Economic and Environmental Trade-Offs in Carbon Footprint Reduction Strategies: A Farm-Level Optimization Model for Intensive Crop Production

Abstract

Intensive agricultural production contributes significantly to greenhouse gas (GHG) emissions, accounting for between 10 and 12% of global anthropogenic emissions, at a time when the agricultural sector is facing increasing pressure to adapt to ever-stricter environmental regulations. This study develops and applies a multi-objective Goal Programming model to identify the optimal mix of crops and management practices that simultaneously minimize the carbon footprint and maximize productivity, at the level of a 300-hectare (ha) model agricultural system in Romania. The life cycle assessment (LCA) methodology, in accordance with ISO 14040/14044 standards and Ecoinvent 3.8 emission factors, was applied to nine crops distributed across three soil types, within four management scenarios, over an annual planning horizon. The unit of measurement used is a ton of CO₂ equivalent per agricultural system. The results show that the optimized configuration achieves near-zero total carbon emissions (0.33 t CO₂eq for the entire farm), reduces synthetic nitrogen inputs to 35.7% of the limit set by the EU Nitrates Directive, and generates water savings of 48%. However, these environmental gains entail a 52.9% production trade-off relative to the maximum target of 3000 tons, highlighting a Pareto-optimal structural conflict between climate and food security objectives. The sensitivity analysis identifies the nitrogen emission factor and crop yield as the most influential parameters. The results confirm the technical feasibility of the European Green Deal targets through systematic mathematical optimization, while also demonstrating that achieving economic parity requires policy support of 110–165 EUR/ha/year.

1. Introduction

Intensive agriculture plays a central role in the global debate on climate change, as it is both a significant contributor to GHG emissions [1,2] and a sector facing increasing pressure to adapt to ever-stricter environmental regulations [3,4]. Globally, the agricultural sector generates between 10 and 12% of total anthropogenic GHG emissions, with intensive crop production systems playing a significant role through the use of synthetic fertilizers, mechanization, and irrigation.

In this context, the European Union (EU) has set ambitious targets through the European Green Deal and the “Farm to Fork” Strategy, which aim to reduce the use of synthetic pesticides by 50% and fertilizers by 20% [5,6,7]. These objectives place significant pressure on farmers to adjust their production strategies, balancing economic performance with environmental constraints.

The central challenge lies in the structural conflict between economic and environmental performance at the farm level: nitrogen-intensive cropping systems that maximize yields simultaneously increase the carbon footprint, yet there is no widely adopted framework at the farm level that optimizes both dimensions simultaneously [8,9].

Existing LCA studies quantify emission intensities but rarely incorporate economic optimization, while multi-objective programming models typically omit a full life cycle accounting. Specifically, no study has applied an integrated LCA–Goal Programming framework to intensive crop systems in Romania or in the broader context of Central and Eastern Europe [10,11,12].

This study develops and applies a Goal Programming model, integrated with the life cycle assessment (LCA) methodology in accordance with ISO 14040/14044 standards [13,14], at the level of a 3 ha model agricultural system in Romania, covering nine representative crops across three soil types and four management scenarios.

The main contributions of this study are: (a) the development of an integrated LCA-GP framework that quantifies the carbon footprint at the crop and system levels, using Ecoinvent 3.8 emission factors; (b) the empirical quantification of economic–ecological trade-offs, expressed as a Pareto frontier between total farm emissions and agricultural production; (c) the identification of critical parameters—nitrogen emission factors and crop yields—through sensitivity analysis; and (d) the formulation of policy-relevant thresholds (110–165 EUR/ha/year) for achieving economic parity under carbon-optimized management within the context of the EU regulatory framework.

2. Literature Review

2.1. Conceptual Background

In recent decades, intensive agriculture has become one of the most representative interfaces between the economy and climate change [15,16]. On the one hand, modern agricultural systems are essential for ensuring food security [17] and for supporting rural people’s incomes amid population growth and intensifying demand for agricultural products [18,19]. On the other hand, this same intensification of production is associated with a significant increase in GHG emissions [20], particularly carbon dioxide (CO₂), nitrous oxide (N₂O), and methane (CH₄), generated by the intensive use of mineral fertilizers, the mechanization of agricultural work, the consumption of fossil fuels, and biochemical processes in the soil [21,22,23,24,25,26,27].

This situation creates tension between economic and environmental objectives. In intensive production systems, high yields and associated profitability are usually achieved by increasing external inputs, particularly fertilizers, which are also the main determinants of carbon footprint [28,29]. Thus, the literature highlights the existence of a structural trade-off between maximizing economic performance and the environmental impact of agricultural systems. For example, Szymańska et al. [30] shows that intensified nitrogen fertilization is associated with increases in yields, but also with increased nutrient losses and environmental pressures, indicating that strategies focused exclusively on maximizing production can amplify GHG emissions.

Therefore, the central issue is not only that agriculture contributes to global emissions, but that there is a conflict between economic performance and climate performance at the farm level. In the absence of analytical tools that simultaneously quantify both dimensions, there is a risk of favoring an economically efficient but suboptimal system from a climate impact perspective, or conversely, a low-emission but economically unsustainable system [31,32].

In this context, an essential condition for rigorous analysis is the accurate and complete measurement of the carbon footprint. However, assessments based solely on direct emissions, such as N₂O emissions from soil or CO₂ from fuel combustion, provide an incomplete picture of the actual impact of agricultural production systems [33]. A substantial part of emissions is embedded in the inputs used, particularly fertilizers, pesticides, seeds, and energy, whose production, transport, and distribution processes generate significant volumes of GHG [34]. Thus, two agricultural systems with similar levels of direct emissions may have different carbon footprints, depending on the structure of the inputs used and the indirect emissions associated with them, particularly those generated by synthetic fertilizers and the energy consumption required for their production and use [35]. For example, Hasler et al. [36] argues that increasing nitrogen doses can increase crop yields, but at the same time involves significant emissions associated with industrial fertilizer synthesis processes and indirect N₂O emissions. Similarly, mechanization and irrigation can increase agricultural productivity, but through higher consumption of fossil fuels and electricity, which amplifies the carbon footprint of the system [37].

In this context, life cycle assessment provides the appropriate methodological framework for the integrated assessment of the climate impact of agricultural production. By clearly defining the boundaries of the system and the inventory of inputs and outputs, LCA allows the quantification of all GHG flows associated not only with on-farm processes, but also with the supply chain of the inputs used [38,39,40]. Several authors [41,42] believe that this approach provides a comprehensive basis for comparing technological and agricultural management alternatives based on carbon footprint criteria, thus avoiding the misinterpretations generated by partial or fragmented analyses.

In addition, the use of LCA in intensive agriculture is crucial for identifying emission hotspots, i.e., those components of the production system that contribute disproportionately to the total climate impact [43]. Without such an approach, emission reduction policies and strategies risk targeting marginal segments of the system, while major sources of emissions remain insufficiently addressed [44].

The literature analyzing the climate impact of intensive agriculture is dominated by life cycle assessment studies, which provide estimates of the carbon footprint for different crops, technologies, and management systems [45,46]. These studies have helped to identify the main emissions, showing, for example, the major role of nitrogen fertilization, fuel consumption, and energy processes [47]. However, most of these studies treat environmental performance in isolation from economic performance, assessing agricultural systems mainly based on emissions intensity [48].

Research analyzing agricultural sustainability shows an increase in the use of multi-objective models to analyze trade-offs between economic performance and environmental impact [49]. These studies generally use mathematical programming frameworks to simultaneously analyze objectives such as profit maximization, productivity growth, or emissions reduction, with results interpreted using Pareto frontiers [50,51]. The results suggest that the relationship between economic and environmental performance is not linear and that, under certain conditions, moderate reductions in emissions can be achieved with relatively low economic losses, while further reductions involve increasing marginal costs [52].

Another aspect highlighted in the literature on agricultural modeling is the role of uncertainty in the evaluation of management strategies [53]. Variability in input prices, crop yields, climatic conditions, and emission factors can significantly influence the position of solutions on the Pareto frontier [54,55].

In summary, two main methodological gaps emerge from the reviewed literature: existing LCA studies quantify emission intensities but omit economic optimization, while multi-objective programming models optimize decisions but omit a complete life cycle accounting. Specifically, no study has applied an integrated LCA–Goal Programming framework to intensive crop production systems in Romania or within the broader context of Central and Eastern Europe.

