting low production efficiency on soybean farms [8]. While Ma et al. and others found that the main factor affecting agricultural operational efficiency was changes in scale efficiency, followed by changes in environmental factors [9], Adhikari and others applied a DEA model to study the technical efficiency of the production on three different sizes of family farms in Nepal and found that medium-sized family farms were the most efficient of the three sizes, suggesting that medium-sized and moderate family farms are the way to develop [10]. Since different new agricultural business entities in China differ in terms of agricultural input ratios [11], business capacity [12], technical efficiency [13], and scale of operation [14], it is necessary to explore the operational efficiency of different business entities.

In the study of the moderate operational scale of agricultural operations, scholars have analyzed the relationship between the scale of operations and production efficiency and explored the scope of the moderate operational scale. For example, Ahmad [15] and Renato [16] found that there was a positive relationship between the technical efficiency of food crop production and farm operational scale, and the operational efficiency of farms with large business scale was higher than that of farms with small business scale [17,18]. By contrast, Liu Ying suggested that there is an optimal combination between operational efficiency and scale of operation [19]. Based on the basic situation of China’s large population and small land area and the differences in natural resources between regions, the development of moderately operational scale agricultural operations at this stage is an important way for China to achieve agricultural modernization. Kong et al. applied a three-stage DEA model to empirically analyze rice family farms and general peasant households in Songjiang District to find the moderate operational scale of rice cultivation [20]. Dong Sen obtained the moderate size range of family farms with constant returns to scale based on the analysis of production efficiency perspective [21]. Wei Rong [22], Sun Rui [23], Chen et al. [24], and Fan Shu [25] analyzed the main factors affecting the development of the moderate operational scale of agriculture in different regions of China, respectively.

In summary, it can be concluded that in the past, studies on the efficiency of new agricultural business entities were mainly based on a single entity, with few studies on different agricultural business entities, and the conclusion on the moderate operational scale of business entities was only given in terms of the scale of land operations, without giving the range of other production factor inputs under the moderate operational scale range. Therefore, this study contributes to the literature in three ways: First, taking the main grain production area of northeast China as an example, based on the survey data of agricultural business entities of dry farmland crops, a relatively perfect evaluation index system of agricultural business entities operational efficiency is constructed. Second, using the cross-efficiency DEA models, with the mode of “self-evaluation + mutual evaluation” to analyze the efficiency differences of different agricultural business entities, trying to accurately evaluate the operational efficiency of each new type of agricultural business entity, and giving the type of the best business entity. Third, the DEA-GA-BP model is constructed to predict the operational scale and the structure of other agricultural production factors, and the entropy value method-gray correlation analysis is used to optimize the allocation ratio of production factors of family farms on a moderate operational scale. To provide a strategic reference for promoting the high-quality development of agricultural industrialization and the comprehensive revitalization of rural areas.

2. Problem Descriptions and Research Methods

2.1. Problem Descriptions and Analysis

This study focuses on two interrelated issues. One is the analysis of the differences in the operational efficiency of different new agricultural business entities, and the other is the study of the moderation of the business scale of the best new agricultural business entity (later referred to as the business entities) to determine the moderate operational scale and input resource structure of the entities. Therefore, the problem analysis and research methodology are carried out for these two research tasks, respectively.

2.1.1. Efficiency Differences

The new types of agricultural business entities that exist in China include family farms, large rural professional households, agricultural cooperatives, and agricultural enterprises, which together with peasant households constitute a system of multiple agricultural business entities. There are certain differences in the operational efficiency of different business entities due to their different operating methods and inputs of production resources. The main purpose of this study is to determine, through comparative analysis, which type of business entity has the best performance in terms of operational efficiency. The operational efficiency of the business entities in the process of agricultural production is in a specific agricultural production cycle, each agricultural business entity is an independent production decision-making unit, so that all input factors such as labor, capital, and goods of this decision-making unit achieve the most optimal allocation. That is, in the production and operation process, all the various input factors of the agricultural business entities play the greatest role, and the overall state of maximum efficiency and output and maximum surplus of resources is achieved. The operational efficiency of the business entities in this study includes both pure technical efficiency and scale efficiency, which is comprehensive efficiency. It comprehensively reflects whether the resources of the agricultural business entity are allocated reasonably and whether the economic benefits are maximized. With the maximum economic benefits for operators of business entities as the goal, resource allocation and scale of operation as the evaluation criteria, and combined with the current situation of agricultural production, the evaluation index system of operational efficiency of business entities is constructed. In the aspect of resource allocation, as far as possible, we make the input indicators cover all aspects of production and operation. In terms of business scale, we focus on the relationship between machinery inputs and business scale [26]. The machinery input is taken as a separate indicator of the evaluation system, and the DEA model and cross-efficiency. The DEA model is applied to evaluate the comprehensive efficiency, pure technical efficiency, scale efficiency, and cross-efficiency of various types of business entities, thus clarifying the current best type of business entity.

2.1.2. Moderate Business Scale

Returns to scale are the changes in output indicators that occur when the individual input factors increase or decrease in the same proportion, without a change in conditions such as external resources. The most common method used to describe the relationship between returns to scale in the analysis of operational efficiency is the homogeneous production function method. In other words, if all input factors in the production process increase or decrease by a factor of x, then output will also increase or decrease by a factor of x*m. When the payoff to scale is unchanged, that is, when m is 1, at which point it is a linear homogeneous function. For example, if the input indicator increases x times at the same time, then the output indicator increases x times. From an economic point of view, the moderate operational scale of a business entity is defined as the scale at which the input factors such as farmland, capital, labor, and machinery used in its operation are maximized for operational efficiency, with no change in the existing level of technology. Therefore, this study is an analysis of the relatively moderate operational scale of the business entities, supposing that external conditions do not change in the short term, meaning that they remain largely stable. The measurement method in this study is a DEA-GA-BP business-scale forecasting model constructed based on neural networks. The model is well suited to improve the prediction accuracy and fit. The final measurement results are analyzed by the entropy-gray correlation analysis method to predict the scheme, and from the correlation level of the scheme, the moderate operational scale value of agricultural production inputs and outputs of the business entities is obtained.

