# Network DEA Models with Stochastic Data to Assess the Sustainability Performance of Agricultural Practices: An Application for Sistan and Baluchestan Province in Iran

Authors: Azizallah Kord; Ali Payan; Saber Saati
Journal: Journal of Mathematics
 (2022)

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## Abstract

This article aims to determine the sustainability of agricultural performance in the cities of Sistan and Baluchestan Province of Iran by introducing a new network structure with weight restrictions in the presence of stochastic data by data envelopment analysis (DEA). Given that the functional structure of agriculture has many details, a closer and deeper look into the performance complexities can lead to a more realistic evaluation of efficiency. Therefore, the cities of Sistan and Baluchestan provinces are considered network units with weight restrictions to determine sustainability based on the environmental, social, and economic aspects. Agricultural practices were divided into two stages: the environmental stage (planting and maintaining) and the economic stage (harvesting), which use shared resources. On the other hand, DEA mainly treats all data as deterministic. Since there is a large amount of data in different periods of various actual-world problems, the use of stochastic programming approaches in DEA is of great importance for studying the behavior of this volume of data. Regarding data collected from agricultural activities in 5 periods and stochastic DEA, new network DEA models were proposed in this article to determine the sustainability levels of agricultural practices.


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## Body

## 1. Introduction

Data Envelopment Analysis (DEA) is a powerful tool to assess the relative efficiency of peer decision-making units (DMUs) with multiple inputs and outputs. In standard DEA models such as the CCR model [1] and BCC model [2], intrasystem interactions of units are neglected, and DMUs are regarded as a black box in which only their initial inputs and final outputs contribute to determining efficiency. However, most DMUs have various complex structures that affect the overall efficiency of a system. This created the network DEA introduced by Charnes et al. [3]. Network DEA has many applications in various fields. For example, Shafiei Kaleibari et al. [4] evaluated the supply chain based on the DEA network structure. The complexity of electricity generation structures was investigated by Alizadeh et al. [5] using a network DEA, in a dynamic programming context. For further clarification, one can refer to Kao [6]. One of the applications of network DEA is to evaluate the sustainability of systems that have been used in various fields such as transport, agriculture, electricity, and so on. Sustainability assessment mainly focuses on prospects for lasting net gains and the acceptability of trade-off rules among the environmental, economic, and social dimensions.It is quite significant to assess the sustainability performance of organizations for future planning and decision-making. A manager can identify an organization’s strengths and weaknesses and make performance improvement plans based on the sustainability performance of the organization. Researchers in different fields usually examine sustainability from an aspect that is more important to them. For example, Sefeedpari et al. [7] evaluated energy in dairy farming systems in Iran and measured the efficiency of 24 provinces in this regard. Ebadi Turkayesh et al. [8] considered air pollution a priority in European countries and a model of decision support based on the best-worst method and measuring options and ranking based on the compromise solution method for comparative analysis of air pollutants. 22 European countries presented. The issue of energy consumption was considered an indicator of sustainability in tomato production in the provinces of Iran by Khoshrou et al. [9]. As can be seen, the discussions and evaluations of all sustainability indicators have received less attention and broadly, one of these indicators has been selected as a top priority in various fields. Of note, the work of Ghaderi et al. [10] is among the research done in the field of sustainability that has evaluated all indicators of sustainability. They presented a multiobjective possibilistic programming problem for designing a bioethanol supply chain network with three environmental, economic, and social objectives. In another article, Gharizadeh Beiragh et al. [11] extracted the economic, environmental, and social indicators of insurance companies to assess their full sustainability. One of the best methods of assessing all sustainability aspects of organizations is network DEA, which has been used for performance assessment in many studies. Lewis et al. [12], Li et al. [13], and Zhou and Hu [14] participated in this research. This brings us to the purpose of this article which is to determine all sustainability aspects of agricultural activities by delving deeper into the functional structure and presenting a new network structure.tMuch research has been done to determine the sustainability of agricultural activities. Angulo-Meza et al. [15] perused the environmental effects on the performance of agricultural activities. The economic efficiency of wheat production in the Sistan region of Iran was measured by Sardar Shahraki et al. [16] using window DEA. Ren et al. [17] evaluated the effect of cultivated areas on sustainable agricultural development. Wang et al. [18] examined the optimal use of water and land for sustainable development. Using the Malmquist productivity index in DEA, Wan and Zhou [19] evaluated the agricultural performance of 12 cities in China’s Hubei Province. By examining the obtained results, they identified the indicators affecting the agricultural growth of different cities. Pan et al. [20] used the Malmquist index to measure the environmental and social sustainability of 31 regions in China’s mainland. There are several important grievances in the field of sustainability in agricultural activities that will be considered in this article. The main items are as follows:(1)
Only one aspect of sustainable development criteria has been investigated not all of them.(2)
Since agriculture products are produced through the planting, maintaining, and harvesting phases, performance improvement and sustainable development of agricultural practices are not possible without paying attention to their internal structures.(3)
Population growth and the shortage of natural resources have great effects on the development of agricultural practices.On the other hand, DEA applies outdated data in comparing the performances of DMUs; thus, the results obtained by solving DEA models that are provided to managers so they can adopt proper strategies are also outdated. This raises the question of which period (day, month, year, etc.) data should be used. A scientific answer to this question is to aggregate data from different periods into stochastic numbers and also that behavior of the data over time can be brought to light. To assess the sustainability performance of DMUs, the DEA method assumes data to be deterministic and defines the efficiency threshold. But decision-makers are challenged by DMUs with stochastic data in most real-world problems. On the flip side, standard DEA models do not allow stochastic variables to be part of inputs and outputs because the presence of such variables can convert efficient DMUs into inefficient ones. To overcome that weakness, researchers have created some variables as inputs and outputs for the DEA method and hence conducted studies on models consisting of stochastic variables. In order to assess performance and measure the efficiency of DMUs with stochastic data, those methods are needed by which statistical properties of data are investigated. A model that makes it possible to predict efficiency by considering event occurrence probabilities and entering predicted data is called stochastic DEA. Figure1 illustrates the difference between the production possibility thresholds of DEA and stochastic DEA (SDEA).Figure 1
Production possibility thresholds of DEA and SDEA. (a) DEA frontier; (b) SDEA frontier.
(a)(b)Sengupta [21], for the first time, proposed stochastic DEA with stochastic constraints while considering concepts such as stochastic variables and measurement errors in linear programming models. The model was later developed by Land et al. [22]. Cooper et al. [23] proposed a stochastic DEA model based on Banker et al. model [2], which involved variable returns to scale, in addition to stochastic outputs and inputs. Khodabakhshi et al. [24] proposed an input-oriented superefﬁciency model based on stochastic DEA. Investigation of environmental sustainability of supply chain networks using DEA by Alizadeh et al. [25] was performed by considering the data as stochastic numbers. Stochastic DEA models incorporate different aspects of the notion of stochastic inputs and outputs, but they are generally similar, which distinguishes them from standard DEA models. Therefore, to evaluate the performance of agricultural activities more realistically and comprehensively, this article uses stochastic data obtained from the aggregation of ordinary data in several periods.As follows, this article aims to assess the sustainability performance of network DMUs with shared resources and weight restrictions by using stochastic data. To do so, the network structure of agricultural activities in Sistan and Baluchestan Province is proposed under shared resources and stochastic data. Indices like water, cultivated area, and farmers’ revenues are very influential in determining the sustainability of agricultural practices. Water is the backbone of agriculture. Therefore, the optimal allocation of water should be taken into account for sustainable agricultural development because the improper use of water resources not only leads to environmental degradation but also makes groundwater salinized and consequently interrupts people’s lives and endangers posterity. Another important contributor to the sustainable development of agricultural practices is cultivated areas. The improper use of cultivated areas can have harmful consequences like environmental degradation. This destroys pasture lands and wipes habitats of beneficial wild animals. As a result, there would be a decrease in livestock farmers’ revenues, and hence they will be forced to migrate from villages to the outskirts and engage in pseudojobs. Revenue is the most important indicator of sustainable development since adequate revenue leads to farmers’ job satisfaction, encourages them to continue agricultural practices, and hence brings about rural sustainability. Therefore, it can be said that the sustainability of agricultural practices will be guaranteed if natural resources, i.e., soil and water, and the life quality of farmers are taken into account. In other words, sustainable TBLs, including the environmental aspect (the optimal use of natural resources), the economic aspect (adequate revenues for farmers), and the social aspect (taking responsibility for the optimal use of water), need to be properly managed to develop sustainable agriculture. Therefore, the significance of this study can be summarized as follows:(1)
Designing a near-reality model for agricultural performance by using network DEA(2)
Achieving realistic agricultural sustainability performance by collecting stochastic agricultural data in consecutive years(3)
Conducting an agricultural sustainability study of different regions of Sistan and Baluchestan Province, given it is an arid geographical areaThus, this article assesses the sustainability performance of agricultural practices based on network structure using stochastic data. Therefore, the stochastic network DEA is used to determine the sustainable levels of agricultural practices with stochastic data. For the first time, the present study divides agricultural processes into the environmental stage, which includes planting and maintaining activities and the economic stage, which includes harvesting activity, and proposes an additive stochastic network DEA with shared resources. Stochastic network DEA is used to analyze the overall and substage stochastic sustainability of agricultural practices of counties of Sistan and Baluchestan Province in terms of the TBLs of sustainability. In this research, the sustainability status of agricultural activities in Sistan and Baluchestan will be determined based on the stochastic data, and major causes of inefficiency in each sustainability index will be identified, which would help the government and the Ministry of Jihad Agriculture to develop sustainable agriculture in Sistan and Baluchestan Province.The rest of this article is organized as follows: Section2 presents the DEA methodology for assessing the overall and stage-wise stochastic sustainable efficiencies in the network structure of agricultural activities in Sistan and Baluchestan under shared resources. Numerical examples of the sustainable levels of agricultural activities in each county of Sistan and Baluchestan are illustrated in Section 3 based on the suggested models in the previous section. Finally, Section 4 presents the concluding remarks and suggestions.