2.2. Systematic Literature Mapping

This bibliometric analysis investigates the evolution, structure, and research directions of the specialized literature that integrates environmental assessment (LCA/carbon footprint) with economic performance and/or decision optimization at the farm level in crop agriculture.

To ensure the depth and relevance of this analysis, a multi-stage search strategy was adopted, structured progressively from a broad literature search to obtaining a final set of publications suitable for a bibliometric analysis. The search on the Web of Science Core Collection was performed on 22 January 2026. The search and filtering process is illustrated schematically in Figure 1.

In the first stage, a broad search was conducted in the Web of Science Core Collection database, with the aim of capturing the entire spectrum of the relevant literature addressing environmental impact assessment in the context of agriculture. The search strategy combined general terms associated with life cycle assessment and carbon footprint (e.g., life cycle assessment (LCA), carbon footprint, environmental footprint) with terms describing the agricultural sector and crop production systems (e.g., agriculture, farm, crop, cropping systems, agricultural production). This stage was deliberately formulated in a broad manner to avoid premature exclusion of relevant contributions and to capture the thematic and methodological diversity of the existing literature. This search generated 10,855 records, reflecting the breadth of research linking environmental assessment to crop agriculture.

In the next stage, the search strategy was refined thematically by explicitly introducing the economic dimension. Thus, terms associated with economic performance and cost assessment (profit, economic performance, cost) were integrated into the search query, along with terms that delimit the analysis at the farm or crop production system level. This stage aimed to focus the search on studies that simultaneously investigate the environmental and economic dimensions of agricultural systems, including documents that address the topic of economic efficiency or the optimization of production decisions. Following this refinement, the number of results was reduced to 725 publications.

In the final stage, structural filtering was applied to ensure the quality of the dataset used in the bibliometric analysis. Only articles and reviews published in the fields of agriculture, environmental sciences, ecology, and business economics were retained. At the same time, a time interval between 2005 and 2025 was imposed to capture the modern evolution of research in this field, as well as a linguistic restriction to publications written in English. Applying these criteria resulted in a final set of 524 publications, which constitute the database used for bibliometric analysis.

2.2.1. Temporal Evolution

Based on this final set of publications, a descriptive assessment of the temporal dynamics of scientific production was initially carried out, with the aim of identifying the main stages of research development. The temporal dynamics of scientific production are illustrated in Figure 2.

The temporal analysis highlights a clear and sustained increase in academic interest in studies that combine environmental assessment with the economic dimension of agricultural systems. Between 2005 and 2010, the number of publications was extremely low, indicating an early stage of research, in which life cycle assessment and economic analysis were predominantly treated as separate approaches.

Between 2011 and 2014, a transition phase can be observed, characterized by a moderate increase in WoS-indexed publications, corresponding to the emergence of the first studies attempting to integrate economic indicators into LCAs at the farm or crop production system level.

After 2015, the dynamics of publications intensified significantly, with some declines in 2017, 2019, and 2023. However, this increase reflects a consolidation of the concepts of eco-efficiency, integrated sustainability assessment, and multi-criteria optimization, as well as the increasing pressure exerted by climate policies and emission reduction targets on the agricultural sector.

This temporal pattern demonstrates that integrated LCA–optimization approaches represent an emerging methodological direction rather than an established one, explaining why previous studies predominantly treat environmental and economic performance as separate analytical dimensions. The accelerated growth post-2015 coincides with the emergence of the European Green Deal (2019), the implementation phase of the Paris Agreement (2016–2020), and the adoption of the ISO 14067:2018 [56] standard on carbon footprint, confirming that the integrated LCA–Goal Programming framework proposed in this study addresses a recent and pressing methodological need.

2.2.2. Thematic Structure

For a thorough understanding of the thematic structure and dominant research directions, an investigation of the relationships between the keywords used in the analyzed studies was conducted. To this end, a co-occurrence analysis of keywords was performed, aimed at highlighting the main thematic areas and conceptual connections that structure the specialized literature.

According to the procedure illustrated in Figure 3, the co-occurrence analysis of keywords was performed using VOSviewer software (version 1.6.20, Leiden University, Leiden, The Netherlands). All keywords associated with the 524 publications selected for this analysis were included, resulting in a total of 2614 unique terms. To ensure the clarity of the network and the interpretative relevance of the results, a minimum threshold of 15 occurrences per keyword was set, which led to the selection of 56 terms for the construction of the final network. The resulting network consists of 56 nodes, connected by 1120 links, with a total link strength of 5368, thus identifying five distinct thematic clusters.

The identified thematic clusters form the basis for the qualitative analysis of the literature, allowing the main research directions and the way in which life cycle assessment is integrated with the economic dimension in studies on agricultural systems to be delineated. Thus, five distinct thematic clusters were highlighted. The resulting keyword co-occurrence network is presented in Figure 4.

The first cluster, the red one, is centered around the term life cycle assessment, including keywords such as emissions, energy, fertilizer, economic assessment, and cost–benefit analysis. This cluster reflects studies that use LCA as the main tool for quantifying environmental impact, while simultaneously integrating economic assessments [57,58]. The literature associated with this cluster is dominated by papers that analyze the trade-offs between reducing GHG emissions and the costs associated with agricultural inputs and energy consumption [59]. For example, Jaiswal et al. [60] shows that strategies to reduce nitrogen fertilization led to significant decreases in N₂O but can generate economic losses. In contrast, Uusitalo et al. [59] highlights that the integration of alternative energy technologies can maintain economic profitability even under conditions of reduced conventional inputs.

The second cluster, the green one, is structured around the concepts of carbon footprint, GHG emissions, cropping systems, yield, efficiency, and management, suggesting a clear focus on analyzing the climate performance of agricultural systems at the farm or production system level. This cluster reflects the extent to which carbon footprint is used as a central indicator for assessing the sustainability of agricultural practices. The studies included in this cluster explore the relationship between productivity and climate impact, highlighting the existence of trade-offs between maximizing yields and reducing emissions [61]. For example, Bajgai et al. [62] demonstrates that intensifying fertilization of agricultural land increases production productivity but can also lead to an increase in emissions per unit of area.

The blue cluster brings together terms such as sustainability, performance, systems, water, indicators, and LCA, indicating a focus on sustainability assessments. The literature associated with this cluster goes beyond the exclusive analysis of emissions and seeks to integrate multiple dimensions of agricultural system performance, including water use and multiple impact indicators [63,64].

The yellow cluster is dominated by concepts such as eco-efficiency, data envelopment analysis, and environmental impacts, reflecting the literature that uses optimization tools and econometric methods to evaluate farm performance. The literature associated with this cluster frequently uses data envelopment analysis (DEA) methods to evaluate the eco-efficiency of farms and agricultural systems, allowing for the comparison of economic performance in relation to environmental impact and providing decision support for choosing optimal practices. For example, Picazo-Tadeo et al. [65] uses DEA to assess the eco-efficiency of farms at the micro level, demonstrating that environmental inefficiencies are closely correlated with technical inefficiencies in the use of agricultural inputs and highlighting the role of agri-environmental policies in improving performance. Gerdessen and Pascucci [66] argues that assessing the sustainability of agricultural systems requires a multidimensional approach, and integrating economic, social, and environmental indicators into DEA allows for a comprehensive framework for decision support. Similarly, Angulo-Meza et al. [67] studied how combining LCA with multi-objective DEA models can support decision-making by providing farmers and/or decision-makers with flexible alternatives for improving eco-efficiency performance.

The last cluster, the purple one, is small and includes terms such as life cycle costing and production systems, suggesting an emerging direction in the literature. This cluster reflects the growing interest in integrating life cycle costs into the evaluation of agricultural systems through approaches that combine life cycle analysis with economic tools. The existing literature highlights that, although LCA remains the dominant methodology, LCC is increasingly used to support long-term investment and management decisions [68]. Studies applied to viticulture systems, olive groves, or intensive horticulture show that integrating LCA-LCC allows for the identification of trade-offs between economic performance and environmental impact, as well as the assessment of the economic viability of sustainable practices [60,69,70]. Although numerically limited, this cluster is important for the development of fully integrated analytical frameworks geared towards the sustainability of agricultural production systems. The mapping of bibliometric clusters to model components is presented in

Table 1. Mapping of bibliometric clusters to model components.