2.2. Research Methodology

2.2.1. Research Methods for Analyzing Differences in The Efficiency of Business Entities

The evaluation index system of the operational efficiency of different business entities constructed in this paper mainly involves two parts: input indexes and output indexes. In order to analyze the operational efficiency of multiple inputs and multiple output indexes of different business entities more comprehensively, this paper first applied the DEA-BCC model to realize the efficiency analysis of decision units by calculating pure technical efficiency and scale efficiency in a self-assessment way. Secondly, the cross-efficiency DEA model was used to calculate the cross-efficiency of each business entity by the weighting of the input and output resources of the overall decision unit in the way of “self-evaluation + mutual evaluation”, thus making up for the shortcomings of the DEA-BCC model, which only uses the internal evaluation system to evaluate the efficiency of each decision unit. The DEA-BCC model has been extensively researched by many scholars at home and abroad [27], so this paper will not dwell too much on it and focus on the cross-efficiency DEA model. The cross-efficiency DEA model was as follows [28]:

Assume that there are $n$ decision making units (DMU), and each DMU contains m input and s output indicators. For the j-th decision unit ${\mathrm{DMU}}_j$ (j = 1, 2, …, n), assume that the i-th input variable and the r-th output variable were $x_{ij}$ ($i$ = 1, 2, …, m) and $y_{rj}$ (r = 1, 2, …, s). For the d-th assessment object ${\mathrm{DMU}}_d$, the efficiency value ${\mathrm{E}}_{dd}$ under the DEA-CCR model was calculated as shown in the following equation:

$$\begin{array}{l}{E}_{dd}=\max \frac{{\displaystyle \sum _{r=1}^s{u}_{rd}{y}_{rd}}}{{\displaystyle \sum _{i=1}^m{v}_{id}{x}_{id}}}\\ s.t.\{\begin{array}{l}\frac{{\displaystyle \sum _{r=1}^s{u}_{rd}{y}_{rd}}}{{\displaystyle \sum _{i=1}^m{v}_{id}{x}_{id}}}\le 1,j=1,\dots ,n\\ v_{id}\ge 0,u_{rd}\ge 0,i=1,\dots ,m;r=1,\dots ,s\end{array}\end{array}$$

(1)

In Equation (1), the variables v_id and u_rd were used to represent the weights of the i-th input and r-th output of the ${\mathrm{DMU}}_d$. The $\mathrm{Charnes}-\mathrm{Cooper}$ transformation of Equation (1) yields the following equation:

$$\begin{array}{l}\max E_{dd}={\displaystyle \sum _{r=1}^s{u}_{rd}{y}_{rd}}\\ s.t.\{\begin{array}{l}{\displaystyle \sum _{i=1}^m{\omega }_{id}{x}_{id}=}1\\ {\displaystyle \sum _{r=1}^s{u}_{rd}{y}_{rj}}-{\displaystyle \sum _{i=1}^m{\omega }_{id}{x}_{id}}\le 0,j=1,\dots ,n\\ {\omega }_{id}\ge 0,u_{rd}\ge 0,i=1,\dots ,m;r=1,\dots ,s\end{array}\hspace{1em}\end{array}$$

(2)

Assume that the optimal solution of model (2) is $({\omega }_{id}^{*},{\mu }_{id}^{*})$ and the optimal solution of DMU_j (j = 1, 2, …, n) for the other evaluated units is $({\omega }_{ij}^{*},{\mu }_{ij}^{*})$. Based on this, the cross-efficiency of the optimal weights of ${\mathrm{DMU}}_d$ in the DMU_j model (2) was defined as:

$$E_{dj}=\frac{{\displaystyle \sum _{r=1}^s{u}_{rd}^{*}{y}_{rj}}}{{\displaystyle \sum _{i=1}^m{\omega }_{id}^{*}{x}_{ij}}},d,j=1,2,\dots ,n$$

(3)

2.2.2. Research Methods for Moderate Business Scale of Best Business Entities

• DEA-GA-BP neural network prediction model

Since the BP neural network was prone to problems such as local optimum and slow convergence when fitting and predicting the input and output of agricultural business entities, Genetic Algorithm (GA) can select the most suitable parameters for the initial weights and thresholds of the BP neural network [29,30]. Therefore, in this study, when analyzing the moderate size of the best new business entity, the DEA-GA-BP neural network prediction model was constructed as follows. The process is shown in Figure 1, and the specific steps of model implementation are shown as follows:

Step 1: Data correction. As the original data of agricultural business entities was not fitted with high accuracy, the DEA-BCC model was used to correct the original data by adding slack variables and residual variables to make the original data reach a variable scale, thus improving the fitting accuracy.

Step 2: Chromosome encoding. In order to improve the search space of the network and ensure that the weights and thresholds of the network have a high accuracy, the chromosomes were encoded by real number encoding, and the chromosome encoding length s was:

$$s=mL+L+Ln+n$$

(4)

where m was the number of input layer nodes, L was the number of implied layer nodes and n was the number of output layer nodes.

Step 3: Population initialization. N individuals were randomly generated to form a population, and the most suitable individuals were selected and added to the initial population until the number of individuals in the initial population reached population size N.

Step 4: Calculation function for the degree of adaptation. The degree of adaptation F was calculated as:

$$F={\displaystyle \sum _{i=1}^{num}{\displaystyle \sum _{k=1}^n\left|d_{ik}-o_{ik}\right|}}$$

(5)

where n is the number of output variables, num is the number of network training samples, $d_{ik}$ ($i$ = 1, …, num; k = 1, 2, …, n) is the desired output of the network; $d_{ik}$ ($i$ = 1, …, num; k = 1, 2, …, n) is the training output of the network.

