Optimizing crop mix with respect to economic and environmental constraints: An integrated MCDM approach

Journal Pre-proof Optimizing crop mix with respect to environmental constraints: An integrated MCDM approach

Tomas Balezentis, Xueli Chen, Aiste Galnaityte, Virginia Namiotko PII:

S0048-9697(19)35891-7

DOI:

https://doi.org/10.1016/j.scitotenv.2019.135896

Reference:

STOTEN 135896

To appear in:

Science of the Total Environment

Received date:

24 September 2019

Revised date:

11 November 2019

Accepted date:

1 December 2019

Please cite this article as: T. Balezentis, X. Chen, A. Galnaityte, et al., Optimizing crop mix with respect to environmental constraints: An integrated MCDM approach, Science of the Total Environment (2018), https://doi.org/10.1016/j.scitotenv.2019.135896

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© 2018 Published by Elsevier.

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OPTIMIZING CROP MIX WITH RESPECT TO ENVIRONMENTAL CONSTRAINTS: AN INTEGRATED MCDM APPROACH Tomas Balezentis a, Xueli Chen b, Aiste Galnaityte a, Virginia Namiotko a a

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Institute of Journalism and Communication, Chinese Academy of Social Sciences, Bejing, China

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b

Lithuanian Institute of Agrarian Economics, Vilnius, Lithuania

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OPTIMIZING CROP MIX WITH RESPECT TO ENVIRONMENTAL CONSTRAINTS: AN INTEGRATED MCDM APPROACH

This study develops an integrated framework for assessment of cropping sustainability at the aggregate (country) level. Such sustainability criteria as total water footprint, Shannon equitability

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index, total output, and downside coefficient of yield variation are used to rank the crop mixes,

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corresponding to different assumptions. Mathematical programming model is applied to generate the

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crop mixes. Then, the three MCDM techniques (SAW, TOPSIS and EDАS) are applied for the ranking. Empirical analysis embarks on the case of Lithuania, which is a new EU member state. Sensitivity

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analysis is carried out by establishing the three weighting schemes (balanced, environment- and

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economy-oriented). The results suggest that scenario minimising labour use render the most sustainable

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crop-mix. Correlation among the ranks of the scenarios suggests that environmental and economic approaches are conflicting between themselves, yet there is no such a serious contradiction among the

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latter two approaches and the balanced approach.

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Keywords: Crop mix; Mathematical programming; Multi-criteria analysis; Sustainability.

1. Introduction

The increasing competition for resources and climate change pose multiple challenges for contemporary economies (Song et al., 2019, 2020). This requires development of sustainable production and consumption practices. Public support is allocated to intensify the aforementioned process. Indeed the concept of sustainability is related to multiple dimensions describing interests of

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different stakeholders. These interests often diverge and the compromise solution is required instead of the optimal one. What is more the concept of sustainability and information used in sustainability analysis is often vague. Accordingly, different evaluation models and criteria have been established to deal with uncertainty and conflicting criteria (Büyüközkan, Karabulut 2018, Gupta et al. 2018, Duman et al. 2018).

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Agricultural sector is particularly vulnerable to such natural effects as the climate change (Trukhachev et al., 2018). The changes in its performance may affect food security, income and

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livelihood. Agriculture performance is important to farmers as well as the rest of population through

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the linkages over the food supply chains. Currently the expansion and development of consumption and

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production of agricultural products in emerging economies (e.g. Asian countries) stimulates the

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dynamics in the global food markets (OECD/FAO 2019, USDA 2019). These questions require development of decision support systems for sustainable agricultural development.

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The tools for assessment of agricultural sustainability (analogously to the other sectors) can be

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grouped in to those following the direct and indirect approaches (Zhou et al. 2008). The major feature of direct approach is that it aggregates multiple indicators of sustainability in to a composite indicator.

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The indirect approach exploits the production frontier to gauge efficiency scores which identify the level of sustainability and is more data intensive. Mishra et al. (2019) applied multi-criteria decision making (MCDM) approach for sustainable crop mix selection in India. The same issue was also addressed by Qureshi et al. (2018) by applying fuzzy TOPSIS technique. Rao et al. (2019) identified indicators for development of climate resilient agriculture in India. Orojloo et al. (2018) developed a fuzzy MCDM approach for water management for sustainable agriculture development. Sulewski et al. (2018), Kelly et al. (2018) and Spicka et al. (2019) exploited FADN data to assess the sustainability of agricultural farming systems. Kamali et al. (2017) offered the multi-criteria framework for evaluation of sustainability of different farming

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practices in Latin America. Therefore the MCDM techniques have been applied for assessment of agricultural systems across different regions based on different criteria. Mathematical programming and MCDM techniques were used to identify the optimal cropping plan by Galán-Martín et al. (2015). Cortignani and Dono (2015) assessed the impact of greening by using mathematical programming. Sofi et al. (2015) used mathematical programming to optimize

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resource allocation and achieve efficiency; Aljabani et al. (2018) used it to optimize crops and reclaimed wastewater allocation in Iraq. Hayashi (2000), Kaim et al. (2018) and Talukder et al. (2018)

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discussed the application of the MCDM techniques for assessment of sustainability do the agricultural

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systems with respect to different criteria. However, integrated application of the quantitative measures

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of sustainability (including water footprint and crop diversity) often remained neglecxted.

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The objective of this paper is to propose an integrated approach towards multi-criteria analysis of different crop mixes. Therefore we use mathematical programming to model optimal crop mixes

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under the different scenarios. In this paper we assume different measures to promote organic farming in

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Lithuania (a new EU member state) and assess their sustainability. Indeed, the organic farming is the most widespread as a sustainable farming practice in Lithuania. The Common Agricultural Policy of

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the EU also supports development of the organic farming. We apply multi-criteria approach to rank the scenarios with respect to economic and environmental criteria. The SAW, TOPSIS and EDAS techniques are applied. The paper contributes to the literature on sustainable agricultural management by devising a framework for scenario analysis based on the water-economy nexus.