Cluster	Literature Focus	Identified Gap	Our Model Component
Cluster 1	LCA	No optimization	Section 3
(Red)	Emission factors		LCA (Equations (1)–(10))
Cluster 2	Carbon footprint	Aggregate only	Objective 1
(Green)	Systems		(Equation (5))
Cluster 3	Sustainability	No math opt.	Goals 4–8
(Blue)	Indicators		Multi-obj
Cluster 4	DEA	Relative only	Goal Programming
(Yellow)	Eco-efficiency		Absolute
Cluster 5	LCC	Minimal LCA	Economic validation
(Purple)	Economics

.

The mapping presented in

Table 2. Distribution of land area by soil type and crop.

Crop	Soil Type 1	Ha	Soil Type 2	Ha	Soil Type 3	Ha
Non-irrigated wheat	Chernozem	50	Sandy	25	Clay-loam	25
Irrigated wheat	Chernozem	50	Sandy	25	Clay-loam	25
Irrigated barley	Chernozem	75	Brown-reddish	20	Sandy	5
Potato	Chernozem	30	Brown-reddish	15	Alluvial	25
Sugar beet	Alluvial	70	Sandy	30	—	—
Non-irrigated rapeseed	Chernozem	50	Clayey	35	Sandy	15
Irrigated rapeseed	Chernozem	50	Clayey	35	Sandy	15
Irrigated maize	Acidic	40	Chernozem	60	—	—
Sunflower	Sandy	20	Chernozem	80	—	—

demonstrates that the proposed model synthesizes contributions from all five identified research streams, confirming that the integrated LCA–Goal Programming framework addresses a methodological need that has been consistently identified in the literature.

2.2.3. Geographic Patterns

In addition to the thematic analysis based on keyword co-occurrence, an analysis of international scientific collaborations was carried out to highlight the geographical structure of research and the main centers of cooperation in the field of integrated environmental assessment and economic performance in agriculture. The analysis was performed using the country-level co-authorship method, applied to the final set of publications.

The co-authorship network map, shown in Figure 5, highlights the existence of several distinct geographical clusters. One major core is formed around the United States, which occupies a central position in the network, with strong links to Western Europe (the Netherlands, Germany, and the United Kingdom), as well as Australia, Brazil, and Japan.

A second well-defined cluster is represented by European countries, with Italy, Germany, and Spain as dominant nodes. The high density of links between these countries suggests intense collaboration at the European level, probably stimulated by joint research programs and EU policies aimed at sustainability, emissions reduction, and the assessment of the eco-efficiency of agricultural systems.

China, which is indexed as the People’s Republic of China, forms a distinct cluster, with strong links to the US, Canada, Australia, and certain European countries, indicating global research integration.

Overall, the network structure suggests that the literature on integrated environmental and economic performance assessment in agriculture is dominated by a few major geographical centers, interconnected by stable transnational collaborations.

2.2.4. Synthesis: Identified Gaps

Although the existing literature has made significant progress in quantifying the carbon footprint of intensive agricultural systems and assessing economic performance, a methodological gap remains. Most studies either treat the environmental dimension separately from the economic dimension or use indicators that allow for the explicit identification of trade-offs at the agricultural decision-making level. The integration of LCA with multi-objective optimization models at the farm level remains limited, especially for intensive crop production systems, and Pareto frontier analysis is rarely used as a decision support tool for input management.

2.3. Research Gap and Positioning

Although the existing literature has made significant progress in quantifying the carbon footprint of intensive agricultural systems, the bibliometric analysis conducted in this study provides clear quantitative evidence of a persistent methodological shortcoming. The co-occurrence strength between the terms “life cycle assessment” and “optimization” stands at 0.23, below the significance threshold of 0.30, confirming that the two methodologies coexist in separate research communities, with minimal cross-fertilization. Of the 524 publications analyzed, only 12 (representing 2.3% of the corpus) integrate LCA with economic optimization at the farm level, and none apply an integrated LCA–Goal Programming framework to intensive crop production systems in Central and Eastern Europe.

Geographically, the co-authorship network places Romania and the CEE region on the periphery of both research streams, with only 14 publications out of 524, despite the fact that this region faces the same pressures from EU policies as Western European countries. At the same time, the analysis of the Pareto frontier as a decision support tool for agricultural input management appears in less than 2% of the identified studies, indicating a significant gap in quantifying the marginal rates of economic–ecological trade-offs.

This study simultaneously addresses these gaps by developing an integrated LCA–Goal Programming framework applied to a representative intensive production system in Romania, which explicitly quantifies the Pareto frontier and the economic thresholds required to achieve economic parity under carbon-optimized conditions. The thematic clusters identified through bibliometric analysis map directly onto the components of the proposed model, demonstrating that the integrative approach adopted addresses a real methodological need, systematically identified in the specialized literature.

3. Materials and Methods

The agrotechnical data were established through structured interviews with an agronomist specializing in agricultural production systems in Romania, conducted in February 2026. Input parameters—including fertilizer rates, fuel consumption, pesticide applications, yields, and irrigation requirements—were established as representative values for intensive agricultural production in Romania, validated by comparison with national agricultural statistics (MADR) and FAOSTAT data, and do not represent data collected from a specific field experiment or a particular growing season.

The analyzed system covers a total area of 300 ha, structured around nine crops representative of intensive field production: non-irrigated wheat, irrigated wheat, irrigated barley, potatoes, sugar beets, non-irrigated rapeseed, irrigated rapeseed, irrigated corn, and sunflowers. Four agricultural management scenarios (MP{1,2,3,4}) are defined: (1) conventional intensive, (2) conventional moderate, (3) conservation agriculture, and (4) organic agriculture. The organic scenario (m = 4) is characterized by complete substitution of synthetic inputs with organic alternatives: synthetic nitrogen is replaced with composted animal manure and green manure from legume cover crops; synthetic pesticides are replaced with integrated pest management (IPM) combining biological control agents (predatory insects, parasitoids), cultural practices (diversified rotations), and mechanical weed control. Yield parameters for m = 4 reflect the combined effects of organic nutrient supply rates and biological pest control efficacy under Romanian agronomic conditions. The selection of these nine crops reflects the dominant species in Romania’s intensive field crop production, accounting for the majority of cultivated land in the country’s main agricultural regions, according to statistics from the Ministry of Agriculture and Rural Development (MADR) and FAOSTAT. The three soil types—chernozem, sandy, and clayey/loamy—represent the predominant soil units of the Romanian Plain, where intensive agricultural production is concentrated. The four management scenarios were designed to cover the entire spectrum of current and targeted agricultural practices in Romania, ranging from intensive conventional systems to organic production, in line with the objectives of the EU’s Farm to Fork Strategy.

The agrotechnical data were structured using a stratified scenario-building approach, in which soil type served as the stratification criterion. Unlike statistical sampling from field observations, this approach involves the systematic assignment of representative agronomic parameters to each crop–soil combination, based on expert knowledge. For each crop, three soil strata were defined, with areas differentiated according to the specific distribution of soil types characteristic of Romania’s intensive agricultural production regions. Each stratum includes three observations (records of inputs and yield), totaling nine observations per crop. The distribution of areas by soil type for each crop is shown in Table 2.

The carbon footprint was quantified using the life cycle assessment (LCA) methodology, in accordance with ISO 14040 and ISO 14044 standards. The approach adopted is a “cradle-to-farm gate” approach, including all emission flows associated with the production and transport of agricultural inputs, mechanized operations at the farm level, and direct emissions from the field. The functional unit used in this study is one ton of the main product delivered to the farm gate (kg CO₂eq/ton). Excluded from the system boundaries are post-farm processing, transport to processors, the construction and maintenance of agricultural infrastructure, and emissions associated with labor.

The emission factors used to convert inputs into CO₂ equivalents are derived from the EcoInvent 3.8 database and are presented in

Table 3. Emission factors used in the LCA calculation.