## 2. Methodology

### 2.1. Network Structure of DMUs with Shared Resources

Suppose a set of DMUs includesn units with a two-stage series structure and shared inputs in the two stages. Following notations are used for each DMUjj=1,…,n as follows:(i)
xiji=1,…,m is the ith input of system.(ii)
xi1ji1=1,…,t is thei1th input that only belongs to the first stage.(iii)
xi2ji2=t+1,…,m is thei2th input that is shared between the two stages.(iv)
zdjd=1,…,D is the dth output from the first stage, that is, the dth input of the second stage (intermediate data).(v)
yrjr=1,…,s is the rth output of system.Figure2 expresses the structure of such DMU.Figure 2
Two-stage structure that includes shared inputs.As mentioned earlier, a technique for measuring the sustainability performance and the sustainable efficiency of such DMUs is the DEA method. In this method, the cost and weight of outputs and those of inputs are freely determined by models. On the other hand, for the sustainable efficiency of DMUs to be measured by DEA models, it is important to determine the weights of indices such that the sustainable efficiency of each DMU is maximized. So, if a DMU is inefficient without weight restrictions, no other models can evaluate it as efficient. As a result, it can be said that free weights of indices are the strength of DEA. But in a DEA model without weight restrictions, the sustainable efficiency of every DMU is obtained in the best conditions of assessment. From this perspective, therefore, free weights of indices are the weakness of DEA. To overcome this problem, the present study applies weight restrictions to inputs and outputs to measure the sustainable efficiency of DMUs.Given the weight restrictions of inputs and outputs, the efficiencies ofDMUo in the first and second stages are determined as follows by considering the variable returns to scale (VRS) assumption [2]. Moreover, the efficiency of each DMU would be measured provided that the shared inputs are fully consumed in the first and second stages:(1)eo1=max∑d=1Dφd1Zdo+v1∑i1=1tγi1xi1o+∑i2=t+1mγi21xi2o,(2)s.t:∑d=1Dφd1Zdj+v1∑i1=1tγi1xi1j+∑i2=t+1mγi21xi2j≤1,∀j,(3)l¯i1≤γi1≤u¯i1,∀i1l¯i2≤γi21≤u¯i2,∀i2l¯d≤φd1≤u¯d,∀d,(4)eo2=max∑r=1suryro+v2∑d=1Dφd2Zdo+∑i2=t+1mγi22xi2o,(5)s.t:∑r=1suryrj+v2∑d=1dφd2Zdj+∑i2=t+1mγi22xi2j≤1,∀j,(6)l¯r≤ur≤u¯r,∀rl¯i2≤γi22≤u¯i2,∀i2l¯d≤φd2≤u¯d,∀d,where φd1,γi1,γi21 and φd2,ur,γi22 are weights related to the data that are determined by solving models (2) and (5).Similar to Liang et al. [26] and Chen et al. [27], assume that the weights intermediate measures as outputs of the first stage are equal to the weights intermediate measures when the data are considered as inputs of the second stage. In other words, φd1=φd2=φd,d=1,…,D. In a similar discussion, we consider γi22=γi21=γi2∀i2.Considerω1,ω2 as weights of the two stages, which ω1+ω2=1. Kao and Hwang [28] proposed ω1∑i1=1tγi1xi1j+∑i2=t+1mγi2xi2j+ω2∑d=1dφdZdj+∑i2=t+1Mγi2xi2j and ω1∑d=1dφdZdj+v1+ω2∑r=1suryrj+v2 as the overall input and the overall output of DMUjj=1,…,n. Thus, the overall efficiency of DMUo is measured by the following model:(7)eo=maxω1∑d=1DφdZdo+v1+ω2∑r=1suryro+v2ω1∑i1=1tγi1xi1o+∑i2=t+1mγi2xi2o+ω2∑d=1DφdZdo+∑i2=t+1mγi2xi2o,(8)s.t:∑d=1DφdZdj+v1∑i1=1tγi1xi1j+∑i2=t+1mγi2xi2j≤1,∀j,(9)∑r=1suryrj+v2∑d=1DφdZdj+∑i2=t+1mγi2xi2j≤1,∀j,(10)l¯i1≤γi1≤u¯i1,∀i1l¯r≤ur≤u¯r,∀rl¯i2≤γi2≤u¯i2,∀i2l¯d≤φd≤u¯d,∀d.For converting the fractional programming model (8) to a linear form, Charnes and Cooper’s transformations [29] are used as follows:(11)ω1∑i1=1tγi1xi1o+∑i2=t+1mγi2xi2o+ω2∑d=1DφdZdo+∑i2=t+1mγi2xi2o=1t.Then, we have the following:(12)eo=maxω1∑d=1DφdZdo+v1+ω2∑r=1suryro+v2,(13)s.t:ω1∑i1=1tγi1xi1o+∑i2=t+1mγi2xi2o+ω2∑d=1DφdZdo+∑i2=t+1mγi2xi2o=1,(14)∑d=1DφdZdj+v1−∑i1=1tγi1xi1j−∑i2=t+1mγi2xi2j≤0∀j,(15)∑r=1suryrj+v2−∑d=1DφdZdj−∑i2=t+1mγi2xi2j≤0,≤∀j,(16)l¯i1≤γi1≤u¯i1,∀i1l¯r≤ur≤u¯r,∀rl¯i2≤γi2≤u¯i2,∀i2l¯d≤φd≤u¯d,∀d.Efficiencies of stages are measured by solving the following models (20) and (26), while the overall efficiency has been calculated by model (72) as follows:(17)eo1=max∑d=1DφdZdo+v1,(18)s.t:∑i1=1tγi1xi1o+∑i2=t+1mγi2xi2o=1,(19)ω1∑d=1DφdZdo+v1+ω2∑r=1suryro+v2ω1+ω2∑d=1DφdZdo+∑i2=t+1mγi2xi2o=eo∗,(20)∑d=1DφdZdj+v1−∑i1=1tγi1xi1j−∑i2=t+1mγi2xi2j≤0∀j,(21)∑r=1suryrj+v2−∑d=1DφdZdj−∑i2=t+1mγi2xi2j≤0,∀j,(22)l¯i1≤γi1≤u¯i1,∀i1l¯r≤ur≤u¯r,∀rl¯i2≤γi2≤u¯i2,∀i2l¯d≤φd≤u¯d,∀d,(23)eo2=max∑r=1suryro+v2,(24)s.t:∑d=1DφdZdo+∑i2=t+1mγi2xi2o=1,(25)ω1∑d=1DφdZdo+v1+ω2∑r=1suryro+v2ω1∑i1=1tγi1xi1o+∑i2=t+1mγi2xi2o+ω2=eo∗,(26)∑d=1DφdZdj+v1−∑i1=1tγi1xi1j−∑i2=t+1mγi2xi2j≤0∀j,(27)∑r=1suryrj+v2−∑d=1DφdZdj−∑i2=t+1mγi2xi2j≤0,∀j,(28)l¯i1≤γi1≤u¯i1,∀i1l¯r≤ur≤u¯r,∀rl¯i2≤γi2≤u¯i2,∀i2l¯d≤φd≤u¯d,∀d.


### 2.2. Agricultural Structure of Counties in Sistan and Baluchestan Province

In this section, the structures of 19 counties of Sistan and Baluchestan’s province as DMUs are studied. In agriculture, Human resources participate in preparing arable land for cultivation and use water, fertilizers, and pesticides to cultivate arable land. Human resources then produce crops in the cultivated areas with the maintenance process and sell them to the market in order to earn money. Accordingly, the nature of agricultural activities has a network structure in which the initial outputs are considered inputs for the next stage. Therefore, the structure consists of two stages: (1) human resources and water are used to prepare the area under cultivation. (2) Human resources are the common input of the two stages, and the area under cultivation produce crops that obtains the other output of the system is income. Certainly, the optimal use of water is an important factor contributing to the development of the agricultural sector. Therefore, utilizing modern methods of irrigation and cultivating crops, which need much less water and provide more revenues, would lead to the expansion of cultivated areas, which is the objective of the first stage. So, the first stage aims to use the least quantities of environmental and social inputs, i.e., water and human resources, to produce the highest environmental output, cultivated area. In the second stage, the human resources should increase crop production per cultivated area and ultimately gain the highest revenue. Therefore, the cultivated area is viewed as an input economic index, and production volume and revenues are considered as output economic indices in the second stage. The planting and maintaining of agricultural products are done in the first stage. This stage is called the environmental stage because plants grow in the environment and the output of this stage is cultivated area. The second stage is related to the harvesting of agricultural products. The second is called the economic stage since one of the outputs is revenues. Figure3 illustrates the network structure of agricultural activities such that proposed in this article.Figure 3
Network structure of agricultural practices.