2. Data and methods

This section presents the preliminaries for modelling the sustainability of the scenarios for agricultural development in Lithuania. First, we turn to the optimization problem rendering the crop-mixes for

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further analysis. Then, we discuss the sustainability criteria which are calculated for the given cropmixes. Finally, the multi-criteria decision making techniques (SAW, TOPSIS and EDAS) applied for an integrated analysis of the crop-mix are discussed. The data used for the analysis are also discussed.

2.1. Scenario modelling

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In order to identify the possible instances of crop-mix, we rely on mathematical programming. The latter approach is especially appealing in the context of agriculture (Hazel, Norton 1986,

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Galnaitytė, Kriščiukaitienė 2016, Galnaitytė et al. 2017). In our case, the solutions of the mathematical

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programming problems serve as the candidate scenarios for sustainability analysis. Crop production

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system in the model mathematically is described by vectors of all kinds of resources and outputs. The

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model supply us with the respective results presenting such production structure, which is solution of optimization problem and maximize the net profit in the agricultural sector considering set of

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restrictions. The mathematical programming model is based on standard economic behaviour (rational

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behaviour, constant return technology, perfect competition) and other (plant seeds, organic and mineral fertilizers are purchased on the market, all production is sold on the market at the prevailing market

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price) assumptions (Galnaitytė, Kriščiukaitienė 2016, Galnaitytė, 2017). As the model aims at identifying the crop mixes for sustainability analysis, the differences in productivity (yield) and economic (cost, price, direct and compensatory payments) indicators are accounted for by modelling the farming practices applied in Lithuania: conventional, organic, organic in conversion and integrated. The model is formulated as a linear programming model, consisting of objective function, constraints, expressed as inequalities and fulfilling non-negative values conditions. The objective function is expressed as follows:

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max 𝑝𝑒𝑘𝑜

𝑥𝑗 ,𝑥𝑘𝑒𝑘𝑜 ,𝑥𝑙

,𝑥𝑟𝑖𝑛𝑡

𝑓(𝑥) [1]

= ∑(𝜈𝑗 − 𝑖𝑗 ) ∙ 𝑥𝑗 + ∑(𝜈𝑘𝑒𝑘𝑜 − 𝑖𝑘𝑒𝑘𝑜 ) ∙ 𝑥𝑘𝑒𝑘𝑜 + 𝑗∈𝑇

𝑘∈𝐸

∑(𝜈𝑙𝑝𝑒𝑘𝑜 𝑙∈𝑃

−

𝑖𝑙𝑝𝑒𝑘𝑜 )

∙

𝑥𝑙𝑝𝑒𝑘𝑜

+ ∑(𝜈𝑟𝑖𝑛𝑡 − 𝑖𝑟𝑖𝑛𝑡 ) ∙ 𝑥𝑟𝑖𝑛𝑡 𝑟∈𝐼

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where:

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𝑇, 𝐸, 𝑃, 𝐼 – sets of crops, produced respectively using conventional, organic, organic in conversion,

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integrated farming practices;

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𝜈𝑗 , 𝜈𝑘𝑒𝑘𝑜 , 𝜈𝑙𝑝𝑒𝑘𝑜 , 𝜈𝑟𝑖𝑛𝑡 – crop production unit value (revenue) including direct payments, payments for

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farmers in less-favoured areas, and other agro-environmental compensatory payments of 𝑗 kind of

practices, EUR/t;

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conventional, 𝑘 kind of organic, 𝑙 kind of organic in transition, 𝑟 kind of integrated farming

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𝑖𝑗 , 𝑖𝑘𝑒𝑘𝑜 , 𝑖𝑙𝑝𝑒𝑘𝑜 , 𝑖𝑟𝑖𝑛𝑡 – crop production cost of 𝑗 kind of conventional, 𝑘 kind of organic, 𝑙 kind of organic

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in transition, 𝑟 kind of integrated farming practices, EUR/t; 𝑥𝑗 , 𝑥𝑘𝑒𝑘𝑜 , 𝑥𝑙𝑝𝑒𝑘𝑜 , 𝑥𝑟𝑖𝑛𝑡 – production output for crop 𝑗, k, l or r, t. Production output is defined as the product of the areas and yield for a certain crop. The objective function is maximized subject to the restrictions: 𝑛

∑ 𝑎𝑖𝑗 𝑥𝑗 ≤ 𝑏𝑖 ; 𝑖 = 1, … , 𝑚 𝑗=1

where:

𝑎𝑖𝑗 – technical coefficients; 𝑥𝑗 – activity or decision variables (production output); 𝑏𝑖 – resources availability.

[2]

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Model was implemented by using GAMS software, which is designed to deal with the problems of agricultural sector and is one of principal languages for agricultural economic modelling (McCarl et al. 2016). The model is verified by comparing simulation results with actual Lithuanian agricultural sector data for year 2015, published by Statistics Lithuania (2016). In order to estimate sustainability of crop production for the different crop mixes analysis of scenarios was conducted. Scenarios for

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simulation were defined by considering factors that may affect the extent of sustainable farming

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practices and are described in Table 1.

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Table 1. Modelled scenarios

Scenario

Description of the Scenario

Objective

Modelled factual situation of Lithuanian Baseline

agriculture in 2015, i.e. areas of individual

scenario

crops were described exactly as they were

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Model verification.

declared in 2015.