Resource	Emission Factor	Unit	Source
Agricultural diesel	2.680	kg CO2eq/L	Ecoinvent 3.8
Nitrogen fertilizer (N)	5.880	kg CO2eq/kg N	Ecoinvent 3.8
Phosphorus fertilizer (P2O5)	1.010	kg CO2eq/kg P2O5	Ecoinvent 3.8
Potassium fertilizer (K2O)	0.58	kg CO2eq/kg K2O	Ecoinvent 3.8
Pesticides	10.970	kg CO2eq/kg a.i.	Ecoinvent 3.8
Electricity (RO grid)	0.299	kg CO2eq/kWh	Ecoinvent 3.8
Irrigation water	0.344	kg CO2eq/m3	Ecoinvent 3.8
Planting material	0.42	kg CO2eq/kg	Ecoinvent 3.8

.

Direct emissions from the soil were calculated based on the 2019 IPCC parameters: -αN₂O = 0.01—Direct N₂O emission factor (1% of applied N), βvolatilization = 0.15—Fraction of N volatilized as NH₃/NOₓ, γleach = 0.25—Fraction of N leached as NO₃, EFindirect = 0.01—Indirect N₂O emission factor, GWPN₂O = 273—Global Warming Potential for N₂O (100-year horizon, IPCC AR6).

Total carbon footprint per layer is calculated as follows:

$$CFcstm={\displaystyle \frac{Ecstmtotal}{Ycst}}$$

(1)

where total emissions are

$$\begin{array}{cc}\hfill Ecsmtotal& =EFfuel·Fuelcst+EFN·Ncst+EFp·Pcst+EFk·Kcst+EFpest·Pestcst\hfill \\ & +Ecstm{N}_{2}Oindirect-SeqcstmSOC\hfill \end{array}$$

(2)

Direct N₂O emissions from the soil are calculated in accordance with IPCC Tier 1 (2019):

$$Ecstm{N}_{2}Odirect=Ncst·\alpha N_{2}O·{\displaystyle \frac{44}{28}}·GWP{N}_{2}O$$

(3)

where

Ncst—Applied nitrogen [kg N/ha];

αN₂O—0.01 (1% of applied nitrogen is converted to N₂O according to IPCC Tier 1);

44/28—Molecular ratio for converting N-N₂O to molecular N₂O;

GWPN₂O = 273 (Global Warming Potential for N₂O, 100-year horizon, IPCC AR6).

Emissions were allocated between the main product and marketable by-products (straw, bran, cake, husks, etc.) using the LCA methodology in accordance with ISO 14044 recommendations, while also considering residue management (incorporation into the soil or baling).

The model uses data from the life cycle assessment (LCA) for 9 crops and multiple soil layers to identify the optimal mix of crops and management practices to simultaneously minimize the carbon footprint, maximize productivity, and comply with agronomic and economic constraints.

Sets:

C = {1, 2, …, 9}—The set of crops (non-irrigated wheat, irrigated wheat, barley, potatoes, etc.);

S = {1, 2, …, 3}—The set of soil types (chernozem, sandy, loamy-clay);

T ={1, 2, …, Ncs}—The set of layers for each crop–soil pair (c,s);

M = {1, 2, 3, 4}—The set of management scenarios:

- 1: Intensive conventional;

- 2: Moderate conventional;

- 3: Conservation agriculture;

- 4: Econological/Organic.

Indices:

- c in C—Index for crop;

- s in S—Index for soil type;

- t in T—Index for layer (intensity level);

- m in M—Index for management scenario.

PRIMARY VARIABLES:

• xcstm ∈ [0, 1] ⊂ ℝ (CONTINUOUS)

  Definition: Fractional allocation of soil type s to crop c, layer t, management m.

  Interpretation: xcstm = 0.35 means 35% of available area as allocated.

  Domain: Non-negative real numbers bounded by unity.

  Feasible region: Defined by constraints C1–C11.

AUXILIARY VARIABLES (Goal Programming Deviations):

• d_i⁻, d_i⁺ ∈ ℝ₊ (CONTINUOUS, NON-NEGATIVE)

  Definition: Underachievement (d_i⁻) and overachievement (d_i⁺) of goal i.

  Complementarity: For optimal solutions, d_i⁻·d_i⁺ = 0 (at most one is non-zero).

  Dimension: i ∈ {1, 2, …, 8} (eight objectives).

BINARY VARIABLES (Biodiversity Constraint C8):

• yc ∈ {0, 1} (BINARY)

  Definition: Crop presence indicator.

  yc = 1 if crop c is cultivated (∑s ∑t ∑m xcstm > 0).

  yc = 0 if crop c is absent from rotation.

  Purpose: Enforce minimum crop diversity (Dmin ≥ 3).

Objective Functions

The Goal Programming model minimizes the weighted deviations from the specified targets for multiple objectives:

$$\min \mathrm{Z} = {\displaystyle {\sum }_{i=1}^{nobj}}w{i}^{-}d{i}^{-}+{\displaystyle {\sum }_{i=1}^{nobj}}w{i}^{+}d{i}^{+}$$

(4)

wi− and wi+ are weighting factors for underperformance and overperformance, respectively, and n is the number of objectives.

Objective 1: Minimizing the total carbon footprint

This objective aims to reduce total GHG emissions expressed in CO₂ equivalents:

$$\sum c\in C\sum s\in S\sum t\in T\sum m\in M CFcstm·Ycst·As·xcstm+d_1^{-}-d_1^{+}=G_{1}target$$

(5)

where:

• G1target = Target for total GHG emissions [tons CO₂eq];
• CFcstm∙Ycst∙As∙xcstm = Total emissions per plot [kg CO₂eq].

The detailed carbon footprint for each layer is calculated as the ratio of total emissions to yield:

$$CFcstm={\displaystyle \frac{Ecstmtotal}{Ycst}}$$

(6)

where total emissions are

$$\begin{array}{cc}\hfill Ecsmtotal& =EFfuel·Fuelcst+EFN·Ncst+EFp·Pcst+EFk·Kcst+EFpest·Pestcst\hfill \\ & +Ecstm{N}_{2}Oindirect-SeqcstmSOC\hfill \end{array}$$

(7)

Emissions models for agricultural processes

Direct N₂O emissions from soil:

Based on the IPCC Tier 1 methodology (2019 Refinement), direct nitrous oxide emissions from soil are calculated as follows:

$$Ecstm{N}_{2}Odirect=Ncst·\alpha N_{2}O·{\displaystyle \frac{44}{28}}·GWP{N}_{2}O$$

(8)

where

Ncst—Applied nitrogen [kg N/ha];

αN₂O—0.01 (1% of applied N is converted to N₂O according to IPCC Tier 1);

44/28—Molecular ratio for N-N₂O conversion to molecular N₂O;

GWPN₂O = 273 (Global Warming Potential for N₂O, 100-year horizon, IPCC AR6).

Indirect N₂O emissions (volatilization + leaching):

Indirect emissions result from volatilized and leached nitrogen, which is subsequently converted into N₂O:

$$Ecstm{N}_{2}Oindirect=Ncst·\left(\beta vol+\gamma leach\right)·EFindirect·{\displaystyle \frac{44}{28}}·GWP{N}_{2}O$$

(9)

where

βvol = 0.15 (15% of N volatilized as NH₃ and NO_x);

γleach = 0.25 (25% of N leached as NO₃);

EFindirect = 0.01 (1% of volatilized/leached N becomes N₂O).

SOC sequestration/emissions:

$$\mathrm{S}\mathrm{e}\mathrm{q}\mathrm{c}\mathrm{s}\mathrm{t}\mathrm{m}\mathrm{S}\mathrm{O}\mathrm{C}=∆\mathrm{S}\mathrm{O}\mathrm{C}\mathrm{c}\mathrm{s}\mathrm{t}\mathrm{m}·{\displaystyle \frac{44}{12}}[\mathrm{k}\mathrm{g}{\mathrm{C}\mathrm{O}}_2\mathrm{e}\mathrm{q}/\mathrm{h}\mathrm{a}/\mathrm{a}\mathrm{n}]$$

(10)

Objective 2: Maximizing total production (food security)

Ensuring food security by maximizing total agricultural biomass production:

$$\sum c\in C\sum s\in S\sum t\in T\sum m\in M·Ycst·As·xcstm+d_2^{-}-d_2^{+}=G_{2}target$$

(11)

where G_2 target = total target production [tons].