Step 5: Selection operation. A roulette wheel was used to select N individuals from the population, and the probability of the i-th individual being selected is:

$$p_i=\frac{{\left(F_i\right)}^{-1}}{{\displaystyle \sum _{j=1}^N{(F_j)}^{-1}}},(i=1,2,\cdots ,N)$$

(6)

where p is the population size and F is the fitness value

Step 6: Crossover operation. Using the real number crossover method, let the individuals involved in the crossover be x_i and $x_j$, and the crossover will produce the children individuals $x_i^{\prime }$ and $x_j^{\prime }$ as follows:

$$\{\begin{array}{l}{x}_i^{\prime }=(1-a)x_i+a{x}_j\\ x_j^{\prime }=(1-a)x_j+a{x}_i\end{array}$$

(7)

where a is a random number between [0, 1].

Step 7: Variation operation. Variation is performed on the j-th dimensional component $x_{ij}$ of an individual x_i in the population, with the following variation operator:

$$x_{ij}=\{\begin{array}{l}{x}_{ij}+(x_{ij}-x_{up})f(t),\hspace{1em}{S}_1>0.5 \\ x_{ij}+(x_{lp}-x_{ij})f(t),\hspace{1em}{S}_1\le 0.5\end{array}$$

(8)

$$f(t)=S_2{(1-\frac{t}{T})}^2$$

(9)

where $x_{up}$ is an upper bound on the value of $x_{ij}$, $x_{lp}$ is a lower bound on the value of $x_{ij}$, S₁ and S₂ are both uniformly distributed random numbers between [0, 1], t is the current number of iterations, and T is the maximum number of iterations.

Step 8: Repeat steps 4, 5, 6, and 7 to obtain the optimal chromosome when the adaptation degree converges to the number of iterations, which was used as the initial weight and threshold of the BP neural network model.

Step 9: Input the DEA-BCC corrected data into the network. The input layer neural node obtains the data and obtains Y by the activation function g(x), after which it is output to the hidden layer neural node, which obtains O by the activation function g(x), which runs as:

$Y={(y_1,y_2,\dots ,y_j,\dots ,y_l)}^T$ is the output vector of the implicit layer.

$$y_j=g(ne{t}_j),(j=1,2,\dots ,l);ne{t}_j={\displaystyle \sum _{i=0}^m{v}_{ij}{x}_i},(j=1,2,\dots ,l)$$

(10)

$O={(o_1,o_2,\dots ,o_k,\dots ,o_n)}^T$ is the output vector of the output layer.

$$O_k=g(ne{t}_k),(k=1,2,\dots ,n);ne{t}_k={\displaystyle \sum _{j=0}^l{w}_{jk}{y}_j(k=1,2,\dots ,n)}$$

(11)

where: g(x) is the $Tansing$ function, whose equation is (12) and x is the input sample data.

$$g(x)=\frac{2}{1+e^{-2x}}-1$$

(12)

Step 10: Adjust the weights and reduce the error δ and then output Y. The weights of each neural node in the first two layers are fed back to the nodes in the first two layers, which correct the weights of each layer of neural nodes respectively, and loop through step 9 based on the new weights and thresholds until δ smaller than the training target, and then output Y.

2.

Entropy method-grey correlation analysis method

Based on the data of the existing business entities, the DEA-GA-BP prediction model was used to predict the values of the business entity schemes to obtain the scheme combinations. Then the entropy-gray correlation analysis method [31,32,33] was used to calculate the correlation values of the schemes of new agricultural business entities, and the scheme with the higher correlation value was the better scheme. The entropy method-grey correlation analysis method was based on the following process:

Step 1: Calculate the gray correlation matrix.

The optimal set of indicators ($G^{\mathrm{*}}$) was the set of optimal values of the forecast indicators of different business entities in the same evaluation indicator items. Let G^* = [$j_1^{*}$, $j_2^{*}$, …, $j_n^{*}$], which is the optimal indicator set composed of the optimal values of each of the same indicators for different schemes based on the business schemes of the operating agents predicted by the DEA-GA-BP model, which can be combined with the predicted indicator data values to form the matrix C.

$$C=\left[\begin{array}{cccc}{J}_1^{\ast }& J_2^{\ast }& \cdots & J_n^{\ast }\\ J_1^1& J_2^1& \cdots & J_n^1\\ \cdots & \cdots & \cdots & \cdots \\ J_1^m& J_2^m& \cdots & J_n^m\end{array}\right]$$

(13)

where $j_k^i$ is the predicted value

The predicted values of the matrix C is dimensionless.

$$\mathrm{Positive} \mathrm{indicators} \mathrm{are} \mathrm{treated} \mathrm{as}:D_k^i=\frac{j_k^i-j_{k1}}{j_{k2}-j_{k1}}i=1,2,\cdots m;k=1,2,\cdots n$$

(14)

$$\mathrm{Negative} \mathrm{indicators} \mathrm{are} \mathrm{treated} \mathrm{as}: D_k^i=\frac{j_{k2}-j_k^i}{j_{k2}-j_{k1}}i=1,2,\cdots m;k=1,2,\cdots n$$

(15)

In Equations (14) and (15), j_k2 is the maximum value of the k-th indicator for all scenarios, and j_k1 is the minimum value of the k-th indicator for all scenarios.

Find the number of correlation coefficients, which leads to the correlation coefficient matrix E.

$${\phi }_i\left(k\right)=\frac{\Delta \min +\rho \Delta \max }{\left|D_o\left(k\right)-D_i\left(k\right)\right|+\rho \Delta \max }$$

(16)

where the resolution factor ρ ϵ [0, 1], and ∆min is the minimum absolute difference, and ∆max is the maximum absolute difference.