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The minimum and maximum bounds were

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into

account

minimum

whether

Lithuania

has

and internal resources for the sustainable

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Scenario 1

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set for the areas of every individual crop, Checking

maximum values of crop areas declared farming development.

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during current five years (2011-2015).

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Three times increasing upper bounds of Checking

whether

Lithuania

has

Scenario 2

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individual crop areas intervals of organic, internal resources for the sustainable

in conversion organic, and integrated farming development.

farming practices. Checking if higher organic production Increasing organic production prices up to

Scenario 3

prices in Lithuania would encourage the exports price. sustainable farming development. Checking if higher organic production Increasing organic production prices up to

Scenario 4

prices in Lithuania would encourage prevailing prices in Germany. sustainable farming development.

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Determination of the crop structure that Scenario 5

Minimization of labour costs. guarantees minimum labour costs.

2.2. Indicators of sustainability The following sustainability criteria are used to compare the scenarios: total output, total water

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footprint, Shannon equitability index, and downside coefficient of yield variation. These indicators

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define economic and environmental aspects of the sustainability of crop mixes. Total output (in million Eur) indicates the economic result related to particular crop mix.

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Water resources are important for sustainable development (Aviso et al., 2018; Silva-Rodríguez

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de San Miguel, 2018; Chen et al., 2018). Water footprint (WF) related to crop production for the simulated

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crop mixes is calculated to account for environmental pressures related to crop farming. As it is suggested in the literature (Hoekstra, Chapagain 2007, Chu et al. 2017), we calculate and compare blue

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WF, green WF, grey WF, and total WF for every scenario under analysis. The total WF related to crop

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production indicates the volume of water consumption required to produce a certain crop mix. For a

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given crop, the blue WF indicates the volume of irrigation water consumed, the green WF is related to the effective rainfall for plants, and the grey WF indicates the volume of water required to dilute pollutants to the agreed maximum acceptable levels (Hoekstra, Chapagain 2007, Chu et al. 2017). Blue WF, green WF, grey WF, and total WF are calculated of 15 crops in Lithuania. Every type of WF (blue, green, and grey) firstly is calculated for each of 15 crops separately and then the sum of all crop production WF for each type is provided. 𝑛

𝑊𝐹𝑎 = ∑ 𝑥𝑗 𝑤𝑗 𝑗=1

where:

𝑊𝐹𝑎 – water footprint of type 𝑎;

[3]

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𝑥𝑗 – harvest of 𝑗 crop, t; 𝑤𝑗 – water footprint factor for crop 𝑗, m3/t. For the calculations we use the scenario results (crop-mixes), yields and footprint factors (m3/ton; provided by Mekonnen and Hoekstra, 2010). The total WF of a crop production is calculated as the sum of the green, blue and grey WF (Chapagain et al. 2006, Chu et al. 2017):

𝑊𝐹𝑡𝑜𝑡𝑎𝑙 – tolal water footprint of crop production;

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where:

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𝑊𝐹𝑡𝑜𝑡𝑎𝑙 = 𝑊𝐹𝑏𝑙𝑢𝑒 + 𝑊𝐹𝑔𝑟𝑒𝑒𝑛 + 𝑊𝐹𝑔𝑟𝑒𝑦

𝑊𝐹𝑏𝑙𝑢𝑒 – blue water footprint of crop production;

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𝑊𝐹𝑔𝑟𝑒𝑒𝑛 – green water footprint of crop production;

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𝑊𝐹𝑔𝑟𝑒𝑦 – grey water footprint of crop production.

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An additional indicator for the environmental dimension of sustainability was calculated for

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crop mix associated with each scenario, i.e. Shannon equitability index (Shannon, Weaner 1949, Magurran 1988, Lazíková et al. 2019). Indeed, the Shannon equitability index is the normalized

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Shannon diversity index. Shannon diversity index was calculated as follows: [5]

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𝑆𝐷𝐼 = − ∑𝑛𝑖=1 𝑝𝑖 ln(𝑝𝑖 ),

where 𝑆𝐷𝐼 is the Shannon diversity index, 𝑛 is the number of crops, 𝑝𝑖 is the share of a given crop in total arable land. Then, Shannon equitability index (𝑆𝐸𝐼) was calculated as: 𝑆𝐷𝐼

𝑆𝐸𝐼 = 𝑆𝐷𝐼

𝑚𝑎𝑥

,

[6]

where 𝑆𝐷𝐼 is the value of the Shannon diversity index from Eq. 5, and 𝑆𝐷𝐼𝑚𝑎𝑥 is calculated as ln 𝑛. The values of Shannon equitability index vary in between 0 and 1. The value of index increases with number of crops. Therefore, higher values show better composition, i.e. richness of the investigated area.

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The downside coefficient of yield variation (Zhang, Wang 2010, Baležentis, Kriščiukaitienė 2016) was calculated for each scenario (crop-mix) as a measure of the economic dimension of sustainability. The downside coefficient of yield variation measures the risk concerned of income loss due to yield fluctuations. As gains in yields are not considered as a risk, we consider only downside movements in the yield. Time series data covering the period of 1990-2017 were analysed in order to

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estimate the coefficient. In order to omit values above the average yield (which is obtained as the average trend values for the time period considered), we employ the idea of semi variance (Hogan,

𝑑 𝑠𝑦 , ̅ 𝑦̂̂

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𝐷𝐶𝑉 =

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Warren 1974). In that regard, we construct the downside coefficient of yield variation as: [7]

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where 𝑦̅̂̂ is the average of the trend values of the given crop yield and 𝑠𝑦𝑑 is the downside standard

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deviation, which is calculated as follows:

1/2

𝑛

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1 2 𝑠𝑦𝑑 = ( ∑(𝑚𝑖𝑛[𝑦(𝑡) − 𝑦̂̂ (𝑡), 0]) ) 𝑛−1

[8]

𝑡=1

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In this manner, the downside coefficient of yield variation only measures yield variation below the

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long-term tendency (or trend).