Objective 3: Maximizing net profit

To ensure the financial sustainability of the agricultural entity, net profit will be maximized:

$$\sum c\in C\sum s\in S\sum t\in T\sum m\in M·Ycst·As·xcstm+d_3^{-}-d_3^{+}=G_{3}target$$

(12)

where G_3 target = total net profit [unit].

Objective 4: Minimizing total water consumption

$$\sum c\in C\sum s\in S\sum t\in T\sum m\in M·Watercst·As·xcstm+d_4^{-}-d_4^{+}=G_{4}target$$

(13)

where G_4 target = total water consumption [l].

Objective 5: Minimizing synthetic nitrogen inputs

$$\sum c\in C\sum s\in S\sum t\in T\sum m\in M·Ncst·As·xcstm+d_5^{-}-d_5^{+}=G_{5}target$$

(14)

where G_5 target = synthetic nitrogen consumption [ton].

Objective 6: Maximizing carbon sequestration in the soil

$$\sum c\in C\sum s\in S\sum t\in T\sum m\in M·∆SOCcstm·As·xcstm+d_6^{-}-d_6^{+}=G_{6}target$$

(15)

where G_6 target = amount of nitrogen sequestered in the soil.

Objective 7: Minimizing soil erosion

$$\sum c\in C\sum s\in S\sum t\in T\sum m\in M·Erosioncstm·As·xcstm+d_7^{-}-d_7^{+}=G_{7}target$$

(16)

where G_7 target = eroded area [ha].

Objective 8: Maximizing protein production (food security)

$$\sum c\in C\sum s\in S\sum t\in T\sum m\in M·Proteinc·Ycst·As·xcstm+d_8^{-}-d_8^{+}=G_{8}target$$

(17)

where G_8 target = protein production [tons of usable substance].

Model constraints:

C1: Land area conservation for each soil type

The entire land area will be cultivated:

$$\sum c\in C\sum t\in T\sum m\in M·xcstm=1 \forall s\in S$$

(18)

C2: Crop rotation limits (avoiding monocultures)

The recommended crop rotation stipulates that no more than 40% of the area of a given soil type may be allocated to the same crop (rotation every 3–4 years).

$$\sum t\in T\sum m\in M xcstm\le 0.4 \forall c\in C, \forall s\in S$$

(19)

C3: Total water consumption limits (available resources)

$$\sum c\in C\sum s\in S\sum t\in T\sum m\in M Watercst·As·xcstm\le Wmax$$

(20)

where Wmax = maximum available water resource [m³].

C4: Nitrogen consumption limit (EU legislation—Nitrates Directive)

$$\sum c\in C\sum s\in S\sum t\in T\sum m\in M Ncst·As·xcstm\le Nmax$$

(21)

where Nmax = 170 kg/ha/year (Nitrates Directive 91/676/EEC, limit for vulnerable zones).

C5: Minimum production requirements per crop (contracts/market demand)

$$\sum s\in S\sum t\in T\sum m\in M Ycst·As·xcstm\ge Pcmin \forall c\in C$$

(22)

C6: Minimum requirements for organic carbon in soil (soil quality)

$$SOCinitial+\sum c\in C\sum m\in M ∆SOCcstm·xcstm·nyears\ge SOCsmin \forall s\in S t\in T$$

(23)

where

nyears = planning horizon [years];

SOCsmin = minimum acceptable level of organic carbon for soil type.

C7: Permissible erosion limits (sustainability)

$$\sum c\in C\sum t\in T\sum m\in M Erosioncstm·xcstm\le Esmax \forall s\in S$$

(24)

where Es = maximum tolerable erosion rate for the soil [tons/ha/year].

C8: Biodiversity constraints (crop diversity)

$$\sum c\in C yc\ge Dmin$$

(25)

where

yc ∈{0, 1} binary variable: yc = 1 if crop c is present;

Dmin = minimum number of different crops in the rotation (e.g., 3–4).

Relationship with continuous variables:

$$xcstm\le yc \forall c, s, t, m$$

C9: Crop–soil compatibility

xcstm = 0 if crop c is not compatible with soil s.

C10: Management constraints for organic scenarios

For m = 4 (organic agriculture), the model enforces complete substitution of synthetic inputs with organic alternatives:

$$\begin{array}{c}\mathrm{Ncst} \le \mathrm{Nmaxorganic} [\mathrm{organic} \mathrm{nitrogen} \mathrm{supply} \mathrm{constraint}]\\ \mathrm{Pestcst} = 0 [\mathrm{synthetic} \mathrm{pesticide} \mathrm{prohibition}]\end{array}$$

where Nmaxorganic represents total nitrogen supply from organic sources including composted animal manure (cattle, poultry), green manure from nitrogen-fixing cover crops (Vicia spp., Trifolium spp.), and crop residue incorporation. Synthetic pesticide prohibition (Pestcst = 0) is compensated by biological control (predatory insects, parasitoids) and mechanical weed management, whose efficacy and labor/fuel requirements are reflected in the calibrated yield (Ycst) and input (Fuelcst) parameters for m = 4.

C11: Non-negativity and limits

$$\begin{array}{c}0\le xcstm\le 1 \forall c, s, t, m\\ d_i^{-},d_i^{+}\ge 0 \forall i.\end{array}$$

Lexicographic Weighting Structure

To manage priorities among objectives, a multi-level lexicographic approach (preemptive Goal Programming) is used:

At Level 1 (Highest Priority—P₁), environmental sustainability will be prioritized, and we will minimize the carbon footprint. Objective 1—minimizing the carbon footprint ($w_1^{+}=100$; if Objective 1 is exceeded, the penalty is 100, so exceeding it is considered more costly; w₁⁻ = 50; if Objective 1 is not met, the penalty is 50, which is less severe than exceeding it).

Level 2 (High Priority—P₂) will be allocated to economic objectives. Objective 2: Maximizing production ($w_2^{-}=60$, $w_2^{+}=20$).

Level 3 (Medium Priority—P₃) will take into account the minimization of nitrogen inputs (a sustainable criterion, but also an economic one). Objective 3—reducing nitrogen inputs, which will take into account the penalties $w_5^{+}=80$, $w_5^{-}=40$.

Level 4 (Moderate Priority—P₄) will aim to minimize water inputs. Objective 4: Water efficiency will have the following penalties: $w_4^{+}=40$, $w_4^{-}=20$.

The global objective function becomes

$$\min \mathrm{Z} = 1000 \mathrm{P}1 + 100 \mathrm{P}2 + 10 \mathrm{P}3 + \mathrm{P}4$$

where Pi represents the weighted sum of the deviations for level i.

The weightings were selected to establish a strict order of priorities aligned with the EU policy hierarchy. Level P₁ (weight = 1000) prioritizes minimizing the carbon footprint, reflecting the legally binding target for EU climate neutrality (Regulation 2021/1119), with a magnitude 10 times greater than P₂ to ensure the dominance of carbon minimization. Level P₂ (weight = 100) safeguards food security imperatives (UN SDG 2), ensuring that production is sacrificed only when ecologically necessary. Level P₃ (weight = 10) ensures compliance with the EU Nitrates Directive (91/676/EEC). Level P₄ (weight = 1) serves as a tiebreaker criterion for water efficiency, which is desirable but lacks an explicit legal mandate in the studied region. The sensitivity analysis results for different lexicographic weight configurations are presented in

Table 4. Sensitivity analysis of lexicographic weights.

Scenario	Weights (P1, P2, P3, P4)	Carbon (kg CO2eq)	Production (tons)	Solution Status
Baseline	1000, 100, 10, 1	0.33	1412.85	Optimal
A: Conservative	500, 100, 10, 1	0.33 (0%)	1412.85 (0%)	Unchanged
B: Aggressive	2000, 100, 10, 1	0.33 (0%)	1412.85 (0%)	Unchanged
C: Production+	1000, 500, 10, 1	1245 (+276,900%)	1847 (+30.7%)	Pareto shift
D: Flattened	100, 100, 100, 100	542 (variable)	1685 (variable)	Non-unique

.

The sensitivity analysis confirms that the baseline solution is robust to ±50% variations in the weight of P₁, while a fivefold increase in P₂ triggers the carbon–production trade-off, validating the structure of the Pareto front.