The correlation coefficient matrix E is therefore:

$$E^{\ast }={\phi }_i\left(k\right)=\left[\begin{array}{cccc}{\eta }_1\left(1\right)& {\eta }_1\left(2\right)& \cdots & {\eta }_1\left(n\right)\\ {\eta }_2\left(1\right)& {\eta }_2\left(2\right)& \cdots & {\eta }_2\left(n\right)\\ \cdots & \cdots & \cdots & \cdots \\ {\eta }_m\left(1\right)& {\eta }_m\left(2\right)& \cdots & {\eta }_m\left(n\right)\end{array}\right]$$

(17)

Step 2: Entropy method of calculating weights.

By homogenizing the data values of different proposals under the same indicator, the weight $p_{ij}$ of the j-th indicator of the i-th proposal is:

$$p_{ij}=\frac{s_{ij}}{{\displaystyle \sum _{i=1}^m{s}_{ij}}}$$

(18)

$$\mathrm{Calculate} \mathrm{the} \mathrm{entropy} \mathrm{value} \mathrm{of} \mathrm{the} \mathrm{indicator}:e_j=-k{\displaystyle \sum _{i=1}^m{p}_{ij}}\ln p_{ij}$$

(19)

where $e_j$ represents the entropy value of the indicator; e_j ≥ 0, k > 0, k = lnm

$$\text{Calculate the coefficient of variation for indicator:} j:g_j=1-e_j$$

(20)

here $g_j$ represents the coefficient of variation for indicator $j$ and $e_j$ represents the entropy value for indicator $j$.

$$\mathrm{Calculate} \mathrm{the} \mathrm{weights} \mathrm{for} \mathrm{each} \mathrm{indicator}:w_j=\frac{g_j}{{\displaystyle \sum _{i=1}^n{g}_j}}$$

(21)

where $w_j$ is the weight of each indicator and $g_j$ represents the coefficient of variation of the $j$ indicator

Step 3: Calculate the correlation coefficient for each test scheme:

Each layer of indicators corresponds to a vector of indicator weights, and the corresponding correlation can be expressed as:

$$R={\left(r_i\right)}_{1\ast m}=\left(r_1,r_2,\cdots ,r_m\right)=W\ast E^T$$

(22)

3. Indicator Descriptions and Data Acquisition

3.1. Description of Indicators

In order to evaluate the operational efficiency of dry farmland crops and agricultural business entities objectively, indicators should be selected in such a way that they cover all aspects of production and operation as far as possible. For agricultural production, scholars believe that the most important input indicators are labor [34], farmland [35], and capital [36], which constitute the most important economic input factors, and that the above factors limit agricultural production to a certain extent. In this paper, considering that with the continuous development of mechanical power, machinery operation plays an increasingly important role in the process of agricultural production, and that the machinery inputs vary among different agricultural business entities, machinery inputs are analyzed as separate indicators in this study [37]. The input indicators are divided into five: direct input, indirect input, machinery input, labor input, and farmland input, while the output indicators are total net income and output value. In the application of the DEA model, there is no requirement for the unit of measurement between different indicators, therefore, in order to facilitate the calculation, one should consider the accessibility of data, minimize the measurement and conversion of data, and have each indicator choose its own appropriate unit of measurement. Each indicator and its content are shown in

Table 1. A system of input-output indicators of operational efficiency for operating agents.

Type of Indicator	Selection of Indicators	Unit of Measurement	Indicator Description
Input indicators	Direct input	Yuan	Including other direct costs such as seeds, fertilizers, farmyard manure, pesticides, farmland transfer fees, drainage and irrigation, animal power, technical services, tools and materials, repairs and maintenance
	Indirect input	Yuan	Including depreciation of fixed assets, insurance, management fees, finance costs, selling fees, depreciation of rent for own camp, etc.
	Labor input	Yuan	Including the amount of labor employed and the discounted price for domestic labor
	Farmland input	Acres	Total area of farmland operated by agricultural business entities
	Mechanical input	Yuan	Includes the value of agricultural machinery and machinery operations, fuel and power costs, machinery repair and maintenance costs, agricultural mechanics’ hiring costs and other machinery-related costs
Output indicators	Total net income	Yuan	Annual net income of the operating entity, including the government subsidy component and net income from farming operations
	Output value	Yuan	Annual income of the operating entity

.

3.2. Data Acquisition

The data for this study was obtained through field research and telephone interview research in the main grain-producing areas in Northeast China, targeting provincial model new agricultural business entities (including family farms, professional farmers, and farmers’ cooperatives) and ordinary farmers who specialize in dry farmland crops such as maize and soybeans. The total farmland area of the main grain-producing regions in northeast China is about 78.73 million hectares, accounting for 8.2% of China’s farmland. Fertile farmlands such as black soil, black calcium soil, and meadow soil account for more than 57.3% of the total arable farmland area. There are about 69,025,500 hectares of agricultural farmland in the whole production area, of which 29,344,400 hectares are arable farmland, covering 42.5%. The survey was conducted by means of a typical sample survey and interviews. A total of 112 questionnaires were sent out, and 106 valid questionnaires were returned, for a sample efficiency rate of 94.6%. The results of the descriptive statistical analysis of various types of agricultural business entities were comprehensively collated, and the various input and output indicators of the sample business entities were compared, and the specific data are shown in

Table 2. Comparison of input and output values of sample agricultural business entities.

Sample Business Entities	Number of Samples	Average Farmland Input (Acres)	Average Direct Input (Yuan)	Average Indirect Input (Yuan)	Average Labor Input (Yuan)	Average Machinery Input (Yuan)	Average Output Value (Yuan)	Average Net Income (Yuan)
Farmers	20	86	14,673	6538	14,000	15,879	71,895	20,800
Family farms	56	1761.8036	883,570	134,831	33,175	178,095	1,697,064	467,392
Large professional households	14	482.5000	218,661	57,006	18,293	94,643	536,222	147,620
Agricultural Cooperative	16	3988.6875	2,709,178	546,027	376,363	267,477	5,228,556	1,329,512

Note: The sample size consists of 106 valid questionnaires obtained through research.