Downside coefficients of yield variation we estimate for each crop, and after we calculate average downside coefficients of yield variation for all crops: 𝑛

𝐴𝐷𝐶𝑉 = ∑ 𝑝𝑖 𝐷𝐶𝑉𝑖

[9]

𝑖=1

where 𝑇𝐷𝐶𝑉 is the weighted average value of the downside coefficients of yield variation for all crops, n is the number of crops, 𝑝𝑖 is the share of a given crop on total arable land.

2.3. Multi-criteria decision making

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Multi-criteria analysis is necessary when dealing with multi-faceted phenomena. In this paper, we seek to compare different scenarios (crop mixes) with regards to heir sustainability. As sustainability comprises multiple dimensions, the use of multi-criteria analysis is also required. We have chosen SAW, TOPSIS and EDAS methods to aggregate the data based on different aggregation principles (utility functions and reference points). The SAW method simply combines values of the

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indicators and their weights into one measure – the criterion of the method. TOPSIS method chooses the option with the shortest distance from the best values of indicators and with the longest distance

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from the worst values of indicators, whereas EDAS takes into account sample average as a reference

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point (Ghorabaee et al. 2014, Zhang et al. 2019; Karabasevic et al., 2018; Ecer, 2018).

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Multi-criteria methods are based on the matrix 𝑅 = ‖𝑟𝑖𝑗 ‖ of the criteria, describing the objects

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compared 𝐴𝑗 (𝑗 = 1,2, … , 𝑛) , criteria Ci (i  1, 2,, m) and the criterion weights 𝜔𝑖 (𝑖 = 1,2, … , 𝑚) ,

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where 𝑚 is the number of criteria and 𝑛 is the number of objects compared. Four indicators describing cropping sustainability were selected as criteria to ascertain the best

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scenario for sustainable crop mix: total output, total water footprint, Shannon equitability index, and

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downside coefficient of yield variation. We generally distinguish these indicators into two groups: environmental indicators group (total water footprint and Shannon equitability index) and profit determining indicators’ group (total output and downside coefficient of yield variation). Three criteria weights’ sets were used when applying selected multi-criteria methods (Table 2). Criteria weights’ set 𝑊1 follows assumption that all four criteria are of equal importance. Criteria weights’ set 𝑊2 assigns three times higher weight to the environmental indicators group, while 𝑊3 set assigns three times higher weights to economic indicators’ group.

Table 2. Weighting combinations applied

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Shannon

Downside coefficient of

Total WF

Total output equitability index

yield variation

0.250

0.250

0.250

0.250

W2

0.375

0.375

0.125

0.125

W3

0.125

0.125

0.375

0.375

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W1

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SAW (Simple Additive Weighting) method is a well-known method relying on the linear utility function for multi-criteria evaluation (Hwang, Yoon 1981, Rozman et al. 2016, Vico 2017). The

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criterion of the method 𝑆𝑗 accurately reflects the idea of the quantitative multi-criteria evaluation

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methods by combining values of the indicators and their weights into one measure – the criterion of the

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method. Method calculates the sum of the normalized values 𝑟̃𝑖𝑗 of all indicators 𝑆𝑗 for each j-object (alternative). It was calculated by the formula:

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𝑚

𝑆𝑗 = ∑ 𝜔𝑖 𝑟̃𝑖𝑗 ,

(10)

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𝑖=1

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where 𝜔𝑖 is the weight of the i-th criterion, 𝑟̃𝑖𝑗 is the normalized value of i-th criterion for j-th alternative. The best option corresponds to the highest criterion 𝑆𝑗 value. The normalized values are obtained in different manner for cost and benefit criteria. For the cost criteria, the linear normalisation relies on calculation of the following ratios: 𝑟̅𝑖𝑗 =

𝑚𝑖𝑛𝑗 𝑟𝑖𝑗 𝑟𝑖𝑗

;

(11)

as for the benefit criteria, the following ratios are computed: 𝑟̅𝑖𝑗 =

𝑟𝑖𝑗 𝑚𝑎𝑥𝑗 𝑟𝑖𝑗

,

(12)

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where rij is the i-th value for the j-object, 𝑚𝑎𝑥𝑗 𝑟𝑖𝑗 – the highest value among all alternatives i-th for jobject, 𝑚𝑖𝑛𝑗 𝑟𝑖𝑗 – the lowest value of i-th alternative. TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method has deep theoretical and practical meaning; therefore it is often applied in practice (Hwang, Yoon 1981, Papathanasiou et al. 2016). The principle of this method is to choose the option with the shortest

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distance from the best values of indicators and with the longest distance from the worst values of

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indicators. The method allows apply maximizing (their best values are highest) and minimizing (their

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best values are minimum) indicators, i. e. minimized indicators do not need to be redesigned to maximized. The TOPSIS applied vector data normalization which is carried out as: 2 √∑𝑛 𝑗=1 𝑟𝑖𝑗

,

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𝑟𝑖𝑗

(i =1, ..., m; j =1,..., n)

(13)

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𝑟̃𝑖𝑗 =

where 𝑟̃𝑖𝑗 is the normalized value of the j-th object according to the i-th indicator.