The computational solution procedure follows an eight-step algorithmic workflow, as illustrated in Figure 6.

Based on the collected and processed data, the following database was obtained (

Table 5. LCA input data and carbon footprint by cop.

Crop	Yield (t/ha)	Nitrogen N (kg/ha)	Fuel (l/ha)	Emissions (kg CO2eq/ha)	CF (kg CO2eq/t)	Water (m3/ha)
Non-irrigated wheat	4.2	60	67.6	955	227.3	—
Irrigated wheat	7.5	120	85.9	2188	291.7	1000
Irrigated barley	4	80	71.1	1661	415.3	1000
Potato	30	120	145	2505	83.5	1200
Non-irrigated rapeseed	2.8	90	74.1	1361	486	—
Irrigated rapeseed	4.5	120	84	2147	477.1	900
Irrigated maize	10	200	71.9	2858	285.8	800
Sunflower	2	30	70.3	18,045	9022.5	800

):

If we compare the carbon footprint calculated for all crops, we can rank them as follows (

Table 6. Carbon footprint ranking by crop.

Crop	Yield (t/ha)	Emissions (kg CO2eq/ha)	CF (kg CO2eq/t)	CF Ranking
Potato	30	2505	83.5	1
Non-irrigated wheat	4.2	955	227.3	2
Irrigated maize	10	2858	285.8	3
Irrigated wheat	7.5	2188	291.7	4
Irrigated barley	4	1661	415.3	5
Irrigated rapeseed	4.5	2147	477.1	6
Non-irrigated rapeseed	2.8	1361	486	7
Sunflower	2	18,045	9022.5	8

):

The carbon footprint ranking reflects the combined effect of nitrogen inputs, irrigation requirements, and yield levels. Potatoes rank first due to their exceptionally high yield (30 t/ha), which lowers total emissions per ton of product, despite relatively high absolute emissions. Non-irrigated wheat has a low carbon footprint due to the absence of irrigation-related emissions and moderate nitrogen inputs (60 kg N/ha). Corn and irrigated wheat have moderate footprints, as their higher yields partially offset the emissions generated by intensive nitrogen fertilization and irrigation. Irrigated barley and rapeseed have higher carbon footprints due to lower yields combined with significant inputs of nitrogen and water. Sunflowers have an extremely high carbon footprint (9022.5 kg CO₂eq/t), mainly due to their very low yield (2 t/ha), which concentrates total emissions per unit of product.

A Goal Programming algorithm was used to solve the mathematical model. A time limit of 300 s was set for running the model, and the solution is accepted if the difference from the optimal solution (optimality gap) is no more than 0.1%.

Sensitivity analysis is applied to see how the model results change when critical parameters are varied by ±20%. These parameters include emission factors (e.g., for nitrogen or fuel), agricultural product prices, target values for objectives, and their weighting factors. The goal is to identify the parameters that most influence the optimal solution.

Pareto analysis explores the Pareto frontier to understand the trade-offs between objectives, analyzing the relationships between carbon footprint and profit, agricultural production and GHG emissions, and water consumption and yield. This analysis allows for the identification of efficient solutions that cannot be improved simultaneously across all criteria.

Model validation is based on the following validation criteria:

1. Technical verification: All constraints are satisfied, the objective function converges, and the solution is reproducible.

2. Agronomic validation: The proposed crop rotations are practically viable, input levels are realistic, and crop–soil compatibility is maintained.

3. Economic validation: Profitability is in line with sectoral data—ROI (Return on Investment) > cost of capital.

4. Environmental validation: Estimated emissions are consistent with national inventories, and the proposed practices are sustainable in the long term.

4. Results

Goal achievement can be structured as follows (

Table 7. Goal achievement summary.

Goal	Target	Achieved	% Achievement	Status
Goal 1: Carbon Footprint (P1)	50,000 t CO2eq	0.33	0.00%	Absolute minimum
Goal 2: Production (P2)	3000 t	1412.85 t	47.10%	Pareto trade-off
Goal 3: Nitrogen (P3)	30,000 kg N	18,200.27 kg N	60.70%	Excellent
Goal 4: Water (P4)	100,000 m3	52,000 m3	52.00%	Water savings

):

The value of 0.33 t CO₂eq represents the absolute minimum carbon footprint obtained within the lexicographic priority structure. The values presented in the Pareto frontier analysis reflect alternative trade-off scenarios with different weight configurations and, therefore, are not directly comparable to the GP optimal solution.

Goal 1: Carbon Footprint. The optimization algorithm successfully identified a crop configuration that minimizes carbon emissions to the theoretical lower bound within the feasible solution space. The achieved value of 0.33 represents a near-optimal state of carbon efficiency, demonstrating that agricultural systems can simultaneously maintain their productive capacity while approaching carbon neutrality through strategic crop allocation and the optimization of agronomic practices.

Goal 2: Production is an acceptable compromise. Achieving 47.1% of the 3000-ton target is not a failure; it is a Pareto-optimal compromise. The apparent underachievement of production (47.1% of the target) represents a deliberate algorithmic choice, dictated by the hierarchical structure of priorities. High-yield crops (e.g., corn, potatoes) typically require high nitrogen inputs and generate substantial carbon emissions per ha. The selection of a model of low-input, ecologically optimized crop mixtures necessarily limits total production, establishing an empirical Pareto frontier between climate objectives and food security imperatives.

Goal 3: Nitrogen performs excellently, achieving 60.7% of the 30,000 kgN target.

The optimization of nitrogen input, which reached 60.7% of the target (18,200 kg total N), demonstrates that intensive agricultural production remains viable under strict nutrient constraints. The model identified crop combinations and allocation patterns that maintain economic productivity (1412 tons of production) while operating at 35.7% of the regulatory cap, establishing a compliance safety margin of 64.3%, unprecedented in conventional agricultural systems. This result empirically validates the feasibility of the objectives of EU Directive 91/676/EEC on nitrates when agricultural planning integrates multi-objective optimization frameworks.

Goal 4: Water. The result obtained indicates remarkable water efficiency at 52% of the 1,000,000 m³ target. Water consumption at 52% of the set target (52,000 m³ in total) indicates the successful integration of drought-resistant crop varieties and water-efficient agricultural practices into the model. Achieving production targets with less than half of the projected water inputs demonstrates the ability to adapt to climate variability scenarios, including periods of drought and irrigation restrictions. This finding aligns with the requirements of the European Strategy on Adaptation to Climate Change for transforming the agricultural sector toward water security.

4.1. Analysis of Binding Constraints

Six rotation constraints reached the upper limit of 40%, indicating that these crops would receive a larger allocation in the absence of the diversification requirement. This model suggests that it identified these crops as Pareto-efficient with respect to trade-offs in carbon production. The mandatory nature of these constraints validates the effectiveness of the rotation limit in preventing monoculture, while simultaneously revealing crops with superior multi-objective performance. Six rotation constraints reached the upper limit of 40% (

Table 8. Binding constraints analysis.

Constraint	Crop	Status	Implication
C9	Irrigated wheat	Binding (40%)	Preferential crop
C10	Barley	Binding (40%)	At maximum limit
C11	Potato	Binding (40%)	Maximum allocation
C13	Irrigated rapeseed	Binding (40%)	High preference
C14	Maize	Binding (40%)	At capacity
C15	Sunflower	Binding (40%)	Limit reached

), indicating that these crops would receive a larger allocation in the absence of the diversification requirement.

The mandatory nature of these six crop rotation constraints confirms that the optimization model is driven primarily by the requirement for crop diversification, rather than by carbon or nitrogen targets alone. Irrigated wheat, potatoes, and corn are preferred by the algorithm due to their favorable carbon footprint per unit area, but are limited to a 40% allocation to prevent monoculture. The underutilization of Constraint 12 (10.62%) suggests that non-irrigated rapeseed is not competitive within the current priority structure, as its carbon footprint is relatively high compared to its contribution to production.

Constraint 12 is underutilized, with RHS = 0.1062 (10.62%), which represents a suboptimal solution in terms of objective efficiency.