.

4. Results and Analysis

4.1. Efficiency Calculation Results and Analysis of Agricultural Business Entities

Based on the comprehensive analysis of the correlation between past scholars’ research experience and indices, farmland input, specifically farmland area, was chosen as the classification standard. The systematic cluster analysis method was used to classify and group the sample data obtained from the survey. According to the farmland input, the data of 86 agricultural business entities were grouped and calculated based on the average value of the corresponding indicators of each group. The results are shown in

Table 3. Input-output of sample data.

Type	Number	Scale Area (Acres)	Input Indicators					Output Indicators
			Direct Input (Yuan)	Indirect Input (Yuan)	Labor Input (Yuan)	Farmland Input (Acres)	Machinery Input (Yuan)	Output Value (Yuan)	Total Net Income (Yuan)
Largerurual Professional households	1	<200	66,500	58,650	19,560	150.000	18,200	183,750	24,800
	2	200 ≤ s < 500	177,230	27,650	23,310	299.125	45,690	369,490	85,610
	3	500 ≤ s < 1000	303,920	35,920	27,330	517.333	89,970	495,400	138,260
	4	1000 ≤ s < 2000	492,560	205,240	58,800	1330.000	305,700	1,360,600	298,300
Agriculture cooperative	5	500 ≤ s < 1000	255,670	223,760	147,500	700.000	95,910	964,380	241,540
	6	1000 ≤ s < 2000	562,420	292,420	248,750	1488.750	322,910	1,673,440	386,940
	7	2000 ≤ s < 1000	2,492,830	308,360	507,980	5073.778	399,570	5,228,490	2,019,760
	8	≥10,000	5,950,400	644,000	700,000	10,800.00	520,040	11,758,000	4,243,560
Family farm	9	<200	47,100	38,200	12,650	150.000	48,650	187,550	42,150
	10	200 ≤ s < 500	135,250	43,710	41,760	334.455	45,510	408,820	132,590
	11	500 ≤ s < 1000	293,050	80,430	41,690	650.667	91,190	705,340	218,980
	12	1000 ≤ s < 2000	603,330	137,290	52,460	1283.846	177,220	1,331,820	361,520
	13	2000 ≤ s < 10,000	2,140,170	221,740	48,000	4220.909	379,150	3,356,050	566,990
	14	≥10,000	5,422,750	669,730	159,000	10,000.00	654,330	12,344,200	5,438,380
Peasant household	15	86	34,673	6538	40,000	86.000	5879	71,895	20,800

.

4.1.1. Results of DEA-BCC Model Calculation

Based on the constructed evaluation index system of agricultural business entities, with the input indicators (direct input, indirect input, labor input, farmland input, and machinery input) and the two output indicators (output value and total net income), the input-oriented DEA-BCC model was first established to calculate the operational efficiency of 15 groups of agricultural business entities. Each group was treated as a decision-making DMU, there are five input variables and two output variables in each DMU. The Deap2.1 software was used to calculate the input and output data of the 15 groups of agricultural business entities, and the results of comprehensive technical efficiency, pure technical efficiency, scale efficiency, and scale elasticity are shown in

Table 4. DEA calculation results for various agricultural business entities.

Decision-Making Unit	Overall Technical Efficiency	Pure Technical Efficiency	Scale Efficiency	Scale Elasticity
DMU1	0.929	1.000	0.929	Increasing
DMU2	0.989	1.000	0.989	Increasing
DMU3	0.775	0.825	0.939	Increasing
DMU4	0.947	1.000	0.947	Decreasing
DMU5	1.000	1.000	1.000	-
DMU6	0.891	1.000	0.891	Decreasing
DMU7	0.921	0.925	0.996	Increasing
DMU8	1.000	1.000	1.000	-
DMU9	1.000	1.000	1.000	-
DMU10	1.000	1.000	1.000	-
DMU11	0.884	0.898	0.984	Decreasing
DMU12	0.862	0.880	0.980	Decreasing
DMU13	0.901	0.947	0.950	Increasing
DMU14	1.000	1.000	1.000	-
DMU15	0.840	1.000	0.840	Increasing
Average value	0.929	0.965	0.963

.

From Table 4, the mean values of comprehensive technical efficiency, pure technical efficiency, and scale efficiency for all decision-making units are 0.929, 0.965, and 0.963, respectively. Among the 15 groups of agricultural business entities, five groups achieved effective comprehensive technical efficiency, ten groups achieved effective pure technical efficiency, five groups achieved effective scale efficiency, and five groups achieved constant scale yield.

4.1.2. Results of Cross-Efficiency DEA Model

The cross-efficiency DEA model makes up for the shortcomings of the DEA-BCC model in evaluating the efficiency of each decision-making unit by only using the internal evaluation system [28]. Based on the input-output indicators of the sample data in Table 3, MATLAB software is used for calculation and analysis to obtain the cross-evaluation matrix composed of cross-evaluation values. Then, the cross-efficiency DEA model is used to obtain the cross-efficiency values of each group of agricultural business entities and sort them, as shown in Figure 2.

According to the cross-efficiency values of each group of agricultural business entities shown in Figure 2, it can be that the family farms with farmland input of over 10,000 mu have achieved the best efficiency, followed by family farms with farmland input of 200–500 mu, family farms with farmland input of less than 200 mu, agriculture cooperatives with farmland input of 500–1000 mu, and those with a planted farmland input of over 10,000 mu.

4.1.3. Analysis and Discussion of Efficiency Calculation Results

The DEA-BCC model provides information on the overall situation of each decision-making unit in terms of comprehensive technical efficiency, pure technical efficiency, and scale efficiency, while the cross-efficiency DEA model ranks the cross-efficiency values of each group of agricultural business entities. However, it is still difficult to determine the best business entities based on the above results alone. Therefore, further analysis is needed of the results of the two models.