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Using the TOPSIS method, ideal solution V* is identified, i. e. each maximized and minimized

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value is multiplied by the corresponding weights 𝜔𝑖 , and the maximum value of maximized and

calculated:

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minimum value of minimized indicators are found. Ideal solution V* and anti-ideal solution 𝑉 − are

𝑉 ∗ = {𝑉1∗ , 𝑉2∗ , … , 𝑉𝑚∗ } = {(max 𝑗

𝜔𝑖 𝑟̃𝑖𝑗 𝜔𝑖 𝑟̃𝑖𝑗 ∈ 𝐼1 ) , (min ∈ 𝐼2 )} , 𝑗 𝑖 𝑖

(14)

𝜔𝑖 𝑟̃𝑖𝑗 𝜔𝑖 𝑟̃𝑖𝑗 ∈ 𝐼1 ) , (max ∈ 𝐼2 )} , 𝑗 𝑖 𝑖

(15)

𝑉 − = {𝑉1− , 𝑉2− , … , 𝑉𝑚− } = {(min 𝑗

where I1 – is the set of indexes for maximized indicators, I2 is the set of indexes for minimized indicators, 𝜔𝑖 – is the weight of the i-th index. Then the total distance 𝐷𝑗∗ between each option and an ideal solution V*, and the total distance 𝐷𝑗− between each option and an anti-ideal solution 𝑉 − are calculated as:

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𝑚

𝐷𝑗∗

= √∑(𝜔𝑖 𝑟̃𝑖𝑗 − 𝑉𝑖∗ )2 .

(16)

𝑖=1

𝑚

𝐷𝑗−

= √∑(𝜔𝑖 𝑟̃𝑖𝑗 − 𝑉𝑖− )2 .

(17)

𝑖=1

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It is important to note that distance measures 𝐷𝑗∗ and 𝐷𝑗− include the values of the criterion significance

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(weights) 𝜔𝑖 , so the weights influence results. The main utility indicator 𝐶𝑗∗ of the TOPSIS method is calculated using:

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𝐷−

𝑗 𝐶𝑗∗ = 𝐷∗+𝐷 −, 𝑗

(𝑗 = 1, . . . , 𝑛)

(0 ≤ 𝐶𝑗∗ ≤ 1)

(18)

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𝑗

The best alternative according to the TOPSIS method corresponds to the highest value of the criterion

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𝐶𝑗∗ .

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EDAS (Evaluation based on Distance from Average Solution) method was proposed by

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Ghorabaee et аl. (2015). The EDAS technique can be identified from the other methods. The distances from the average solution are measured when using EDAS method. Therefore the best option is less

environment.

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affected by the outlying observations. Kahraman et аl. (2017) extended the EDAS technique into fuzzy

The positive distance from the average (PDA) and negative distance from the average (NDA) are calculated. The best option corresponds to the highest PDA value and lowest PDA value. Then for the each criterion we calculate the average: 𝐴𝑉 = [𝐴𝑉𝑗 ]1×𝑚 ,

(19)

where each element of AV is calculated using: 𝐴𝑉𝑗 =

∑𝑛 𝑖=1 𝑟𝑖𝑗 𝑛

.

(20)

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Then we construct 𝑃𝐷𝐴 and 𝑁𝐷𝐴 matrices. The results indicate the positions in comparison with the average solution. These are expressed as: 𝑃𝐷𝐴 = [𝑃𝐷𝐴𝑖𝑗 ]𝑛×𝑚 ,

(21)

𝑁𝐷𝐴 = [𝑁𝐷𝐴𝑖𝑗 ]𝑛×𝑚 .

(22)

The elements of the matrices PDA and NDA in Eqs. 21 and 22 are calculated differently with

of

respect to criterion 𝑗. If the j-th criterion is benefit one (to be maximized), then elements of the matrices

𝐴𝑉𝑗

,

mаx(0,(𝐴𝑉𝑗 −𝑟𝑖𝑗 ))

.

𝐴𝑉𝑗

re

𝑁𝐷𝐴𝑖𝑗 =

mаx(0,(𝑟𝑖𝑗 −𝐴𝑉𝑗 ))

-p

𝑃𝐷𝐴𝑖𝑗 =

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𝑃𝐷𝐴𝑖𝑗 and 𝑁𝐷𝐴𝑖𝑗 are calculated as follows:

(23) (24)

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In case the j-th criterion is cost one (to be minimized), then elements of the matrices 𝑃𝐷𝐴𝑖𝑗 and 𝑁𝐷𝐴𝑖𝑗

na

are calculated according to formulae below:

ur

𝑃𝐷𝐴𝑖𝑗 =

𝐴𝑉𝑗

,

mаx(0,(𝑟𝑖𝑗 −𝐴𝑉𝑗 )) 𝐴𝑉𝑗

.

(25) (26)

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𝑁𝐷𝐴𝑖𝑗 =

mаx(0,(𝐴𝑉𝑗 −𝑟𝑖𝑗 ))

Thus, the positive and negative distances for alternative 𝑖 with regards to criterion 𝑗 are specified by 𝑃𝐷𝐴𝑖𝑗 аnd 𝑁𝐷𝐴𝑖𝑗 .