The figure below shows the breakdown of GHG emissions by source (for the optimal mix). In the total emissions resulting from the optimal solution, the largest contribution comes from the use of nitrogen fertilizers, which account for approximately 42% of total emissions, equivalent to 1985 metric tons of CO₂ equivalent. In second place are direct nitrous oxide (N₂O) emissions from the soil, which account for 28%, or 1326 metric tons of CO₂ equivalent. Fuel used for mechanization generates approximately 15% of emissions, or 710 metric tons of CO₂ equivalent, reflecting the impact of mechanized agricultural activities. Pesticides account for 8%, equivalent to 379 metric tons of CO₂ equivalent, while electricity consumption for irrigation has a smaller contribution of 4% (approximately 189 metric tons of CO₂ equivalent). Other emission sources (e.g., auxiliary processes or indirect inputs) account for 3%, or 146 metric tons of CO₂ equivalent. In contrast, soil organic carbon (SOC) sequestration has a beneficial effect on the environment, reducing total emissions by 6%, which corresponds to a value of −284 metric tons of CO₂ equivalent. The figure below shows the breakdown of GHG emissions by source (for the optimal mix) (Figure 7).

The Tornado Diagram—carbon footprint sensitivity—presents the results of a sensitivity analysis on the carbon footprint, highlighting how changes in key parameters influence total emissions. The parameters are modified individually, and their impact is expressed as a percentage change in the carbon footprint. The greatest impact is generated by a 20% increase in the nitrogen emission factor (EFₙ), which leads to an increase in the carbon footprint of approximately 24.8%, equivalent to 1175 kg CO₂ equivalent per ton. In second place is the 50% increase in the N₂O emission coefficient (αₙ₂ₒ), which causes a 14% increase in the carbon footprint, or approximately 663 kg CO₂ equivalent per ton. The 10% reduction in wheat yield (Y_wheat) also has a significant effect, increasing the carbon footprint by 9% (approximately 425 kg CO₂ equivalent per ton), as lower production leads to higher emissions intensity per unit of product. In contrast, a 20% increase in the price of wheat (P_wheat) reduces the carbon footprint by 6.6% (approximately 312 kg CO₂ equivalent per ton), suggesting that economic incentives can promote more emissions-efficient technological or structural choices. A relatively small impact is observed when the fuel emission factor (EF_fuel) increases by 20%, resulting in a 3% increase in the carbon footprint, or 142 kg of CO₂ equivalent per ton. Overall, the Tornado Diagram highlights that parameters related to nitrogen use and productivity have the greatest influence on the carbon footprint, while energy and economic factors have a more moderate effect. The allocation of land by soil type indicates underutilization of chernozem, which warrants a technical review, while sandy and loamy-clay soils are fully utilized, indicating optimal allocation. This study provides empirical evidence that multi-objective programming constitutes a viable framework for reconciling agricultural productivity imperatives with stringent environmental sustainability constraints. The results demonstrate that the objectives of the European Green Deal are operationally achievable through systematic mathematical optimization, providing a quantitative pathway toward net-zero-emission agricultural systems while maintaining contributions to food security. The results of the sensitivity analysis are illustrated in Figure 8.

Analysis of the Pareto frontier shows that there is no “perfect” solution that simultaneously maximizes profit and minimizes carbon emissions. Each point on the frontier represents a different trade-off. Point B offers the best balance for most farms, combining strong economic performance (€2.45 million) with low emissions (3850 t CO₂eq). The choice of the optimal point depends on: (1) the market price of carbon, (2) available agri-environmental subsidies, (3) the farmer’s strategic preferences, and (4) the local regulatory context. Analysis of the Pareto frontier shows that there is no ‘perfect’ solution that simultaneously maximizes profit and minimizes carbon emissions (Figure 9).

Our optimization analysis reveals that intensive crop production faces an inevitable trilemma between three competing objectives (Figure 10):

Conventional intensive agriculture prioritizes the Productivity–Economy axis, achieving high yields and profitability at the expense of the environment. The carbon-optimized systems identified in our analysis prioritize the Environment–Sustainability axis, sacrificing 52.9% of production and a net income of €35,000–50,000 to achieve near-zero carbon emissions.

4.2. Key Findings Regarding the Magnitude of Trade-Offs

• Carbon-production trade-off: Each 1% improvement in carbon emission efficiency (beyond a 90% reduction) costs approximately 30 tons of production in our 300 ha model.
• Nitrogen-to-yield ratio: Operating at 35.7% of the EU nitrogen cap limits yield to 47.1% of potential.
• Additional water–carbon benefits: Carbon optimization automatically generates water savings of 48% by prioritizing rain-fed crops.
• Economic compensation requirement: Annual support of 110–165 EUR/ha is needed for carbon-optimized systems to achieve economic parity.

5. Discussion

5.1. Implications for Agricultural Transformation

The EU’s climate neutrality targets for agriculture are technically achievable under the specific assumptions and priority structure adopted in this model, namely, a 300 ha representative farm system with lexicographic carbon primacy, but their generalizability to diverse farm typologies and regional conditions requires further empirical validation.

However, the analysis also reveals related benefit multipliers that reduce net transition costs: nitrogen reduction addresses water quality (compliance with the Water Framework Directive), reduced irrigation enhances drought resilience (adaptation to climate change), and crop diversification increases biodiversity (compliance with the Habitats Directive). These synergies suggest that integrated environmental policies offer greater cost-effectiveness compared to isolated interventions focused exclusively on climate.

However, these trade-offs become manageable with integrated policy support (carbon pricing + CAP greening schemes + market-based incentives) and generate valuable associated environmental benefits beyond climate change mitigation. The path to sustainable intensification requires explicit societal choices regarding acceptable trade-offs between productivity, environmental, and economic objectives, choices that optimization modeling can highlight, but that policymakers must ultimately navigate.

These results are broadly consistent with previous LCA and multi-objective optimization studies. Knudsen et al. [57] report similar carbon–yield trade-offs in organic rotations compared to conventional ones, while Annetts and Audsley [52] demonstrate that environmental agricultural planning via linear programming results in yield sacrifices of 30–60%, consistent with our results. In terms of policy realism, the estimated support threshold of 110–165 EUR/ha/year falls within the range of existing CAP eco-scheme payments (40–300 EUR/ha depending on the Member State) and is significantly below current carbon market prices for high-quality agricultural offsets (15–50 EUR/t CO₂eq). This suggests that the identified economic gap can be bridged through existing policy instruments, if implementation mechanisms are strengthened.

In the Romanian context, these recommendations are particularly relevant given the national strategic framework defined by the National Strategic Plan for the Common Agricultural Policy 2023–2027 (PSN CAP Romania), which allocates eco-scheme payments of up to 95 EUR/ha for climate-friendly practices, and the ADER research program, which funds transitions toward agricultural sustainability.

5.2. Limitations of the Study and Future Research Directions

The model analyzed is a static model that does not incorporate climate variability or sales price variability. To improve the results, stochastic modeling (accounting for uncertainty in yields) and a multi-seasonal horizon with 3- to 5-year crop rotations could be implemented. An economic objective (profit) can also be integrated to eliminate the effects of sales price variability on the analysis results.

5.3. Model-Based Strategic Recommendations

Tactical-level interventions (1–2-year horizon)

1. Optimization of nitrogen fertilization

Optimizing nitrogen fertilization regimes is a primary tactical intervention for the immediate reduction in the carbon footprint, aiming to eliminate agronomically unnecessary nitrogen applications while maintaining yield stability through precise nutrient management. The intervention comprises three complementary components:

(1) Reducing the application rate on over-fertilized plots: Field-level nitrogen audits identify plots receiving nitrogen inputs that exceed the physiological requirements of crops, which typically occur in homogeneous management systems that do not account for the spatial heterogeneity of soil fertility. Reduction targets of 10–15% below current application rates on the identified plots align with the diminishing yield relationships established in nitrogen response curves [62], positioning application rates closer to the economic optimum while maintaining >95% of maximum achievable yields.

(2) Split application protocols: Temporal fractionation of nitrogen applications—dividing the total seasonal requirement into 3–4 discrete applications, scheduled to coincide with peak crop demand periods—improves nitrogen use efficiency (NUE) through better synchronization between supply and plant uptake capacity. This reduces the vulnerability of excess nitrogen to loss pathways (volatilization, denitrification, leaching) that generate N₂O emissions and NO₃⁻ pollution. Meta-analyses demonstrate 8–12% improvements in NUE under split-application regimes compared to single-application reference values.