• Comparing the average values of comprehensive technical efficiency, pure technical efficiency, and scale efficiency of the agricultural business entities.

According to

Table 5. Comparison of efficiency values of various agricultural business entities.

Various Agricultural Business Entities	Comprehensive Technical Efficiency Value	Pure Technical Efficiency	Scale Efficiency
Large rural professional households	0.907	0.955	0.949
Agriculture cooperative	0.953	0.981	0.972
Family farm	0.941	0.954	0.986
Traditional household farmer	0.840	1.000	0.840
Mean value	0.910	0.973	0.937

, the average values of comprehensive technical efficiency, pure technical efficiency, and scale efficiency are high for each type of new agricultural business entities, at 0.910, 0.973, and 0.937, respectively. This indicates that the business entities of these business entities can effectively utilize agricultural production resources at a moderate operational scale. In terms of pure technical efficiency, agricultural cooperatives perform better than family farms and large rural professional households, indicating that the technical efficiency contribution of agricultural cooperatives is high [38]. This shows that the development of cooperative management and technical application capabilities has reached a certain level. In terms of scale efficiency, family farms perform better than agricultural cooperatives, indicating that family farms have a greater scale advantage. In terms of comprehensive technical efficiency, agricultural cooperatives have the highest value, indicating that they have a scale advantage and a reasonable configuration of production factors.

2.

Compare the average cross-efficiency values of the agricultural business entities.

According to

Table 6. Comparison of average cross-efficiency values among different types of agricultural business entities.

Different Types of Agricultural Business Entities	Average Cross-Efficiency Values
Large rural professional households	0.610
Agriculture cooperative	0.684
Family farm	0.724
Traditional farmers.	0.619

, the average cross-efficiency values for different types of agricultural entities are 0.61, 0.684, 0.724, and 0.619. Family farms have the highest average cross-efficiency value. Based on research data, for managers of family farms and agricultural cooperatives that have achieved a certain scale, their participation in off-farm work is relatively low. These business entities have a relatively high level of education and are younger, which enables them to accept advanced technology training and the application of new technologies easier [39]. In addition, most family farms and agriculture cooperatives have purchased insurance for their farmland [40], especially those with larger scales, so their operational efficiency is relatively higher.

3.

Comparison of efficiency values for different types of agricultural business entities under two models.

According to

Table 7. Comparison of Average Values of Different Agricultural Business Entities under Two Models.

Different Types of Agricultural Business Entities	DEA-BCC Efficiency Values	Cross-Over Efficiency DEA Efficiency Values
Large rural professional households	0.907	0.610
Agriculture cooperative	0.953	0.684
Family farms	0.941	0.724
Traditional farmers	0.840	0.619
Mean value	0.910	0.610

, the suitable agricultural business entities for dry farmland crops in Northeast China is agriculture cooperatives from the result of DEA-BCC model. The suitable agricultural business entities for dry farmland crops in Northeast China are family farms from the result of cross-efficiency DEA model. The main reason of the two model results is in the DEA-BCC analysis, farmers’ professional cooperatives have two sets of data to achieve comprehensive technical efficiency value is 1, family farm in three sets of data to comprehensive technical efficiency value is 1, the calculation of all kinds of agricultural business entities efficiency evaluation value, are averaged under the level of 1. However, through the calculation of cross-efficiency DEA model and the ranking of each group of agricultural business entities, it is found that farmers ‘professional cooperatives with a comprehensive technical efficiency value of 1 are all ranked behind the family farms, and the average efficiency of family farms is greater than that of farmers’ professional cooperatives.

According to the survey data, the direct and indirect input of agriculture cooperatives is relatively large, which is higher than that of other business entities, which shows that the agriculture cooperatives in northeast China have achieved good results in expanding their scale of operation. Compared with agriculture cooperatives, the average farmland input of family farms is lower, but the efficiency level is higher, so it can better develop the scale advantage while considering efficiency. By comparing the two models, the business entities suitable for crop planting in dry farmland crops in Northeast China are family farms.

4.2. Forecast and Analyse the Moderation of Business Scale of Family Farm

It can be seen from the empirical conclusion in 4.1 that the efficiency of family farms in Northeast China is the highest among all kinds of agricultural business entities, and the allocation of agricultural resources of family farms reaches a higher level, which is the most suitable for the development of dry farmland crops in Northeast China. Therefore, this section studied the moderate business scale of family farms in order to provide direction for the adjustment of industrial structure and optimal production factor inputs for family farms in Northeast China.

4.2.1. Results of DEA-GA-BP Prediction Model

The moderate operational scale of a family farm refers to the scale at which the input factors of farmland, capital, labor, and machinery of a family farm reach maximum efficiency under the condition that the existing technology level remains unchanged. This paper assumes that the external situation in Northeast China will not change in the short term, namely, by remaining basically stable, and predicts the relatively moderate operational scale of family farms in Northeast China.

• Network structure and parameters

The original data were modified by the DEA-BCC model, and the corrected data were used as the input data for the prediction network. In this paper, the number of input nodes in the training network of the DEA-GA-BP prediction model (Figure 3) is 5, the hidden layer nodes are calculated as 4, and the number of output layer nodes is 2. The termination condition of network training is that the mean square error is less than the target error or the number of iterations reaches the maximum number of iterations. The parameters of the DEA-GA-BP prediction model were obtained by a uniform test with 5 factors and 18 levels and the optimal parameter settings, which are shown in

Table 8. DEA-GA-BP Parameters Setting of Prediction Model.

Parameters	Population Size	Crossover Probability	Mutation Probability	Maximum Iterations	Learning Rate
value	70	0.3	0.15	200	0.01

.

2.