After that, positive and negative distances of each alternative are aggregated by the applying weighted sum approach. Weighted sums 𝑆𝑃𝑖 and 𝑁𝑃𝑖 are calculated as follows: 𝑆𝑃𝑖 = ∑𝑚 𝑗=1 𝑤𝑗 𝑃𝐷𝐴𝑖𝑗 ,

(27)

𝑆𝑁𝑖 = ∑𝑚 𝑗=1 𝑤𝑗 𝑁𝐷𝐴𝑖𝑗 ,

(28)

where 𝑤𝑗 is the weight associated with criterion 𝑗. Aggregated indicators 𝑆𝑃𝑖 and 𝑁𝑃𝑖 are normalized with respect to the maximum values:

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𝑆𝑃

𝑖 𝑁𝑆𝑃𝑖 = 𝑚𝑎𝑥 (𝑆𝑃 , ) 𝑖

(29)

𝑖

𝑆𝑁

𝑖 𝑁𝑆𝑁𝑖 = 1 − 𝑚𝑎𝑥 (𝑆𝑁 . ) 𝑖

𝑖

(30)

Each of the alternatives is evaluated by assigning a composite score, representing multiple dimensions of the criteria involved in the analysis. The composite score is calculated as an average of two normalized aggregates: 1

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𝐴𝑆𝑖 = 2 (𝑁𝑆𝑃𝑖 + 𝑁𝑆𝑁𝑖 ),

(31)

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where 0 ≤ 𝐴𝑆𝑖 ≤ 1. Finally, all the alternatives are ranked in descending order in terms of composite

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score.

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The model requires data on the crop areas, yield and prices for Lithuania and Germany. Data for

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the calculations were collected from Eurostat, Statistics Lithuania, Lithuanian Institute of Agrarian Economics, the Ministry of Agriculture of the Republic of Lithuania and Agricultural Information and

3. Results and discussion

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ur

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Rural Business Centre data bases.

Crop structure in Lithuania has changed significantly during 2005-2015 due to the effects of the EU Common Agricultural Policy. These changes occurred due to expansion of the total areas sown (scale effect) and changes in areas sown under certain crops (structural effect). Besides yields have increased over the decade (Table 3).

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Table 3. Harvested areas (thousand ha) and yields (t/ha) of the main crops in Lithuania, 2005–2015 Harvested area (thousand ha)

2005

2010

Per

Per

cent

cent

change

change

2015

2005

2010

2015 in

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in

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Crop

Yield (t/ha)

Barley

349.4

240.4

50.9

Oats

80.9

Triticale

2015

2015

837.1

127

3.73

3.30

5.24

40

202.5

-42

2.71

2.37

4.01

48

38.8

-24

2.12

1.76

2.78

31

84.8

81.6

1

1.90

1.66

2.54

34

75.2

111.8

122.5

63

2.67

2.37

3.84

44

19.9

36.8

30

0.55

0.73

1.00

82

1.6

7.2

12.0

650

3.08

6.68

4.81

56

35.8

54.8

157.4

340

1.64

1.41

2.90

77

Potatoes

74.0

37.5

23.6

-68

12.10

13.02

16.98

40

Field vegetables

20.7

14.0

10.9

-47

16.11

12.04

18.28

13

Sugar beet

21.0

15.4

12.3

-41

38.06

46.26

50.61

33

109.4

256.7

164.6

50

1.84

1.65

3.13

70

0.2

1.8

5.0

2400

0.57

0.62

0.75

32

30.1

20.0

18.9

-37

4.64

2.81

5.56

20

na

51.7

ur

Rye

2005-

-p

525.3

re

369.5

lP

Wheat

2005-

Buckwheat

Legumes

Rape Other oilseeds Orchards

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Grain maize

28.4

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Berry plantations

8.5

9.5

11.5

35

1.46

0.91

0.95

-35

The data in Table 3 were used to construct the status quo scenario which corresponds with the actual land use in Lithuania. The assumptions outlined in Table 1 were modelled by applying Eq. 1. Therefore the crop structure was optimized subject to profit maximization and constraints related to the

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assumptions. Table A1 presents the resulting crop-mixes. Profit maximization induced the growth in

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the area sown under rape and annual grasses irrespectively on scenario assumed. The decline in area sown under rye, maize, the other oilseeds, herbs and berry plantations was observed irrespectively of

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scenario assumed.

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The changes in crop structure induce a number of economic and environmental effects. As it

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was discussed in the previous section, we consider two environmental effects, namely water footprint and Shannon equitability index. As for the economic effects we look in to total output and yield risk.

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Due to changes in areas harvested and yields there has also been increase in the total harvest.

ur

Given the changes in scale and structure of crop farming, the total water footprint (WF) associated with crop production has doubled over the decade and reached 10.1 km3 in 2015. The green WF accounts for

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the vast majority of the total WF (9.8 km3, 96.7 per cent), whereas the grey WF accounts for a negligible share of the total WF (0.3 km3, 3.3 per cent). The blue WF is the least important in Lithuania as the precipitation is the main source of water used in crop farming. In the light of addressing the sustainability goals, one should seek to maximize agricultural output ensuring the lowest possible footprint level. In this regard, the growth in the total WF observed in Lithuania due to expansion of area harvested (Table 3) calls for particular attention for the environment-friendly solutions. Seeking to identify the most sustainable path for development of Lithuanian agriculture, we model baseline and five simulated scenarios of sustainable crop mix. The resulting values of the total

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WF (Table 4) enter multicriteria analysis. As one can note, the total WF ranges between 8.6 km3 and

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na

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re

-p

ro

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11.8 km3 depending on the underlying crop structure.

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Table 4. Water footprint (km3) in Lithuania in 2015 and under the modelled scenarios

Scenario

Green WF

Baseline scenario

Blue WF

Grey WF

Total WF

0.0039

0.33

10.1

Scenario 1

11.4

0.0043

0.34

11.8

Scenario 2

10.7

0.0045

0.35

11.1

Scenario 3

10.6

0.35

11.0

Scenario 4

10.5

0.0045

0.35

10.9

Scenario 5

8.3

0.0041

0.27

8.6

of

9.8

re

-p

ro

0.0044

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We also take into account the other indicator of environmental effect – Shannon equitability index. This allows adjusting the utility scores obtained during multi-criteria analysis with respect to the

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biodiversity level associated with different crop structures. The Shannon equitability index varies

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between 0.516 and 0.562. Turning to the economic dimension we measure the total output and

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downside coefficient of yield variation. The total output varies between 1601 million Eur and 1917 million Eur. In order to account the risk associated with crop yields variation, downside coefficient of yield variation is applied to the different crop structures. Resulting values fluctuate in between 0.0944 and 0.1118 (Table 5). The four indicators used in the multi-criteria analysis follow different directions of optimization. In the environmental dimension we seek to minimize the environmental pressures by minimizing the total WF maximizing Shannon equitability index. As regards the economic dimension total output (million Eur) is maximized whereas downside coefficient of yield variation is minimised (Table 5).