### 2.3. Sustainability of Agricultural Processes under the Weight Restrictions

Water is an important index in determining the sustainability of agricultural practices. Farmers in some parts of the country are still using traditional methods of irrigation for different reasons, such as the lack of knowledge about agriculture and the lack of awareness of water resources. Sustainable development of agriculture will be achieved if the optimal use of water is taken into account.Proper water use prevents environmental degradation and, consequently, the life of posterity from being threatened. Therefore, the Water Resources Management Company and the Ministry of Jihad Agriculture have supplied water at a low price to encourage farmers to use modern irrigation methods and cultivate crops that need less water and yield more valuable products. As a result, water price is considered a weight restriction to determine the sustainability level of agricultural activities.Human resources are an important and influential factor in the sustainable development of agricultural practices. Human resources are nowadays viewed as one of the most important elements or resources of every country. Therefore, agricultural practices would be sustainable if they are economically beneficial to human resources. Agricultural practices will be economically provided that minimum human resources create maximum cultivated area and maximum production volume per cultivated area. This encourages farmers to be engaged in agricultural practices and, hence leads to rural sustainability. Since the human, social dimensions and rural regeneration have an impact on developing sustainable agriculture, minimum wages are determined for every 8 working hours of human resources every year, given the current economic situation and inflation rates. Minimum wages can be regarded as a weight restriction to determine the sustainability of agricultural activities using DEA.As previously mentioned, the sustainability of agricultural practices in the different counties depends on adequate revenues and the improvement of the quality of life of farmers. On the other hand, farmers’ revenues in each county are measured by the production volume and value of that county. So, ifu1represents the revenue weight and u2 represents the production volume weight of the counties under study, we have(29)Revenues of a CountyProduction Volume of a County=u1u2.Equation (29) can be rewritten as follows:(30)Revenues of a County×u2−Production Volume of a County×u1=0.Equation (30) can be considered as a weight restriction for revenues and production volume to determine the sustainable efficiency of agricultural practices using DEA.Based on the proposed structure, agricultural practices in thejth county have the two environmental and economic stages, and human resources are the shared input of both stages. Suppose that the relative importance of the two stages is the same. In the jth county, in the environmental stage, xj and hj represent water and human resources inputs, respectively, and zj represents cultivated area output, which is the input of the economic stage, and in the economic stage, y1j and y2j represent revenues and production volume inputs, respectively. Given that ω1=ω2=1/2, models (14), (20), and (26) can be reformulated as follows to measure the overall sustainable efficiency and the sustainable efficiency of the environmental and economic stages, respectively, with respect to weight restrictions in the oth county:(31)eo=max12φZo+v1+12∑r=12uryro+v2,(32)s.t:12vxo+who+12φZ0+who=1,(33)φZj+v1−vxj−whj≤0∀j=1,…,19,(34)∑r=12uryrj+v2−φZj−whj≤0∀j=1,…,19,(35)u2y1o−u1y2o=0,(36)v≤uv,lw≤w,(37)φ,u1,u2,v,w≥0.For calculating the environmental efficiency, we have the following:(38)eo1=maxφZo+v1,(39)s.t:vxo+who=1,(40)1/2φZo+v1+1/2∑r=12uryro+v21/2+1/2φZ0+who=eo∗,(41)φZj+v1−vxj−whj≤0,∀j=1,…,19,(42)∑r=12uryrj+v2−φZj−whj≤0,∀j=1,…,19,(43)u2y1o−u1y2o=0,(44)v≤uv,lw≤w,(45)φ,u1,u2,v,w≥0.For calculating the economic efficiency, we have the following:(46)eo2=max∑r=12uryro+v2,(47)s.t:φZ0+who=1,(48)1/2φZo+v1+1/2∑r=12uryro+v21/2vxo+who+1/2=eo∗,(49)φZj+v1−vxj−whj≤0,∀j=1,…,19,(50)∑r=12uryrj+v2−φZj−whj≤0,∀j=1,…,19,(51)u2y1o−u1y2o=0,(52)v≤uv,lw≤w,(53)φ,u1,u2,v,w≥0.In models (33), (41), and (49), the linear relationship u2y1o−u1y2o=0 is used as a weight restriction for revenues and production volume outputs. Also, the maximum price of water per cubic meter represented by uv and the minimum wages of human resources per 8 hours’ daily work represented by lw are used as weight restrictions for water and human resources inputs.


### 2.4. Determining the Sustainable Efficiency of Agricultural Practices in Sistan and Baluchestan Province with Stochastic Data