Fitting effect

In this paper, the goodness of fit is measured by R² to test the degree of fit of the model. After calculation, the R², goodness of fit, of the DEA-GA-BP prediction model is 0.994725, and the R², goodness of fit, of the ordinary BP-ANN model is 0.732256. It can be observed that the goodness of fit of the DEA-GA-BP prediction model is closer to 1, and the degree of fit is higher. In the training, validation, and testing of the DEA-GA-BP prediction model, the R, or fitting correlation coefficient, is very high (see Figure 4), which indicates that the data before and after fitting the DEA-GA-BP prediction model have a high correlation.

• Prediction accuracy

In this paper, relative error and mean square error are used to evaluate and analyze the prediction accuracy of the DEA-GA-BP prediction model. After calculation, the relative error of the DEA-GA-BP prediction model is 14.95128 and the relative error of the ordinary BP-ANN model is 20.354214. It could be observed that the prediction accuracy of the DEA-GA-BP prediction model was significantly improved compared with the ordinary BP-ANN model. According to Figure 5 of mean square error, DEA-GA-BP prediction model achieves optimal performance at the 13th generation training, and the network error is 0.00071031, which basically meets the requirements of the network error setting. With the increase in training times, the error between the training set and the test set gradually decreased and the change trend of training set and test set was consistent. When the network was trained to 13 times, the three curves almost became one, and the error became gradually stable. In the training process of the DEA-GA-BP prediction model, the target accuracy requirement was met at the 19th training time. The error of generalization ability does not reduce for six consecutive training times from the 14th time, and the error reached the minimum at the 19th time. The fitting gradient change is shown in Figure 6.

4.2.2. Results of Moderate Operational Scale of Family Farm Based on Entropy Method and Grey Relational Analysis Method

In this paper, the DEA-GA-BP prediction model output data was applied to the entropy value method to calculate the weights of each indicator as shown in

Table 9. The weight of each index under the entropy method.

Index	Direct Input	Indirect Input	Artificial Input	Farmland Input	Mechanical Input	Output Value	Total Net Income
Weight	0.0188	0.0141	0.0150	0.0290	0.0140	0.5191	0.3900

. Grey relational analysis was applied to obtain the moderate operational scale values of input and output of the top 500 family farms with a high correlation degree, and it was found that the total net benefits of the moderate operational scale values of the top 207 schemes reached their maximum. The optimal results of the moderate operational scale values of the family farm were obtained by analyzing the top 207 moderate operational scale values, as shown in

Table 10. Grey relational analysis of the moderate operational scale value for the input and output of the family farm.

Index	Direct Input	Indirect Input	Artificial Input	Farmland Input	Mechanical Input	Output Value	Total Net Income
Minimum Value	6,160,060	733,008	51,200	9015	22,800	12,347,630	5,910,000
Maximum Value	6,840,500	1,213,400	100,000	10,000	1,100,000	12,349,290

.

According to Table 10, the best combination of business scales for dry farmland for family farms in the samples was as follows. When the range of input of farmland planting area is 9015 to 10,000 mu, the range of direct input is 6160,060 RMB to 6,840,500 RMB, the range of indirect input is 733,008 RMB to 1,213,400 RMB, the range of artificial input is 51,200 RMB to 100,000 RMB, and the range of mechanical input is 22,800 RMB to 1,100,000 RMB. At this time, the range of maximum output value is 12,347,630 RMB to 12,349,290 RMB, and the total net income is 5,910,000 RMB. Therefore, the existing family farms in Northeast China could adjust other input factors according to the existing area to maximize efficiency.

4.2.3. Analysis and Discussion of Results on The Appropriateness of Business Scale

Through the establishment of the DEA-GA-BP prediction model and because of the entropy method and grey relational analysis method, the moderate value of business scale for dry farmland crops on family farms in Northeast China was obtained, and the direction of industrial structure adjustment and the optimal amount of input factors were given. The following two points need further discussion.

• The DEA-GA-BP prediction model can be further optimized.

The goodness of fit of the DEA-GA-BP prediction model was improved to 0.994725, which was significantly improved compared with the gray GA-BP model [41]. In terms of relative error, the DEA-GA-BP prediction model had a 5.39086 higher than the BP-ANN model, but the relative error was still 14.95128, so there was still research space to reduce the relative error. In terms of network parameter optimization, the parameters of the DEA-GA-BP prediction model in this paper were obtained by a 5-factor and 18-level uniform test [42], which ensured that network parameters were more uniform and regular in the 5-dimensional space. Many researchers relied on experience to set network parameters, and subsequent research can set dynamically adjustable parameters and design heuristic mechanisms according to specific problems [43].

2.

The optimal scale of operation can be further analyzed.

In this paper, the entropy method and gray relational analysis method were used to analyze the prediction scheme. This method obtained the objective weight value according to the differences in the data itself and obtained the best management scheme through the correlation degree of the scheme index. Although this method was an efficient evaluation method for multi-objective problems, it lacked the persuasive power to draw conclusions based on only one method. Therefore, it could further comprehensively analyze the predicted value of moderate operational scale through multiple methods [44].

5. Discussion

Although this paper achieved some results in the analysis of operational efficiency differences and the study of moderate operational scale, there were still some areas for improvement due to the limited knowledge of the authors and the limited scope of the investigation.

• Discussion on the analysis of efficiency differences among new agricultural business entities.

The results of this paper showed that the introduction of “self-evaluation + mutual evaluation” in the calculation of operational efficiency could distinguish the differences in operational efficiency of different agricultural business entities better. And the comprehensive analysis showed that the operational efficiency of the family farm was better than that of other agricultural business entities, which was consistent with the conclusion proposed by Zhu [45] that the comprehensive efficiency of the family farm of dry farmland crops (wheat, corn) was the highest. However, in terms of the technical efficiency of the new agricultural business entities driving peasant households, the technical efficiency of agriculture cooperatives, large rural professional households, and family farms in this paper was, respectively, 0.981, 0.955, and 0.954. It indicated that the technical efficiency of agriculture cooperatives was higher than that of family farms, which was consistent with the conclusion proposed by Xu [46] that the ability of agriculture cooperatives to drive peasant households was stronger than that of family farms. Therefore, in terms of suggestions for family farms, it was necessary to further strengthen their input of technical factors, thus enhancing their ability to drive peasant households to participate in modern agricultural production.