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Scenario 4 assumes a decline in the area sown under barley, legumes, oilseeds, herbs, maize, silage crops, berry plantations and meadows and pastures along with an increase of area sow under rye, oats, buckwheat, potatoes, vegetables, sugar beets, rape, annual and perennial grasses if compared to the baseline scenario. Scenarios 3 and 1 show similar levels of the total output. Compared to the baseline scenario, they both show a decline of the area sown under the rye and silage crops (besides

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changes common to all the scenarios as described in the data and methodology section). Scenario 3 shows larger area sown under oats, buckwheat and annual and perennial grasses if compared to

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scenario 1. Scenario 2 comes next in terms of the total output due to a number of minor differences in

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the crop mix. The lowest total output is observed in the scenario 5. This scenario results in the largest

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areas of oats, annual and perennial grasses, meadows and natural pastures, and fallows. In addition, the

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latter scenario results in the smallest area sown under wheat, legumes, triticale, and sugar beets. The decision matrix given in Table 5 suggests that Scenario 5 minimizes the total WF,

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maximizes value of Shannon equitability index and minimizes value of downside coefficient of yield

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variation. Scenario 4 maximizes the total output. This implies that multi-criteria analysis is required to model the trade-offs among multiple criteria and identify the most promising scenario for developing

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Lithuanian crop farming in terms of sustainability.

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Tаble 5. Initiаl decision-mаking mаtrix

Scenario

Baseline

Scenario

Scenario

Scenario

Scenario

Scenario

scenario

1

2

3

4

5

min

10.1

11.8

11.1

11.0

10.9

8.6

max

0.531

0.547

0.533

0.538

0.516

0.562

max

1705

1892

1865

1900

1917

1601

min

0.1075

0.1022

0.1026

0.1010

0.0944

Direction

Total WF Shannon

of

equitability

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index Total output,

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million Eur

0.1118

lP

coefficient of

re

Downside

na

yield variation

ur

As it was described in the data and methodology section, three multi-criteria methods (SAW,

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TOPSIS and EDАS) and three weighting sets were used for this analysis. This allows accounting for differences in utility function and weighting when ranking the alternatives. Table 6 shows the results of multi-criteria analysis of the scenarios analysed. Each column in the Table 6 corresponds to a particular combination of multi-criteria method and weight vector.

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Table 6. Scenario rankings according to SAW, TOPSIS and EDАS methods with different weights

SAW

TOPSIS

EDAS

W1

W2

W3

W1

Baseline scenario

5

2

6

4

Scenario 1

6

6

5

6

Scenario 2

4

4

4

Scenario 3

2

3

3

Scenario 4

3

5

Scenario 5

1

1

W1

W2

W3

2

6

5

2

6

6

5

6

6

5

5

3

4

4

3

3

4

2

2

3

2

1

2

3

1

3

5

1

2

1

1

4

1

1

4

re

-p

5

na

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W2

of

W3

ro

Scenario

Scenario 5 appears as the most appealing one in six out of the nine possible cases defined by

ur

different multi-criteria methods and weighting schemes. The exceptions include cases associated with

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weight vector W3. This indicates that Scenario 5 is underperforming of economic criteria which are assigned with higher importance under W3. This can be explained by considering the constraints on the crop structure implied by minimization by labour cost. Indeed scenario 5 shows the lowest total output. Scenario 4 is the most desirable alternative assuming economic oriented weighting (W3) under to all the MCDM techniques. Scenario 5 appears as the second-best alternative under the SAW technique yet it goes down the ranking in case TOPSIS or EDAS is applied. This shows that the compensatory technique, SAW, results in higher utility scores in Scenario 5 than it is the case for reference point techniques (TOPSIS and EDAS). Indeed scenario 5 shows the lowest value downside coefficient of yield variation, which somehow improves its performance in the economic dimension.

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Baseline scenario appears as the second most desirable scenario under environment-oriented weighting (W2). However, baseline scenario is attributed with ranks 4 to 6 at the different weighting schemes. In this regard switching from balanced weighting (W1) to any other weighting scheme may result the highest gains in utility for the baseline scenario. Indeed the baseline scenario shows moderate environmental performance (total WF and Shannon equitability index) and its economic performance

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(total output and downside coefficient of yield variation) is not the worst. We further perform correlation analysis to present an overview of the differences in the ranking

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of cropping scenarios due to different methods and weights (Table 7). The results can be analysed in

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two ways. First, the differences in ranking rendered by a certain MCDM technique due to application

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of different weighting schemes can be analysed by considering parts of Table 6 where the same

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technique appears on the rows and columns. Second, one can analyse differences among MCDM

na

techniques by considering by other section of Table 6.