Following Cooper et al. [23] and Khodabakhshi [30], suppose that, in the jth county, xj and hj represent the deterministic data of water and human resources inputs of the environmental stage, respectively, and z¯j and y¯rjr=1,2 represent the stochastic data of the intermediate measures and outputs of the second stage with multivariate normal distribution and known parameters. Moreover, suppose that all the stochastic variables have a normal distribution with known means and standard deviations. By introducing stochastic data into models (33), (41), and (49), the overall stochastic efficiency, environmental stochastic efficiency, and economic stochastic efficiency can be obtained by solving the following models:(54)eo=max12φz¯o+12v1+12u1y¯1o+12u2y¯2o+12v2,(55)s.t:12vxo+who+12φz¯o+who=1,(56)φz¯j+v1−vxj−whj≤0,∀j=1,…,19,(57)u1y¯1j+u2y¯2j+v2−φz¯j−whj≤0,∀j=1,…,19,(58)u2y¯1o−u1y¯2o=0,(59)v≤u¯v,l¯w≤w,(60)φ,u1,u2,v,w≥0,(61)eo1=maxφz¯o+v1,(62)s.t:vxo+who=1,(63)1/2φz¯o+1/2v1+1/2u1y¯1o+1/2u2y¯2o+1/2v21/2+1/2φz¯o+who=eo∗,(64)φz¯j+v1−vxj−whj≤0,∀j=1,…,19,(65)u1y¯1j+u2y¯2j+v2−φz¯j−whj≤0,∀j=1,…,19,(66)u2y¯1o−u1y¯2o=0,(67)v≤u¯v,l¯w≤w,(68)φ,u1,u2,v,w≥0.Model (64) can be expressed as follows:(69)eo1=maxφz¯o+v1,(70)s.t:vxo+who=1,(71)12−12eo∗φz¯o−12eo∗who+12u1y¯1o+12u2y¯2o12v1++12v2=12eo∗,(72)φz¯j+v1−vxj−whj≤0,∀j=1,…,19,(73)u1y¯1j+u2y¯2j+v2−φz¯j−whj≤0,∀j=1,…,19,(74)u2y¯1o−u1y¯2o=0,(75)v≤u¯v,l¯w≤w,(76)φ,u1,u2,v,w≥0,(77)eo2=maxu1y¯1o+u2y¯2o+v2,(78)s.t:φz¯o+who=1,(79)1/2φz¯o+1/2v1+1/2u1y¯1o+1/2u2y¯2o+1/2v21/2vxo+who+1/2=eo∗,(80)φz¯j+v1−vxj−whj≤0,∀j=1,…,19,(81)u1y¯1j+u2y¯2j+v2−φz¯j−whj≤0,∀j=1,…,19,(82)u2y¯1o−u1y¯2o=0,(83)v≤u¯v,l¯w≤w,(84)φ,u1,u2,v,w≥0.Model (80) can be rewritten as follows:(85)eo2=maxu1y¯1o+u2y¯2o+v2,(86)s.t:φz¯o+who=1,(87)12φz¯o+12u1y¯1o+12u2y¯2o−12eo∗vxo−12eo∗who+12v1+12v2=12eo∗,(88)φz¯j+v1−vxj−whj≤0,∀j=1,…,19,(89)u1y¯1j+u2y¯2j+v2−φz¯j−whj≤0,∀j=1,…,19,(90)u2y¯1o−u1y¯2o=0,(91)v≤u¯v,l¯w≤w,(92)φ,u1,u2,v,w≥0.For simplicity in calculating the overall and stage-wise stochastic efficiencies, the duals of models (56), (72), and (88) can be used as follows:(93)eo=minθ1+u¯vθ3−l¯wθ4,(94)s.t:p∑j=119μjy¯1j−θ2y¯2o−12y¯1o≥0≥1−α,(95)p∑j=119μjy¯2j+θ2y¯1o−12y¯2o≥0≥1−α,(96)p∑j=119γj−μjz¯j+12θ1−12z¯o≥0≥1−α,(97)−∑j=119γjxj+12θ1xo+θ3≥0,(98)−∑j=119γj+μjhj+θ1ho−θ4≥0,(99)∑j=119γj=12,∑j=119μj=12,(100)γj,μj,θ3,θ4≥0.Model (96) can be expressed as follows:(101)eo=minf,s.t:p−u¯vθ3+l¯wθ4≥−f+θ1≥1−α,a,p∑j=119μjy¯1j−θ2y¯2o−12y¯1o≥0≥1−α,b,p∑j=119μjy¯2j+θ2y¯1o−12y¯2o≥0≥1−α,c,p∑j=119γj−μjz¯j+12θ1−12z¯o≥0≥1−α,d,−∑j=119γjxj+12θ1xo+θ3≥0,−∑j=119γj+μjhj+θ1ho−θ4≥0,∑j=119γj=12,∑j=119μj=12,γj,μj,θ3,θ4≥0,(102)eo1=minθ1+12eo∗β+u¯vθ3−l¯wθ4,(103)s.t:p∑j=119μjy¯1j−θ2y¯2o+12βy¯1o≥0≥1−α,(104)p∑j=119μjy¯2j+θ2y¯1o+12βy¯2o≥0≥1−α,(105)p∑j=119γj−μjz¯j+12β−12eo∗β−1z¯o≥0≥1−α,(106)−∑j=119γjxj+θ1xo+θ3≥0,(107)−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,(108)∑j=119γj+12β=1,∑j=119μj+12β=0,(109)γj,μj,θ3,θ4≥0.Model (105) can be revised as follows:(110)eo1=minf,s.t:p−u¯vθ3+l¯wθ4≥−f+θ1+12eo∗β≥1−α,a,p∑j=119μjy¯1j−θ2y¯2o+12βy¯1o≥0≥1−α,b,p∑j=119μjy¯2j+θ2y¯1o+12βy¯2o≥0≥1−α,c,p∑j=119γj−μjz¯j+12β−12eo∗β−1z¯o≥0≥1−α,d,−∑j=119γjxj+θ1xo+θ3≥0,−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,∑j=119γj+12β=1,∑j=119μj+12β=0,γj,μj,θ3,θ4≥0,(111)eo2=minθ1+12eo∗β+u¯vθ3−l¯wθ4,(112)s.t:p∑j=119μjy¯1j−θ2y¯2o+12βy¯1o−y¯1o≥0≥1−α,(113)p∑j=119μjy¯2j+θ2y¯1o+12βy¯2o−y¯2o≥0≥1−α,(114)p∑j=119γj−μjz¯j+12βz¯o+θ1z¯o≥0≥1−α,(115)−∑j=119γjxj−12eo∗βxo+θ3≥0,(116)−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,(117)∑j=119γj+12β=0,∑j=119μj+12β=1,(118)γj,μj,θ3,θ4≥0.Model (114) can be rewritten as follows:(119)eo2=minf,s.t:p−u¯vθ3+l¯wθ4≥−f+θ1+12eo∗β≥1−α,a,p∑j=119μjy¯1j−θ2y¯2o+12βy¯1o−y¯1o≥0≥1−α,b,p∑j=119μjy¯2j+θ2y¯1o+12βy¯2o−y¯2o≥0≥1−α,c,p∑j=119γj−μjz¯j+12βz¯o+θ1z¯o≥0≥1−α,d,−∑j=119γjxj−12eo∗βxo+θ3≥0,−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,∑j=119γj+12β=0,∑j=119μj+12β=1,γj,μj,θ3,θ4≥0.In models (101), (110), and (119), constraints (a), (b), (c), and (d) are stochastic in which p implies probability and α is constraint risk, a number between 0 and 1. In order to calculate the stochastic efficiency of the above models using DEA, stochastic constraints should be changed to deterministic constraints. In model (101), stochastic constraint (a) can be converted to deterministic constraint as follows:(120)p−u¯vθ3+l¯wθ4≥−f+θ1+s=1−α.The stochastic variablels is introduced as follows:(121)l=−u¯vθ3+l¯wθ4.The mean ofl equals(122)μl=−uvθ3+lwθ4,where uv and lw are the means of u¯v and l¯w, respectively. The variance of l is determined as follows:(123)varl=YTVY,σl=varl,where(124)YT=−θ3,θ4,V=varu¯vcovu¯v,l¯wcovl¯w,u¯vvarl¯w.The new standard random variablez¯l is defined as follows:(125)z¯l=l−μlσl.Ifμl is subtracted from both sides of equation (112) and divided by σl, then we have(126)p−u¯vθ3+l¯wθ4−μlσl≥−f+θ1+s−μlσl=1−α.Thus,(127)pz¯l≥−f+θ1+s−μlσl=1−α.Equation (127) can be rewritten as follows:(128)pz¯l≤−f+θ1+s−μlσl=α.Therefore,(129)φ−f+θ1+s−μlσl=α⟶φ−1α=−f+θ1+s−μlσl.Consequently, the following deterministic constraint is substituted for the stochastic constraint (a) in model (101):(130)uvθ3−lwθ4−f+θ1+s−σlφ−1α=0.Accordingly, the stochastic constraint (b) in model (101) can be converted as follows:(131)p∑j=119μjy¯1j−θ2y¯2o−12y¯1o≥s1=1−α.Here, the random variabley1 is defined as follows:(132)y1=∑j=119μjy¯1j−θ2y¯2o−12y¯1o.The mean ofy1 is calculated as follows:(133)μy1=∑j=119μjy1j−θ2y2o−12y1o.In relation (134), y1j is the mean of y¯1j. The variance of y1 is calculated as follows:(134)vary1=XTV1X,(135)σy1=vary1,where(136)XT=μ1,μ2,…,μ19,−θ2,μo−12,V1=vary11covy11,y12…covy11,y119covy11,y2ocovy11,y1ocovy12,y11vary12…covy12,y119covy12,y2ocovy12,y1o⋅⋅⋅covy119,y11covy119,y12…vary119covy119,y2ocovy119,y1ocovy119,y11covy119,y12…vary119covy119,y2ocovy119,y1ocovy1o,y11covy1o,y12…covy1o,y119covy1o,y2ovary1o.The new standard random variablez¯1 is defined as follows:(137)z¯1=y1−μy1σy1.Now, ifμy1 is subtracted from both sides of equation (131) and divided by σy1, then we have(138)p∑j=119μjy¯1j−θ2y¯2o−1/2y¯1o−μy1σy1≥s1−μy1σy1=1−α.Thus,(139)pz¯1≥s1−μy1σy1=1−α.Relation (139) can be rewritten as follows:(140)pz¯1≤s1−μy1σy1=α.Therefore,(141)φs1−μy1σy1=α⟶s1−μy1σy1=φ−1α.As a result,(142)s1−μy1−φ−1ασy1=0.By inserting relation (133) in the above equation, we have(143)−∑j=119μjy1j+θ2y2o+12y1o+s1−φ−1ασy1=0.Similarly, the deterministic equivalents of stochastic constraints (c) and (d) are obtained. As a result, the deterministic equivalent of model (101) is calculated as follows:(144)eo=minf,s.t:uvθ3−lwθ4−f+θ1+sl−σlφ−1α=0,−∑j=119μjy1j+θ2y2o+12y1o+s1−φ−1ασy1=0,−∑j=119μjy2j−θ2y1o+12y2o+s2−φ−1ασy2=0,−∑j=119γj−μjzj−12θ1−12zo+sz−φ−1ασz1=0,−∑j=119γjxj+12θ1xo+θ3≥0,−∑j=119γj+μjhj+θ1ho−θ4≥0,∑j=119γj=12,∑j=119μj=12,γj,μj,θ3,θ4≥0,where(145)σ2l=θ32varu¯v+θ42varl¯w−2θ3θ4covu¯v,l¯w,σ2y1=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯1i,y¯1j−2θ2∑i=1i≠o19μicovy¯1i,y¯2o+2μo−12∑i=1i≠o19μicovy¯1i,y¯1o−2θ2μo−12covy¯2o,y¯1o+μo−122vary¯1o+θ22vary¯2o,σ2y2=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯2i,y¯2j+2θ2∑i=1i≠o19μicovy¯2i,y¯1o+2μo−12∑i=1i≠o19μicovy¯2i,y¯2o+2θ2μo−12covy¯1o,y¯2o+μo−122vary¯2o+θ22vary¯1o,σ2z1=∑i=1i≠o19∑j=1j≠o19μi−γiμj−γjcovz¯i,z¯j+2μo−γo+12θ1−12,∑i=1i≠o19μi−γicovz¯i,z¯o+μo−γo+12θ1−122varz¯o.Similarly, the deterministic equivalents of models (110) and (119) are, respectively, as follows:(146)eo1=minf,s.t:uvθ3−lwθ4−f+θ1+12eo∗β+sl−σlφ−1α=0,−∑j=119μjy1j+θ2y2o−12βy1o+s1−φ−1ασy1=0,−∑j=119μjy2j−θ2y1o−12βy2o+s2−φ−1ασy2=0,−∑j=119γj−μjzj−12β−12eo∗β−1zo+sz−φ−1ασz1=0,−∑j=119γjxj+θ1xo+θ3≥0,−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,∑j=119γj+12β=1,∑j=119μj+12β=0,γj,μj,θ3,θ4≥0,where(147)σ2l=θ32varu¯v+θ42varl¯w−2θ3θ4covu¯v,l¯w,σ2y1=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯1i,y¯1j−2θ2∑i=1i≠o19μicovy¯1i,y¯2o+2μo+12β∑i=1i≠o19μicovy¯1i,y¯1o−2θ2μo+12βcovy¯2o,y¯1o+μo+12β2vary¯1o+θ22vary¯2o,σ2y2=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯2i,y¯2j+2θ2∑i=1i≠o19μicovy¯2i,y¯1o+2μo+12β∑i=1i≠o19μicovy¯2i,y¯2o+2θ2μo+12βcovy¯1o,y¯2o+μo+12β2vary¯2o+θ22vary¯1o,σ2z1=∑i=1i≠o19∑j=1j≠o19μi−γiμj−γjcovz¯i,z¯j+2μo−γo+12β−12eo∗β−1,∑i=1i≠o19μi−γicovz¯i,z¯o+μo−γo+12β−12eo∗β−12varz¯o.(148)eo2=minf,s.t:uvθ3−lwθ4−f+θ1+12eo∗β+sl−σlφ−1α=0,−∑j=119μjy1j+θ2y2o−12β−1y1o+s1−φ−1ασy1=0,−∑j=119μjy2j−θ2y1o−12β−1y2o+s2−φ−1ασy2=0,−∑j=119γj−μjzj−12β+θ1zo+sz−φ−1ασz1=0,−∑j=119γjxj−12eo∗βxo+θ3≥0,−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,∑j=119γj+12β=0,∑j=119μj+12β=1,γj,μj,θ3,θ4≥0,where(149)σ2l=θ32varu¯v+θ42varl¯w−2θ3θ4covu¯v,l¯w,σ2y1=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯1i,y¯1j−2θ2∑i=1i≠019μicovy¯1i,y¯2o+2μo+12β−1∑i=1i≠019μicovy¯1i,y¯1o−2θ2μo+12β−1covy¯2o,y¯1o+μo+12β−12vary¯1o+θ22vary¯2o,σ2y2=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯2i,y¯2j+2θ2∑i=1i≠019μicovy¯2i,y¯1o+2μo+12β−1∑i=1i≠019μicovy¯2i,y¯2o+2θ2μo+12β−1covy¯1o,y¯2o+μo+12β−12vary¯2o+θ22vary¯1o,σ2z1=∑i=1i≠o19∑j=1j≠o19μi−γiμj−γjcovz¯i,z¯j+2μo−γo+12β+θ1∑i=1i≠019μi−γicovz¯i,z¯o+μo−γo+12β+θ12varz¯o.