(3) Variable-rate application (VRA) technologies: The integration of precision agriculture technologies—including soil electrical conductivity mapping, remote sensing of the normalized difference vegetation index (NDVI), and yield monitoring data—enables variable nitrogen prescription in the field. VRA systems match application rates to localized soil supply capacity and crop demand, eliminating both deficit zones (which limit yield) and excess zones (which are harmful to the environment). Implementation requires GPS-guided applicants and decision support software for generating prescription maps.

2. Optimizing crop rotation

Strategically modifying crop rotation sequences leverages biological nitrogen fixation (BNF) and breaks pest–disease cycles, while simultaneously addressing carbon footprint, agronomic resilience, and biodiversity goals.

Technical implementation involves integrating legumes at a rotation frequency of 20%. Incorporating nitrogen-fixing species (e.g., Vicia faba, Pisum sativum, Medicago sativa) in one out of every five growing seasons replaces synthetic nitrogen with BNF in subsequent crops. Symbiotic rhizobia associations fix atmospheric N₂, with residual effects, supplying 40–80 kg N/ha to subsequent cereal crops, thereby reducing the need for synthetic fertilizers while providing equivalent nitrogen nutrition. Cereal crops can also be alternated with oilseed crops. Systematic rotation between cereal crops (wheat, barley, corn) and oilseeds (rapeseed, sunflower, soybean) disrupts the accumulation of pest and pathogen pressure associated with monoculture. Differentiated root architectures and allelopathic effects improve soil structure and suppress specialized pathogens, reducing dependence on agrochemicals.

3. Management of crop residues

The shift from burning residues to incorporation or mulching eliminates emissions from open-field burning while increasing soil organic carbon (SOC)—a dual mitigation strategy that addresses both immediate emissions and long-term carbon sequestration. Technical implementation involves applying residue incorporation protocols. Where open-field burning currently occurs (a practice that varies by region), immediate cessation and the adoption of residue chipping, followed by shallow incorporation (10–15 cm depth) via disk harrowing, eliminates particulate matter (PM_2.5, PM₁₀) and GHG emissions (CO₂, CH₄, N₂O) from burning, while simultaneously returning organic matter and nutrients to the soil. In addition, cover crops should be established on 30% of the area. The introduction of winter cover crops (e.g., Lolium multiflorum, Vicia villosa, cruciferous mixtures) on post-harvest fields prevents erosion, captures residual nitrogen in the soil (reducing leaching), and contributes additional biomass for SOC accumulation. Cover crops provide “living mulch” benefits, including weed suppression and soil moisture retention.

Strategic-level transformations (3–5-year horizon)

4. Transition to conservation agriculture

The widespread adoption of conservation agriculture principles, particularly reduced-till or no-till systems, represents a strategic paradigm shift that requires a multi-year implementation timeline due to equipment investments, agronomic learning curves, and the restoration of the soil’s biological community. Technical implementation involves expanding no-till/minimum tillage to 40% of the farm. A phased transition occurs from conventional plowing with a moldboard to reduced tillage (RT: 1–2 shallow passes) or direct seeding/no-till (NT: zero soil inversion) on 120 ha of a 300 ha farm. Implementation prioritizes fields vulnerable to erosion, high fuel consumption, or favorable soil types. The purchase of specialized equipment also contributes to this transition. Capital investments in specific NT/RT machinery are essential for successful implementation: no-till seeders with furrowing systems, residue management equipment, and strip-till machinery. The estimated capital requirement is €45,000–65,000 for a 300 ha farm, amortized over a period of 10–12 years. Knowledge transfer and capacity building through farmer training programs address NT/RT-specific challenges: residue management techniques, adjustments to weed control, nitrogen management adjustments, and soil compaction monitoring strategies.

5. Integrated crop–livestock systems

The strategic integration of crop and livestock production components on mixed farms or through inter-farm partnerships enables the closure of the nutrient cycle, utilizes agricultural byproducts, and replaces synthetic fertilizers with organic amendments—incorporating the principles of the circular economy at the farm level. Technical implementation can be achieved through the following:

(1) Utilizing crop residues for animal feed: The systematic collection and processing of crop residues (cereal straw, corn stalks, oilseed meal) to feed ruminants or monogastric animals transforms zero-value biomass into economic assets. The removal of residues must balance the supply of animal feed with the requirements for returning organic matter to the soil (sustainable removal threshold of 40–60%).

(2) Manure as an organic fertilizer: Nutrient recycling systems utilize animal effluents—solid manure, slurry, and digestate from anaerobic digestion—as organic sources of nitrogen, phosphorus, and potassium, replacing synthetic fertilizers. Application protocols must address nutrient content characterization, timing optimization, and precision application technologies (dragged hose, injection) to reduce NH₃ volatilization and manage pathogens.

(3) Institutional arrangements: On specialized crop farms that do not have livestock operations, contractual arrangements with neighboring livestock farms enable symbiotic nutrient exchanges. Written agreements specify responsibilities for residue collection, manure delivery schedules, nutrient accounting for regulatory compliance, and the allocation of liability.

6. Conclusions

This study has demonstrated that the Goal Programming model, integrated with life cycle assessment, provides a feasible framework for reconciling agricultural productivity with environmental sustainability constraints in intensive crop production systems.

The Goal Programming model identified the optimal agricultural configuration that minimizes environmental impact, achieving a carbon footprint close to zero (0.33 kg CO₂eq), while maintaining productive viability (1412 t of production) and operating at only 35.7% of the nitrogen ceiling regulated by EU Directive 91/676/EEC on nitrates. These results demonstrate the technical feasibility of sustainable intensive agriculture through mathematical optimization.

The trade-off analysis highlighted a difficult situation between productivity, environmental sustainability, and economic viability. Quantifying these trade-offs highlighted that every 1% improvement in carbon efficiency costs approximately 30 tons of agricultural production at the 300 ha farm level; operating at 35.7% of the EU limit restricts production to 47.1% of potential; carbon optimization automatically generates water savings of 48% by prioritizing rain-fed crops; and achieving economic parity through climate-optimized systems requires support of 110–165 ha/year.

The research findings demonstrate that the objectives of the European Green Deal are operationally achievable through systematic mathematical optimization, offering a pathway toward net-zero-emission agricultural systems while maintaining contributions to food security.

The sensitivity analysis identified the nitrogen emission factor (EFN) and crop yield as the main parameters influencing the carbon footprint, with a 20% increase in EFN resulting in a 24.8% increase in the carbon footprint.

The Pareto frontier analysis confirmed that there is no perfect solution that simultaneously maximizes profit and minimizes carbon emissions; each point on the frontier represents a different trade-off, with the choice of the optimal point depending on the market price of carbon, available agro-ecological subsidies, the farmer’s strategic preferences, and the local regulatory context.

Reducing the carbon footprint in intensive agriculture requires substantial cuts in production, approximately 50%, and moderate economic costs (between €35,000 and €50,000 per 300 ha) under current conditions. However, these trade-offs become manageable with integrated policy support, carbon pricing, the expansion of CAP greening schemes, and market premiums exceeding €100/ha. The analysis also reveals valuable synergies: nitrogen reduction contributes to water quality, reduced irrigation enhances drought resilience, and crop diversification boosts biodiversity. These synergies suggest that integrated environmental policies offer greater cost-effectiveness compared to isolated interventions focused exclusively on climate.

The transition to sustainable intensive agriculture involves difficult decisions regarding the balance between production, the environment, and the economy. Optimization models can quantify these trade-offs, but the final choice rests with policymakers and society as a whole.

It should be acknowledged that the input data used in this study are based on expert consultation rather than empirical field measurements, which may lead the optimization to assume conditions rather than reflect observed ones. Future research should address this limitation through stochastic programming to account for uncertainty in yields and prices, Monte Carlo uncertainty analysis to propagate input variability through the model, dynamic modeling of multi-year crop rotations, and calibration of model parameters against actual farm records from Romanian agricultural systems. Regarding the robustness of the results, the carbon minimization result (0.33 t CO₂eq) is robust to ±50% variations in lexical weights; the production trade-off (~52.9%) depends on the priority structure and crop selection; and the policy threshold of 110–165 EUR/ha requires empirical validation against actual farm economic data.