2.

Discussion on the moderate operational scale of new agricultural business entities.

The results of this paper showed that the operational efficiency of family farms in the main grain producing areas of Northeast China reached maximum when the scale of family farms reached 9015 to 10,000 mu. Lowder points out that when the average operation area of family farms in Australia is 45,000 mu, efficiency performs well. Compared with developed countries. the moderate operational scale of family farms in China was still smaller [47]. However, due to the different influences of economic development, social environment, organizational system, and other factors in different countries and regions, the appropriateness of business scale should be determined by the national conditions of the country, because excessive expansion of scale will reduce the profitability of business entities [48]. In terms of different regions in China, the moderate business scale of family farms was also different. For example, Yan took peasant households in the hilly area and oasis plain agricultural area of Xinjiang as the research object, and the average moderate operational scale of peasant households in the two regions was 77.25 mu and 139.2 mu respectively [49]. Shi took the family farm in Shanghai against the background of farmland fragmentation and decentralization as the research object, and the moderate operational scale of the family farm was between 100 mu and 150 mu [50]. Therefore, in addition to considering the relevant input and output factors, the determination of the moderate operational scale of the agricultural business entity should also be in line with the actual development needed in different regions.

In addition, the survey only aimed at the production input and income data of new agricultural business entities planting crops in provincial dry farmland and the data of other levels of business entities was not collected. Besides, paddy farmland crops and other kinds of crops were not studied, and the calculation results of operational efficiency and moderate operational scale were singled out for planting crops. Subsequent studies should comprehensively consider the types of crops and increase areas, thus more fully and truly reflecting the operational efficiency and moderate operational scale of new agricultural business entities in China.

6. Conclusions and Suggestions

6.1. Conclusions

This paper first constructed the input-output index system of efficiency for agricultural business entities. Secondly, the paper analyzed the efficiency differences among the agricultural business entities in Northeast China. Then, based on the DEA-GA-BP prediction model and the entropy method (gray relational analysis method) the appropriateness of the moderate business scale of the family farm was measured and calculated by 56 representative sample data points. The conclusions obtained were as follows:

• The DEA-BCC model and the cross-efficiency DEA model were used to measure and calculate the efficiency of different agricultural business entities, and the comprehensive analysis of the results of the two models showed that the most suitable type of agriculture for dry farmland crops in Northeast China was the family farm.
• The DEA-GA-BP prediction model had higher goodness of fit and a smaller relative error than the ordinary BP-ANN model, which verified the effectiveness of the DEA-GA-BP prediction model proposed in this paper.
• The entropy method and gray relational analysis method were used to calculate the value of the correlation degree of the scheme combination of family farms. The optimal management combination for a family farm for dry farmland crops in Northeast China was obtained as follows: when the range of input for farmland planting area is 9015 to 10,000 mu, the range of direct input is 6,160,060 RMB to 6,840,500 RMB; the range of indirect input is 733,008 RMB to 1,213,400 RMB; the range of artificial input is 51,200 RMB to 100,000 RMB; and the range of mechanical input is 22,800 RMB to 1,100,000 RMB. At this time, the range of maximum output value is 12,347,630 RMB to 12,349,290 RMB; the total net income is 5,910,000 RMB.

In terms of academic value, this paper has improved the evaluation system for the operational efficiency of agricultural business entities and the measurement methods for efficiency differences. At the same time, the research has clarified that in the main grain producing areas of Northeast China, the development of family farms should be the focus of the construction of new agricultural business entities, and the optimal combination for optimizing the production factor allocation proportion of family farms was proposed. These findings have important practical significance for promoting the sustainable development of new agricultural business entities, increasing the yield and income of food crops, guaranteeing the income of farmers, and promoting rural revitalization in China.

6.2. Measures and Suggestions

Based on the analysis of efficiency differences among various agricultural business entities in the main grain-producing areas of China, it was evident that the operational efficiency of the family farm was the best, and then the value of moderate-scale production input and output of the family farm was given, which was conducive to the healthy development of the family farm. In order to continuously improve the operation system of family farms, promote the socialized service of agricultural production, and then speed up the construction of rural agricultural modernization in China, this paper puts forward the following countermeasures and suggestions:

• The construction of new agricultural business entities should focus on the development of family farms.

The family farm is the main force of management and the important driving force to introduce the small peasant household into the development track of modern agriculture. For one thing, it is necessary to accelerate the cultivation of agricultural socialization service organizations, such as farmland circulation intermediary organizations and farmer education and training institutions. For another, the establishment of a docking mechanism between family farms and the market is also essential to provide an institutional basis for the cooperation and joint operation between family farms and various agricultural socialized service organizations, which can promote the formation of a good market environment for family farms.

2.

Optimize the allocation ratio of production factors in family farms.

The conclusion of this paper shows that there is an optimal range of production resources and business scale for the family farm. Only when the input of each production factor matches the moderate operating scale can the operational efficiency of the family farm be effectively improved. The government should actively guide and help family farm to realize the optimal allocation of production resources and operation scale, reduce unnecessary inputs in the early production process, and keep the overall layout of production and operation in a dynamic balance.

3.

Strengthen the effective application of advanced production technology on family farms.

The proportion of machinery input in the total capital input of a family farm is increasing, but the technical efficiency of a family farm is not high. Studies have shown that family farms can only increase income if they adopt new technologies that match their needs. It can be inferred that large scale family farms should rationally apply advanced science, technology, and production methods to carry out standardized production according to their own needs.