## 2.1. Network Structure of DMUs with Shared Resources

Suppose a set of DMUs includesn units with a two-stage series structure and shared inputs in the two stages. Following notations are used for each DMUjj=1,…,n as follows:(i)
xiji=1,…,m is the ith input of system.(ii)
xi1ji1=1,…,t is thei1th input that only belongs to the first stage.(iii)
xi2ji2=t+1,…,m is thei2th input that is shared between the two stages.(iv)
zdjd=1,…,D is the dth output from the first stage, that is, the dth input of the second stage (intermediate data).(v)
yrjr=1,…,s is the rth output of system.Figure2 expresses the structure of such DMU.Figure 2
Two-stage structure that includes shared inputs.As mentioned earlier, a technique for measuring the sustainability performance and the sustainable efficiency of such DMUs is the DEA method. In this method, the cost and weight of outputs and those of inputs are freely determined by models. On the other hand, for the sustainable efficiency of DMUs to be measured by DEA models, it is important to determine the weights of indices such that the sustainable efficiency of each DMU is maximized. So, if a DMU is inefficient without weight restrictions, no other models can evaluate it as efficient. As a result, it can be said that free weights of indices are the strength of DEA. But in a DEA model without weight restrictions, the sustainable efficiency of every DMU is obtained in the best conditions of assessment. From this perspective, therefore, free weights of indices are the weakness of DEA. To overcome this problem, the present study applies weight restrictions to inputs and outputs to measure the sustainable efficiency of DMUs.Given the weight restrictions of inputs and outputs, the efficiencies ofDMUo in the first and second stages are determined as follows by considering the variable returns to scale (VRS) assumption [2]. Moreover, the efficiency of each DMU would be measured provided that the shared inputs are fully consumed in the first and second stages:(1)eo1=max∑d=1Dφd1Zdo+v1∑i1=1tγi1xi1o+∑i2=t+1mγi21xi2o,(2)s.t:∑d=1Dφd1Zdj+v1∑i1=1tγi1xi1j+∑i2=t+1mγi21xi2j≤1,∀j,(3)l¯i1≤γi1≤u¯i1,∀i1l¯i2≤γi21≤u¯i2,∀i2l¯d≤φd1≤u¯d,∀d,(4)eo2=max∑r=1suryro+v2∑d=1Dφd2Zdo+∑i2=t+1mγi22xi2o,(5)s.t:∑r=1suryrj+v2∑d=1dφd2Zdj+∑i2=t+1mγi22xi2j≤1,∀j,(6)l¯r≤ur≤u¯r,∀rl¯i2≤γi22≤u¯i2,∀i2l¯d≤φd2≤u¯d,∀d,where φd1,γi1,γi21 and φd2,ur,γi22 are weights related to the data that are determined by solving models (2) and (5).Similar to Liang et al. [26] and Chen et al. [27], assume that the weights intermediate measures as outputs of the first stage are equal to the weights intermediate measures when the data are considered as inputs of the second stage. In other words, φd1=φd2=φd,d=1,…,D. In a similar discussion, we consider γi22=γi21=γi2∀i2.Considerω1,ω2 as weights of the two stages, which ω1+ω2=1. Kao and Hwang [28] proposed ω1∑i1=1tγi1xi1j+∑i2=t+1mγi2xi2j+ω2∑d=1dφdZdj+∑i2=t+1Mγi2xi2j and ω1∑d=1dφdZdj+v1+ω2∑r=1suryrj+v2 as the overall input and the overall output of DMUjj=1,…,n. Thus, the overall efficiency of DMUo is measured by the following model:(7)eo=maxω1∑d=1DφdZdo+v1+ω2∑r=1suryro+v2ω1∑i1=1tγi1xi1o+∑i2=t+1mγi2xi2o+ω2∑d=1DφdZdo+∑i2=t+1mγi2xi2o,(8)s.t:∑d=1DφdZdj+v1∑i1=1tγi1xi1j+∑i2=t+1mγi2xi2j≤1,∀j,(9)∑r=1suryrj+v2∑d=1DφdZdj+∑i2=t+1mγi2xi2j≤1,∀j,(10)l¯i1≤γi1≤u¯i1,∀i1l¯r≤ur≤u¯r,∀rl¯i2≤γi2≤u¯i2,∀i2l¯d≤φd≤u¯d,∀d.For converting the fractional programming model (8) to a linear form, Charnes and Cooper’s transformations [29] are used as follows:(11)ω1∑i1=1tγi1xi1o+∑i2=t+1mγi2xi2o+ω2∑d=1DφdZdo+∑i2=t+1mγi2xi2o=1t.Then, we have the following:(12)eo=maxω1∑d=1DφdZdo+v1+ω2∑r=1suryro+v2,(13)s.t:ω1∑i1=1tγi1xi1o+∑i2=t+1mγi2xi2o+ω2∑d=1DφdZdo+∑i2=t+1mγi2xi2o=1,(14)∑d=1DφdZdj+v1−∑i1=1tγi1xi1j−∑i2=t+1mγi2xi2j≤0∀j,(15)∑r=1suryrj+v2−∑d=1DφdZdj−∑i2=t+1mγi2xi2j≤0,≤∀j,(16)l¯i1≤γi1≤u¯i1,∀i1l¯r≤ur≤u¯r,∀rl¯i2≤γi2≤u¯i2,∀i2l¯d≤φd≤u¯d,∀d.Efficiencies of stages are measured by solving the following models (20) and (26), while the overall efficiency has been calculated by model (72) as follows:(17)eo1=max∑d=1DφdZdo+v1,(18)s.t:∑i1=1tγi1xi1o+∑i2=t+1mγi2xi2o=1,(19)ω1∑d=1DφdZdo+v1+ω2∑r=1suryro+v2ω1+ω2∑d=1DφdZdo+∑i2=t+1mγi2xi2o=eo∗,(20)∑d=1DφdZdj+v1−∑i1=1tγi1xi1j−∑i2=t+1mγi2xi2j≤0∀j,(21)∑r=1suryrj+v2−∑d=1DφdZdj−∑i2=t+1mγi2xi2j≤0,∀j,(22)l¯i1≤γi1≤u¯i1,∀i1l¯r≤ur≤u¯r,∀rl¯i2≤γi2≤u¯i2,∀i2l¯d≤φd≤u¯d,∀d,(23)eo2=max∑r=1suryro+v2,(24)s.t:∑d=1DφdZdo+∑i2=t+1mγi2xi2o=1,(25)ω1∑d=1DφdZdo+v1+ω2∑r=1suryro+v2ω1∑i1=1tγi1xi1o+∑i2=t+1mγi2xi2o+ω2=eo∗,(26)∑d=1DφdZdj+v1−∑i1=1tγi1xi1j−∑i2=t+1mγi2xi2j≤0∀j,(27)∑r=1suryrj+v2−∑d=1DφdZdj−∑i2=t+1mγi2xi2j≤0,∀j,(28)l¯i1≤γi1≤u¯i1,∀i1l¯r≤ur≤u¯r,∀rl¯i2≤γi2≤u¯i2,∀i2l¯d≤φd≤u¯d,∀d.


## 2.2. Agricultural Structure of Counties in Sistan and Baluchestan Province

In this section, the structures of 19 counties of Sistan and Baluchestan’s province as DMUs are studied. In agriculture, Human resources participate in preparing arable land for cultivation and use water, fertilizers, and pesticides to cultivate arable land. Human resources then produce crops in the cultivated areas with the maintenance process and sell them to the market in order to earn money. Accordingly, the nature of agricultural activities has a network structure in which the initial outputs are considered inputs for the next stage. Therefore, the structure consists of two stages: (1) human resources and water are used to prepare the area under cultivation. (2) Human resources are the common input of the two stages, and the area under cultivation produce crops that obtains the other output of the system is income. Certainly, the optimal use of water is an important factor contributing to the development of the agricultural sector. Therefore, utilizing modern methods of irrigation and cultivating crops, which need much less water and provide more revenues, would lead to the expansion of cultivated areas, which is the objective of the first stage. So, the first stage aims to use the least quantities of environmental and social inputs, i.e., water and human resources, to produce the highest environmental output, cultivated area. In the second stage, the human resources should increase crop production per cultivated area and ultimately gain the highest revenue. Therefore, the cultivated area is viewed as an input economic index, and production volume and revenues are considered as output economic indices in the second stage. The planting and maintaining of agricultural products are done in the first stage. This stage is called the environmental stage because plants grow in the environment and the output of this stage is cultivated area. The second stage is related to the harvesting of agricultural products. The second is called the economic stage since one of the outputs is revenues. Figure3 illustrates the network structure of agricultural activities such that proposed in this article.Figure 3
Network structure of agricultural practices.


## 2.3. Sustainability of Agricultural Processes under the Weight Restrictions

Water is an important index in determining the sustainability of agricultural practices. Farmers in some parts of the country are still using traditional methods of irrigation for different reasons, such as the lack of knowledge about agriculture and the lack of awareness of water resources. Sustainable development of agriculture will be achieved if the optimal use of water is taken into account.Proper water use prevents environmental degradation and, consequently, the life of posterity from being threatened. Therefore, the Water Resources Management Company and the Ministry of Jihad Agriculture have supplied water at a low price to encourage farmers to use modern irrigation methods and cultivate crops that need less water and yield more valuable products. As a result, water price is considered a weight restriction to determine the sustainability level of agricultural activities.Human resources are an important and influential factor in the sustainable development of agricultural practices. Human resources are nowadays viewed as one of the most important elements or resources of every country. Therefore, agricultural practices would be sustainable if they are economically beneficial to human resources. Agricultural practices will be economically provided that minimum human resources create maximum cultivated area and maximum production volume per cultivated area. This encourages farmers to be engaged in agricultural practices and, hence leads to rural sustainability. Since the human, social dimensions and rural regeneration have an impact on developing sustainable agriculture, minimum wages are determined for every 8 working hours of human resources every year, given the current economic situation and inflation rates. Minimum wages can be regarded as a weight restriction to determine the sustainability of agricultural activities using DEA.As previously mentioned, the sustainability of agricultural practices in the different counties depends on adequate revenues and the improvement of the quality of life of farmers. On the other hand, farmers’ revenues in each county are measured by the production volume and value of that county. So, ifu1represents the revenue weight and u2 represents the production volume weight of the counties under study, we have(29)Revenues of a CountyProduction Volume of a County=u1u2.Equation (29) can be rewritten as follows:(30)Revenues of a County×u2−Production Volume of a County×u1=0.Equation (30) can be considered as a weight restriction for revenues and production volume to determine the sustainable efficiency of agricultural practices using DEA.Based on the proposed structure, agricultural practices in thejth county have the two environmental and economic stages, and human resources are the shared input of both stages. Suppose that the relative importance of the two stages is the same. In the jth county, in the environmental stage, xj and hj represent water and human resources inputs, respectively, and zj represents cultivated area output, which is the input of the economic stage, and in the economic stage, y1j and y2j represent revenues and production volume inputs, respectively. Given that ω1=ω2=1/2, models (14), (20), and (26) can be reformulated as follows to measure the overall sustainable efficiency and the sustainable efficiency of the environmental and economic stages, respectively, with respect to weight restrictions in the oth county:(31)eo=max12φZo+v1+12∑r=12uryro+v2,(32)s.t:12vxo+who+12φZ0+who=1,(33)φZj+v1−vxj−whj≤0∀j=1,…,19,(34)∑r=12uryrj+v2−φZj−whj≤0∀j=1,…,19,(35)u2y1o−u1y2o=0,(36)v≤uv,lw≤w,(37)φ,u1,u2,v,w≥0.For calculating the environmental efficiency, we have the following:(38)eo1=maxφZo+v1,(39)s.t:vxo+who=1,(40)1/2φZo+v1+1/2∑r=12uryro+v21/2+1/2φZ0+who=eo∗,(41)φZj+v1−vxj−whj≤0,∀j=1,…,19,(42)∑r=12uryrj+v2−φZj−whj≤0,∀j=1,…,19,(43)u2y1o−u1y2o=0,(44)v≤uv,lw≤w,(45)φ,u1,u2,v,w≥0.For calculating the economic efficiency, we have the following:(46)eo2=max∑r=12uryro+v2,(47)s.t:φZ0+who=1,(48)1/2φZo+v1+1/2∑r=12uryro+v21/2vxo+who+1/2=eo∗,(49)φZj+v1−vxj−whj≤0,∀j=1,…,19,(50)∑r=12uryrj+v2−φZj−whj≤0,∀j=1,…,19,(51)u2y1o−u1y2o=0,(52)v≤uv,lw≤w,(53)φ,u1,u2,v,w≥0.In models (33), (41), and (49), the linear relationship u2y1o−u1y2o=0 is used as a weight restriction for revenues and production volume outputs. Also, the maximum price of water per cubic meter represented by uv and the minimum wages of human resources per 8 hours’ daily work represented by lw are used as weight restrictions for water and human resources inputs.