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Table 7. Correlation matrix of the results obtained using SAW, TOPSIS and EDАS methods

W1

SAW

TOPSIS

with different weights

SAW W2

TOPSIS W3

W1

W2

W1

1.00

W2

0.60

1.00

W3

0.77

0.03

1.00

W1

0.89

0.60

0.77

1.00

W2

0.60

0.83

0.31

0.83

1.00

W3

0.54

-0.26

0.83

0.43

-0.09

EDAS W3

1.00

W1

W2

W3

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EDAS

W1

1.00

0.60

0.77

0.89

0.60

0.54

1.00

W2

0.60

1.00

0.03

0.60

0.83

-0.26

0.60

1.00

W3

0.54

-0.26

0.83

0.43

-0.09

1.00

0.54

-0.26

1.00

As one can note, all the elements in Table 6 are positive with exception of correlation between rankings associated with environment and economic approaches (W2, W3). This finding is valid for all

of

MCDM techniques applied for the analysis as well as for cross-technique comparisons. Thus

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environmental and economic approaches are conflicting between themselves, yet there is no such a

-p

serious contradiction among the latter two approaches and the balanced approach.

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The average coefficients of correlation for rankings rendered by SAW, TOPSIS and EDAS

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range in between 0.65 and 0.73 with the lowest (resp. highest) value being observed for EDAS (resp. SAW). Looking at the average coefficients of correlation for cross-technique ranking reveals rather

na

similar results (values of the coefficients range in between 0.50 and 0.57). The lowest value is observed for rankings rendered by EDAS and TOPSIS. All in all, rankings tend to differ across the weighting

ur

schemes to a higher extent than is the case across MCDM techniques.

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Note that results of this research cannot be directly compared to the earlier literature in a direct manner as we take economic approach in generating the crop-mixes and then apply different sustainability criteria in the second stage multi-criteria analysis. This is different from, e.g., GalánMartín et al., (2015), who applied economic modelling with certain constraints without further considerations on the sustainability. Our approach allows generating certain crop-mixes based on the farmers’ profit-maximizing behaviour under different scenarios and, subsequently, analyse sustainability of those scenarios.

4. Conclusions

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This paper proposed an integrated framework for assessment of cropping sustainability at the aggregate level. Specifically, different crop-mixes were compared in terms of environmental and economic criteria involving total water footprint, Shannon equitability index, total output, and downside coefficient of yield variation. The crop mixes were generated by applying mathematical

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programming. We applied three MCDM techniques (SAW, TOPSIS and EDАS) thus ensuring robustness of the analysis.

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The proposed framework was applied for the case of Lithuania, which is a new EU member

-p

state. Indeed direct payments have considerable impact on crop mix in Lithuania and other new EU

re

member states. Thus different assumptions, related to the major agricultural support schemes were

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applied to define scenarios leading to associated mathematical programming problems. The resulting crop mixes were then assessed in terms of sustainability criteria. Sensitivity analysis was carried out by

na

establishing the three weighting schemes (balanced, environment- and economy-oriented).

ur

The results showed that scenario assuming minimization of labour costs appeared to be the most sustainable one for most of combinations of MCDM techniques and weighting schemes. Indeed, such a

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scenario is likely to be implemented in the context of Lithuania due to depopulation of the rural areas. Switching to the economy-oriented approach, scenario assuming increasing organic production prices up to prices prevailing in a leading market (Germany) appears as the most attractive one. Assuming environment-oriented preferences, the baseline scenario showed an increase in ranking. Correlation among the ranks of the scenarios suggested that environmental and economic approaches are conflicting between themselves, yet there is no such a serious contradiction among the latter two approaches and the balanced approach. The present study relies on the aggregate data for Lithuania. Further studies could develop similar models for different levels of aggregation or different regions. Different modelling approaches

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could be applied to elicit scenarios for agricultural development. In addition, livestock farming could also be covered. As regards to the quantitative models applied, fuzzy sets or stochastic programming could be involved in the analysis to account for uncertainty.

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Annex A

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Table A1. Modelled harvested crop areas (thousand ha) under the different scenarios:

Baseline Crops

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Scenario 5

938.20

938.20

616.60

170.60

170.60

170.60

31.40

31.40

66.70

31.50

108.20

108.20

117.50

836.24

872.20

938.20

Barley

202.39

266.20

170.60

Rye

38.81

31.40

Oats

81.07

79.30

108.20

122.00

148.13

118.90

107.52

118.90

97.80

Buckwheat

36.71

34.30

50.50

50.50

50.50

27.20

Grain maize

11.69

10.70

10.70

10.70

10.70

10.70

212.70

103.22

114.60

68.42

55.80

32.63

32.94

32.94

32.94

21.53

13.12

14.53

14.53

14.53

10.82

12.20

19.20

19.20

19.20

19.20

10.10

0.20

0.21

0.85

0.19

0.19

0.13

163.53

258.73

255.03

255.03

255.03

255.03

Other oilseeds

5.09

2.04

2.04

2.04

2.04

2.04

Herbs

3.38

2.76

2.76

2.76

2.76

2.76

Annual grasses

7.87

9.93

15.79

15.79

15.79

9.93

29.28

32.22

22.77

22.77

22.27

21.72

156.97

Potatoes

23.46

Sugar beet Fodder root

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Vegetables

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Legumes

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Triticale

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Wheat

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scenario

crops Rape

Maize for

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silage and green fodder 4.03

1.78

1.78

1.78

1.78

4.37

339.01

308.30

442.50

442.50

442.50

512.70

Orchards

18.82

20.60

Berry

11.55

11.30

798.90

550.00

Silage crops Perennial grasses (5

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years and

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19.10

17.00

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90.92

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Fallows

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natural pastures

19.10

7.40

7.40

7.40

7.40

550.00

550.00

550.00

879.00

87.67

87.67

87.67

123.32

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Meadows and

19.10

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plantations

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more)

87.67

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Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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Highlights The paper develops a framework for assessment of crop farming sustainability. Mathematical programming is exploited to define the scenarios. MCDM methods are applied to assess the sustainability.

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Biodiversity, water footprint and economic indicators are considered.