## 2.4. Determining the Sustainable Efficiency of Agricultural Practices in Sistan and Baluchestan Province with Stochastic Data

Following Cooper et al. [23] and Khodabakhshi [30], suppose that, in the jth county, xj and hj represent the deterministic data of water and human resources inputs of the environmental stage, respectively, and z¯j and y¯rjr=1,2 represent the stochastic data of the intermediate measures and outputs of the second stage with multivariate normal distribution and known parameters. Moreover, suppose that all the stochastic variables have a normal distribution with known means and standard deviations. By introducing stochastic data into models (33), (41), and (49), the overall stochastic efficiency, environmental stochastic efficiency, and economic stochastic efficiency can be obtained by solving the following models:(54)eo=max12φz¯o+12v1+12u1y¯1o+12u2y¯2o+12v2,(55)s.t:12vxo+who+12φz¯o+who=1,(56)φz¯j+v1−vxj−whj≤0,∀j=1,…,19,(57)u1y¯1j+u2y¯2j+v2−φz¯j−whj≤0,∀j=1,…,19,(58)u2y¯1o−u1y¯2o=0,(59)v≤u¯v,l¯w≤w,(60)φ,u1,u2,v,w≥0,(61)eo1=maxφz¯o+v1,(62)s.t:vxo+who=1,(63)1/2φz¯o+1/2v1+1/2u1y¯1o+1/2u2y¯2o+1/2v21/2+1/2φz¯o+who=eo∗,(64)φz¯j+v1−vxj−whj≤0,∀j=1,…,19,(65)u1y¯1j+u2y¯2j+v2−φz¯j−whj≤0,∀j=1,…,19,(66)u2y¯1o−u1y¯2o=0,(67)v≤u¯v,l¯w≤w,(68)φ,u1,u2,v,w≥0.Model (64) can be expressed as follows:(69)eo1=maxφz¯o+v1,(70)s.t:vxo+who=1,(71)12−12eo∗φz¯o−12eo∗who+12u1y¯1o+12u2y¯2o12v1++12v2=12eo∗,(72)φz¯j+v1−vxj−whj≤0,∀j=1,…,19,(73)u1y¯1j+u2y¯2j+v2−φz¯j−whj≤0,∀j=1,…,19,(74)u2y¯1o−u1y¯2o=0,(75)v≤u¯v,l¯w≤w,(76)φ,u1,u2,v,w≥0,(77)eo2=maxu1y¯1o+u2y¯2o+v2,(78)s.t:φz¯o+who=1,(79)1/2φz¯o+1/2v1+1/2u1y¯1o+1/2u2y¯2o+1/2v21/2vxo+who+1/2=eo∗,(80)φz¯j+v1−vxj−whj≤0,∀j=1,…,19,(81)u1y¯1j+u2y¯2j+v2−φz¯j−whj≤0,∀j=1,…,19,(82)u2y¯1o−u1y¯2o=0,(83)v≤u¯v,l¯w≤w,(84)φ,u1,u2,v,w≥0.Model (80) can be rewritten as follows:(85)eo2=maxu1y¯1o+u2y¯2o+v2,(86)s.t:φz¯o+who=1,(87)12φz¯o+12u1y¯1o+12u2y¯2o−12eo∗vxo−12eo∗who+12v1+12v2=12eo∗,(88)φz¯j+v1−vxj−whj≤0,∀j=1,…,19,(89)u1y¯1j+u2y¯2j+v2−φz¯j−whj≤0,∀j=1,…,19,(90)u2y¯1o−u1y¯2o=0,(91)v≤u¯v,l¯w≤w,(92)φ,u1,u2,v,w≥0.For simplicity in calculating the overall and stage-wise stochastic efficiencies, the duals of models (56), (72), and (88) can be used as follows:(93)eo=minθ1+u¯vθ3−l¯wθ4,(94)s.t:p∑j=119μjy¯1j−θ2y¯2o−12y¯1o≥0≥1−α,(95)p∑j=119μjy¯2j+θ2y¯1o−12y¯2o≥0≥1−α,(96)p∑j=119γj−μjz¯j+12θ1−12z¯o≥0≥1−α,(97)−∑j=119γjxj+12θ1xo+θ3≥0,(98)−∑j=119γj+μjhj+θ1ho−θ4≥0,(99)∑j=119γj=12,∑j=119μj=12,(100)γj,μj,θ3,θ4≥0.Model (96) can be expressed as follows:(101)eo=minf,s.t:p−u¯vθ3+l¯wθ4≥−f+θ1≥1−α,a,p∑j=119μjy¯1j−θ2y¯2o−12y¯1o≥0≥1−α,b,p∑j=119μjy¯2j+θ2y¯1o−12y¯2o≥0≥1−α,c,p∑j=119γj−μjz¯j+12θ1−12z¯o≥0≥1−α,d,−∑j=119γjxj+12θ1xo+θ3≥0,−∑j=119γj+μjhj+θ1ho−θ4≥0,∑j=119γj=12,∑j=119μj=12,γj,μj,θ3,θ4≥0,(102)eo1=minθ1+12eo∗β+u¯vθ3−l¯wθ4,(103)s.t:p∑j=119μjy¯1j−θ2y¯2o+12βy¯1o≥0≥1−α,(104)p∑j=119μjy¯2j+θ2y¯1o+12βy¯2o≥0≥1−α,(105)p∑j=119γj−μjz¯j+12β−12eo∗β−1z¯o≥0≥1−α,(106)−∑j=119γjxj+θ1xo+θ3≥0,(107)−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,(108)∑j=119γj+12β=1,∑j=119μj+12β=0,(109)γj,μj,θ3,θ4≥0.Model (105) can be revised as follows:(110)eo1=minf,s.t:p−u¯vθ3+l¯wθ4≥−f+θ1+12eo∗β≥1−α,a,p∑j=119μjy¯1j−θ2y¯2o+12βy¯1o≥0≥1−α,b,p∑j=119μjy¯2j+θ2y¯1o+12βy¯2o≥0≥1−α,c,p∑j=119γj−μjz¯j+12β−12eo∗β−1z¯o≥0≥1−α,d,−∑j=119γjxj+θ1xo+θ3≥0,−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,∑j=119γj+12β=1,∑j=119μj+12β=0,γj,μj,θ3,θ4≥0,(111)eo2=minθ1+12eo∗β+u¯vθ3−l¯wθ4,(112)s.t:p∑j=119μjy¯1j−θ2y¯2o+12βy¯1o−y¯1o≥0≥1−α,(113)p∑j=119μjy¯2j+θ2y¯1o+12βy¯2o−y¯2o≥0≥1−α,(114)p∑j=119γj−μjz¯j+12βz¯o+θ1z¯o≥0≥1−α,(115)−∑j=119γjxj−12eo∗βxo+θ3≥0,(116)−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,(117)∑j=119γj+12β=0,∑j=119μj+12β=1,(118)γj,μj,θ3,θ4≥0.Model (114) can be rewritten as follows:(119)eo2=minf,s.t:p−u¯vθ3+l¯wθ4≥−f+θ1+12eo∗β≥1−α,a,p∑j=119μjy¯1j−θ2y¯2o+12βy¯1o−y¯1o≥0≥1−α,b,p∑j=119μjy¯2j+θ2y¯1o+12βy¯2o−y¯2o≥0≥1−α,c,p∑j=119γj−μjz¯j+12βz¯o+θ1z¯o≥0≥1−α,d,−∑j=119γjxj−12eo∗βxo+θ3≥0,−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,∑j=119γj+12β=0,∑j=119μj+12β=1,γj,μj,θ3,θ4≥0.In models (101), (110), and (119), constraints (a), (b), (c), and (d) are stochastic in which p implies probability and α is constraint risk, a number between 0 and 1. In order to calculate the stochastic efficiency of the above models using DEA, stochastic constraints should be changed to deterministic constraints. In model (101), stochastic constraint (a) can be converted to deterministic constraint as follows:(120)p−u¯vθ3+l¯wθ4≥−f+θ1+s=1−α.The stochastic variablels is introduced as follows:(121)l=−u¯vθ3+l¯wθ4.The mean ofl equals(122)μl=−uvθ3+lwθ4,where uv and lw are the means of u¯v and l¯w, respectively. The variance of l is determined as follows:(123)varl=YTVY,σl=varl,where(124)YT=−θ3,θ4,V=varu¯vcovu¯v,l¯wcovl¯w,u¯vvarl¯w.The new standard random variablez¯l is defined as follows:(125)z¯l=l−μlσl.Ifμl is subtracted from both sides of equation (112) and divided by σl, then we have(126)p−u¯vθ3+l¯wθ4−μlσl≥−f+θ1+s−μlσl=1−α.Thus,(127)pz¯l≥−f+θ1+s−μlσl=1−α.Equation (127) can be rewritten as follows:(128)pz¯l≤−f+θ1+s−μlσl=α.Therefore,(129)φ−f+θ1+s−μlσl=α⟶φ−1α=−f+θ1+s−μlσl.Consequently, the following deterministic constraint is substituted for the stochastic constraint (a) in model (101):(130)uvθ3−lwθ4−f+θ1+s−σlφ−1α=0.Accordingly, the stochastic constraint (b) in model (101) can be converted as follows:(131)p∑j=119μjy¯1j−θ2y¯2o−12y¯1o≥s1=1−α.Here, the random variabley1 is defined as follows:(132)y1=∑j=119μjy¯1j−θ2y¯2o−12y¯1o.The mean ofy1 is calculated as follows:(133)μy1=∑j=119μjy1j−θ2y2o−12y1o.In relation (134), y1j is the mean of y¯1j. The variance of y1 is calculated as follows:(134)vary1=XTV1X,(135)σy1=vary1,where(136)XT=μ1,μ2,…,μ19,−θ2,μo−12,V1=vary11covy11,y12…covy11,y119covy11,y2ocovy11,y1ocovy12,y11vary12…covy12,y119covy12,y2ocovy12,y1o⋅⋅⋅covy119,y11covy119,y12…vary119covy119,y2ocovy119,y1ocovy119,y11covy119,y12…vary119covy119,y2ocovy119,y1ocovy1o,y11covy1o,y12…covy1o,y119covy1o,y2ovary1o.The new standard random variablez¯1 is defined as follows:(137)z¯1=y1−μy1σy1.Now, ifμy1 is subtracted from both sides of equation (131) and divided by σy1, then we have(138)p∑j=119μjy¯1j−θ2y¯2o−1/2y¯1o−μy1σy1≥s1−μy1σy1=1−α.Thus,(139)pz¯1≥s1−μy1σy1=1−α.Relation (139) can be rewritten as follows:(140)pz¯1≤s1−μy1σy1=α.Therefore,(141)φs1−μy1σy1=α⟶s1−μy1σy1=φ−1α.As a result,(142)s1−μy1−φ−1ασy1=0.By inserting relation (133) in the above equation, we have(143)−∑j=119μjy1j+θ2y2o+12y1o+s1−φ−1ασy1=0.Similarly, the deterministic equivalents of stochastic constraints (c) and (d) are obtained. As a result, the deterministic equivalent of model (101) is calculated as follows:(144)eo=minf,s.t:uvθ3−lwθ4−f+θ1+sl−σlφ−1α=0,−∑j=119μjy1j+θ2y2o+12y1o+s1−φ−1ασy1=0,−∑j=119μjy2j−θ2y1o+12y2o+s2−φ−1ασy2=0,−∑j=119γj−μjzj−12θ1−12zo+sz−φ−1ασz1=0,−∑j=119γjxj+12θ1xo+θ3≥0,−∑j=119γj+μjhj+θ1ho−θ4≥0,∑j=119γj=12,∑j=119μj=12,γj,μj,θ3,θ4≥0,where(145)σ2l=θ32varu¯v+θ42varl¯w−2θ3θ4covu¯v,l¯w,σ2y1=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯1i,y¯1j−2θ2∑i=1i≠o19μicovy¯1i,y¯2o+2μo−12∑i=1i≠o19μicovy¯1i,y¯1o−2θ2μo−12covy¯2o,y¯1o+μo−122vary¯1o+θ22vary¯2o,σ2y2=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯2i,y¯2j+2θ2∑i=1i≠o19μicovy¯2i,y¯1o+2μo−12∑i=1i≠o19μicovy¯2i,y¯2o+2θ2μo−12covy¯1o,y¯2o+μo−122vary¯2o+θ22vary¯1o,σ2z1=∑i=1i≠o19∑j=1j≠o19μi−γiμj−γjcovz¯i,z¯j+2μo−γo+12θ1−12,∑i=1i≠o19μi−γicovz¯i,z¯o+μo−γo+12θ1−122varz¯o.Similarly, the deterministic equivalents of models (110) and (119) are, respectively, as follows:(146)eo1=minf,s.t:uvθ3−lwθ4−f+θ1+12eo∗β+sl−σlφ−1α=0,−∑j=119μjy1j+θ2y2o−12βy1o+s1−φ−1ασy1=0,−∑j=119μjy2j−θ2y1o−12βy2o+s2−φ−1ασy2=0,−∑j=119γj−μjzj−12β−12eo∗β−1zo+sz−φ−1ασz1=0,−∑j=119γjxj+θ1xo+θ3≥0,−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,∑j=119γj+12β=1,∑j=119μj+12β=0,γj,μj,θ3,θ4≥0,where(147)σ2l=θ32varu¯v+θ42varl¯w−2θ3θ4covu¯v,l¯w,σ2y1=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯1i,y¯1j−2θ2∑i=1i≠o19μicovy¯1i,y¯2o+2μo+12β∑i=1i≠o19μicovy¯1i,y¯1o−2θ2μo+12βcovy¯2o,y¯1o+μo+12β2vary¯1o+θ22vary¯2o,σ2y2=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯2i,y¯2j+2θ2∑i=1i≠o19μicovy¯2i,y¯1o+2μo+12β∑i=1i≠o19μicovy¯2i,y¯2o+2θ2μo+12βcovy¯1o,y¯2o+μo+12β2vary¯2o+θ22vary¯1o,σ2z1=∑i=1i≠o19∑j=1j≠o19μi−γiμj−γjcovz¯i,z¯j+2μo−γo+12β−12eo∗β−1,∑i=1i≠o19μi−γicovz¯i,z¯o+μo−γo+12β−12eo∗β−12varz¯o.(148)eo2=minf,s.t:uvθ3−lwθ4−f+θ1+12eo∗β+sl−σlφ−1α=0,−∑j=119μjy1j+θ2y2o−12β−1y1o+s1−φ−1ασy1=0,−∑j=119μjy2j−θ2y1o−12β−1y2o+s2−φ−1ασy2=0,−∑j=119γj−μjzj−12β+θ1zo+sz−φ−1ασz1=0,−∑j=119γjxj−12eo∗βxo+θ3≥0,−∑j=119γj+μjhj+θ1ho−12eo∗βho−θ4≥0,∑j=119γj+12β=0,∑j=119μj+12β=1,γj,μj,θ3,θ4≥0,where(149)σ2l=θ32varu¯v+θ42varl¯w−2θ3θ4covu¯v,l¯w,σ2y1=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯1i,y¯1j−2θ2∑i=1i≠019μicovy¯1i,y¯2o+2μo+12β−1∑i=1i≠019μicovy¯1i,y¯1o−2θ2μo+12β−1covy¯2o,y¯1o+μo+12β−12vary¯1o+θ22vary¯2o,σ2y2=∑i=1i≠o19∑j=1j≠o19μiμjcovy¯2i,y¯2j+2θ2∑i=1i≠019μicovy¯2i,y¯1o+2μo+12β−1∑i=1i≠019μicovy¯2i,y¯2o+2θ2μo+12β−1covy¯1o,y¯2o+μo+12β−12vary¯2o+θ22vary¯1o,σ2z1=∑i=1i≠o19∑j=1j≠o19μi−γiμj−γjcovz¯i,z¯j+2μo−γo+12β+θ1∑i=1i≠019μi−γicovz¯i,z¯o+μo−γo+12β+θ12varz¯o.


## 3. Data Analysis

The sustainable development of agricultural practices will be realized provided that such practices do not lead to environmental degradation and the disturbance of posterity’s life while fulfilling today’s needs. Sustainable development is measured in terms of the TBLs of sustainability, namely, coordinated economic, environmental, and social development. Thus, this article aims to survey the sustainability of agricultural activities in the counties of Sistan and Baluchestan Province reported in Figure4 with respect to the economic, environmental, and social aspects with stochastic data.Figure 4
Map of Sistan and Baluchestan Province.Sistan and Baluchestan Province, with an area of around 187,502 square kilometers and a population of around 2.8 million people, is located in the southeast of Iran. Approximately 49% of its population live in cities and the rest live in rural areas. Desirable natural conditions have made agricultural and horticultural practices possible during all four seasons in a year, enabling economic development without depletion of natural resources of the agricultural sector. The sustainable development of agricultural practices in every county of the province is measured based on the optimal use of natural resources, improvement in production per cultivated area, and adequate revenues of farmers. The Ministry of Agriculture Jihad in this province collects data related to water consumption levels, cultivated areas, and production volumes in the previous years and sets forth improvement strategies. Yet, extending the past results to the future periods does not bring about desirable outcomes regarding the environmental, social, and economic dimensions of sustainable development. As a result, the present study concludes and provides Agriculture Jihad authorities with some strategies using DEA based on the data of 5 consecutive years reported by these authorities.The problem data are related to the available information from 2015 to 2019. These data include the amounts of water used, human resources, the areas under cultivation, the amounts of crops harvested, and the revenues from the sales of the products. Based on the mentioned indices, the data related to the areas under cultivation, the number of harvested crops, and revenues for each year of agriculture are available. Therefore, the collection of these data in the form of stochastic numbers is possible, the results of which are stated in the last three columns of Table1 as normal stochastic numbers. However, the data of water resources and human resources in the 2015–2019 period were only reported in 2017, and thus these two indices were considered crisp data, which are reported in the second and third columns of Table 1.Table 1
Stochastic data of agricultural practices in Sistan and Baluchestan Province.
CountyWaterHuman resourcesCultivated areaProduction volumeRevenuesVarianceMeanVarianceMeanVarianceMeanIranshahr0.5802030.6608050.1625720.7330730.0024510.0024510.0111490.733709Chabahar0.297896110.7186260.0172210.0172210.0365711Khash0.3566640.6484380.02340310.0062780.0062780.0191100.944023Dalgan10.3370750.1428210.7352460.0139200.0139200.0388560.838329Zabol0.0237550.1576540.1049970.3813590.0134060.0134060.0349320.28257Zahedan0.2956480.4661660.0192590.3255390.0036100.0036100.3916920.721294Zehak0.0237550.3603450.0816410.5688780.0085840.0085840.0112580.400248Saravan0.2044350.5876220.0510050.4348390.0017720.0017720.0013380.365122Sarbaz0.1823180.9252650.0144600.43461110.3330700.892607Sib and Suran0.1128910.4089400.0175700.2541770.0004890.0004890.0010870.266257Fanuj0.0131050.2113320.0125930.1094890.0003360.0003360.0007580.15486Qasr-e Qand0.0474100.2896800.0195500.1462860.0004400.0004400.0007210.204591Konarak0.0789130.2983460.0754510.339630.0214020.0214020.0361980.625585Mehrestan0.1017060.3415770.0465140.2738520.0027630.0027630.0020850.255315Mirjaveh0.4888140.2107880.0193600.2941440.0001720.00017210.819971NikShahr0.0697620.6651380.0315120.2274480.4130410.4130410.0058240.359071Nimruz0.0237550.2618130.0978550.4009630.0019200.0019200.0156110.244152Hamun0.0237550.1909670.1296680.4649440.0017810.0017810.0015010.195173Hirmand0.0237550.3358620.1537390.6008380.0115150.0115150.0129940.531958Table2 reports the performance of different agricultural areas of Sistan and Baluchestan Province using different α values. A value of α=0.5 with a probability distribution function of φ−1α=0 converts the proposed models into crisp models. In this case, the data of the DMUs will be the mean values of the stochastic numbers. Also, the agricultural sustainability value in the different regions is once equal to α=0.4 0, which is less than 0.5, and again the value is α=0.65, which is greater than 0.5 in Table 2.Table 2
Sustainability performance assessment of agricultural practices.
Countyα=0.4α=0.5α=0.65Environmental efficiencyEconomic efficiencyOverall efficiencyEnvironmental efficiencyEconomic efficiencyOverall efficiencyEnvironmental efficiencyEconomic efficiencyOverall efficiencyIranshahr0.7460.90160.77420.60990.75780.62730.35660.55110.4731Chabahar0.707110.75140.426410.69940.15760.5790.5903Khash0.456710.95430.41850.97640.760.34980.65020.5562Dalgan1110.467710.87970.46770.7210.6464Zabol111111111Zahedan0.354210.72130.33820.67340.42680.33820.47660.3749Zehak10.68340.71720.82970.61490.63460.48810.52630.5342Saravan0.40930.4750.40890.30460.4060.35570.26830.35630.3114Sarbaz0.250510.68460.193310.65680.170410.2745Sib and Suran0.38550.70960.45420.38550.59670.42710.38550.51690.4081Fanuj0.757210.77110.756610.76360.755710.7567Qasr-e Qand0.544210.57630.54420.84240.56590.54420.6950.556Konarak0.596710.86130.528410.78510.52840.970.7392Mehrestan0.46150.79180.5520.46150.66440.5160.46150.56830.4849Mirjaveh0.748910.89290.747910.8740.74790.88620.8198NikShahr0.242810.57860.24250.85270.3630.2420.46490.2739Nimruz0.89620.77620.71090.63860.69130.6710.60870.60220.6365Hamun10.89460.869110.82560.86060.82840.82560.848Hirmand1110.980310.95740.519310.7755According to the columnα=0.40 of Table 2, it can be concluded that six counties in the environmental stage and twelve counties in the economic stage are stochastically sustainable. Zabol, Dalgan, and Hirmand Counties enjoy overall stochastic sustainable efficiency since they are stochastically sustainable in both the environmental and economic stages at the same time. Furthermore, because the mean stochastic efficiencies of the counties are 0.660884 and 0.906953, respectively, and their standard deviations of stochastic efficiency are 0.272065 and 0.150908, respectively, in both the environmental and economic stages; the distribution of stochastic efficiency in the economic stage is less than that of the other stage. Therefore, it can be said that the counties have better performance in the economic stage.From columnα=0.5, it becomes clear that, compared to α=0.40, the number of stochastic efficient DMUs in the environmental and economic stages decreases to two and eight counties, respectively. Since Zabol County is simultaneously stochastically efficient in both stages, it reaches the threshold of the overall stochastic sustainable efficiency. On the other hand, because the mean stochastic efficiencies of the counties are 0.572305 and 0.836926, respectively, and their standard deviations of the stochastic efficiency are 0.253183 and 0.183981, respectively, in both the environmental and economic stages, the distribution of the stochastic efficiency in the environmental stage is less than that of the economic stage; hence, the counties have a better performance in the economic stage, in comparison to the environmental stage. The same is also true for the column α=0.65. Also, according to Table 2, in the environmental and economic stages, and the overall stochastic sustainable efficiency levels of all the counties are constant or decrease with an increase in α.According to Figure5, it can be concluded that the overall stochastic sustainable efficiency of Zabol County is constant and reaches the threshold of stochastic sustainable efficiency as α increases. With an increase in α, the overall stochastic sustainable efficiency of Mirjaveh and Hamun Counties has an insignificant decrease compared to those of Hirmand and Dalgan Counties. The same is also true for Zahedan and Nik Shahr Counties, with low levels of the overall stochastic sustainable efficiency.Figure 5
Overall stochastic sustainable efficiencies of the counties in Sistan and Baluchestan Province with different values ofα.Table3 shows a comparison of unit’s performance between classical and network structures. In the classical structure, labor, water, and cultivated area are the inputs. And harvested products and income are considered as the outputs. In the classical structure, the performance of the units was evaluated with and without weight restrictions. As can be seen in Table 3, the efficiency of the units without weight restrictions is not less than their efficiency with the weight restrictions. The reason is that the limitations of the models without weight restrictions are less than those of the models with weight restrictions. However, network models are not theoretically comparable to classical models. Thus, the performance values of these two methods are not comparable. We only know that the network structure of the units is more detailed in performance models than in the classical structure. As can be seen in Table 3, in most cases, the network efficiency of a unit is less than its classical efficiency. However, the efficiency of Hamun county in network structure is more than its efficiency in classical structure, for α=0.5 and α=0.65, respectively. Also, the efficiency of Nimruz county considering the network structure is slightly more than the classic structure, for α=0.65.Table 3
Comparison of agricultural activity performance between classical and network DEA.
Countyα=0.40α=0.5α=0.65Ordinary units without weight restrictionsOrdinary units with weight restrictionsNetwork units with weight restrictionsOrdinary units without weight restrictionsOrdinary units with weight restrictionsNetwork units with weight restrictionsOrdinary units without weight restrictionsOrdinary units with weight restrictionsNetwork units with weight restrictionsIranshahr0.90160.90160.77420.75780.75780.62730.55110.55110.4731Chabahar110.7514110.699410.60360.5903Khash110.9543110.760.71160.63070.5562Dalgan111110.87970.72100.72100.6464Zabol111111111Zahedan110.72130.95980.75550.42680.51910.49950.3749Zehak0.97340.71390.71720.84340.63970.63460.78520.53410.5342Saravan0.55620.47980.40890.44590.41380.35570.36600.36160.3114Sarbaz110.6846110.6568110.2745Sib and Suran0.77650.70960.45420.61050.59670.42710.51690.51690.4081Fanuj110.7711110.7636110.7567Qasr-e Qand110.57630.86450.84240.56590.69640.69500.556Konarak110.8613110.7851110.7392Mehrestan0.81280.79180.5520.66440.66440.5160.56830.56830.4849Mirjaveh110.8929110.87410.88620.8198Nik Shahr110.578610.85260.3630.60570.46480.2739Nimruz0.86940.78970.71090.77500.69600.6710.74380.60870.6365Hamun0.89460.89460.86910.89280.82870.86060.89280.82840.848Hirmand111110.9574110.7755


## 4. Concluding Remarks and Suggestions

The sustainable development of DMUs depends on their sustainability in the environmental, economic, and social aspects. This study used the DEA method to determine the performance and sustainability levels of agricultural practices in the counties of Sistan and Baluchestan Province. In order to make a more realistic assessment of the complexities of agricultural activities, three measures were taken: (1) A two-stage structure with shared resources (network structure) was introduced for agricultural activities. In this new structure, agricultural practices were divided into two environmental and economic stages. The former includes water and human resources as inputs and cultivated area as an output. The latter involves human resources and cultivated area as inputs and revenues and production volume as outputs. (2) Based on the studies and observations, weight control was applied to the coefficients of some indicators. (3) The stochastic data consist of the given mean and variance related to the input and output data of five consecutive years reported by the authorities of the Ministry of Agriculture Jihad in Sistan and Baluchestan Province. The results showed that a county would achieve overall stochastic sustainability if it reached the threshold of the stochastic sustainable efficiency in both stages. Suppose a county is not stochastically sustainable in the environmental stage; in that case, the Agriculture Jihad Organization of that county should encourage it to replace traditional irrigation methods with modern irrigation methods to increase production volume per cultivated area with less water consumption by granting farmers long-term interest-free loans. If a county is not stochastically sustainable at the economical stage, the respective authorities should consider some measures such as the establishment of cooperatives, guaranteed purchase of agricultural products, and the encouragement of farmers to cultivate those products with less adverse harmful effects on the environment and higher yields to be able to reach sustainability efficiency threshold in the future. Providing a pattern for predicting the agricultural performance of cities in the future using the results obtained in this article can complement the present study. Simultaneous calculation of environmental, economic, and social efficiencies by multiobjective programming problems based on the network structure and comparing the results with the perspective presented in this article can also be considered alternative research. Finally, due to the data availability for five consecutive periods, we can state that the dynamic network DEA can be used to evaluate the performance of agricultural activities in Sistan and Baluchestan provinces for future research.



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*Source: 1119630-2022-07-13.xml*