# Managing trade-offs between economic, environmental, and animal welfare performance in French suckler cattle farms through feeding practices

Larissa Mysko, Claire Mosnier, Patrick Veysset, Isabelle Veissier, Jean-Joseph Minviel

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## ► To cite this version:

Larissa Mysko, Claire Mosnier, Patrick Veysset, Isabelle Veissier, Jean-Joseph Minviel. Managing trade-offs between economic, environmental, and animal welfare performance in French suckler cattle farms through feeding practices. Agricultural Systems, 2026, 234, pp.104692. 10.1016/j.agsy.2026.104692. hal-05535790

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# Managing trade-offs between economic, environmental, and animal welfare performance in French suckler cattle farms through feeding practices

Larissa Mysko<sup>a,b,*</sup>, Claire Mosnier<sup>a</sup>, Patrick Veysset<sup>a</sup>, Isabelle Veissier<sup>a</sup>, Jean-Joseph Minviel<sup>a</sup>

## HIGHLIGHTS

* Multiperformance on sucker cattle farms is rarely achieved.

* Economic, environmental and animal welfare indicators can be in conflict.

* Compromise programming linked to a bioeconomic model was used to handle trade-offs.

* A 15% feed margin reduction can improve environmental impact and animal welfare.

* Political is needed to incentivise farmers to achieve compromise solutions.

## GRAPHICAL ABSTRACT

<figure><img src="image_3.png" /><figcaption>Environmental and animal welfare performance can be improved by limiting economic losses to 15% of the optimum values</figcaption></figure>

## ARTICLE INFO

Editor: Paul Crosson

**Keywords:**

Compromise programming

Bioeconomic model

Farm economics

Welfare proxies

Multiperformance

## ABSTRACT

**CONTEXT:** Economic, environmental and animal welfare performance objectives are often not achieved simultaneously due to antagonistic relationships related to farming practices.

**OBJECTIVE:** Here, we aim to 1) understand which performance objectives are in conflict on suckler cattle farms and 2) examine how these conflicts can be managed.

**METHODS:** We first determine the relationships between the different performance indicators via a bioeconomic model focusing on variables impacting feeding and analyse the conflicts between performance indicators. We then explore how the trade-offs can be managed via a compromise programming approach.

**RESULTS AND CONCLUSIONS:** The obtained compromise solutions show that, compared with feed margin-driven optimisation, environmental and animal welfare performance can be substantially enhanced, with foregone feed margins of approximately 15% of the optimum values. These compromises can be achieved by reducing herd size and animal fattening, increasing the share of grassland in farmland and reducing the purchase of concentrate feed.

**SIGNIFICANCE:** Combining bioeconomic modelling with compromise programming is a promising first step in providing farmers with guidance on how to ensure good performance in multiple objectives and in providing public policy-makers with the means to develop policies along these lines.

<footnote><sup>a</sup> Université Clermont Auvergne, INRAE, VetAgro Sup, UMR Herbivores, 63122 Saint-Genès-Champanelle, France</footnote>

<footnote><sup>b</sup> Université Clermont Auvergne, VetAgro Sup, INRAE, AgroParisTech, UMR Territoires, 63370 Lempdes, France</footnote>

<footnote>* Corresponding author at: Université Clermont Auvergne, INRAE, VetAgro Sup, UMR Herbivores, 63122 Saint-Genès-Champanelle, France.
E-mail address: larissa.mysko@vetagro-sup.fr (L. Mysko).</footnote>
# 1. Introduction

Studies analysing multiple performance dimensions have shown that good performance in terms of economic, environmental, and animal welfare indicators is rarely achieved simultaneously for different animal types and production systems (Mysko et al., 2025); this can be explained by antagonistic relationships between the targeted multiple objectives depending on practices. For example, increased productivity per animal may reduce the environmental impact, such as greenhouse gas (GHG) emissions, expressed per unit of production, but it may impair animal welfare when functional traits, such as good foot and limb conformations, deteriorate (Place, 2018). Furthermore, practices aimed at improving animal welfare, such as more building space per animal or lower stocking rates, can lead to a decrease in the global economic efficiency of the production system; this suggests that not all objectives may reach their optimum value at the same time. Here, we focused on how farms can get as close as possible to the best performance of each indicator defining an objective when performance objectives in economic, environmental, and animal welfare terms are conflicting, i.e., have antagonistic relationships with a set of practices and farming conditions.

French suckler cattle farms are criticised for their poor economic performance (Cour des comptes, 2022) and high GHG emissions (Citepa, 2024). Furthermore, consumers are concerned with animal welfare (European Commission, 2015), and the French beef sector is currently integrating animal welfare requirements into quality labels, such as *Label Rouge* (Interbev, 2022). The scientific literature on multiperformance has focused on more intensive livestock systems, such as dairy cows, pigs and broilers (Mysko et al., 2025). Thus, there is a need for multiperformance studies dedicated to suckler cattle farming.

Managing multiple criteria simultaneously in a formalised way requires the use of a multicriteria decision-making (or decision-aided) (MCDM or MCDA) method. There are two major approaches within MCDM: multiple-attribute decision-making (MADM) and multiple-objective decision-making (MODM). MADM addresses discrete, limited numbers of alternatives and comprises methods such as multi-attribute utility theory (MAUT), analytic hierarchy process (AHP), or outranking (e.g., ELECTRE, PROMETHEE) methods. MODM addresses a large number of alternatives and comprises methods such as goal, multi-objective, or compromise programming (Rehman and Romero, 1993; Sadok et al., 2008). In this paper, we aim to explain the links between practices and several indicators based on quantitative variables to make explicit the antagonisms, i.e., deviations from optima, between indicators within a performance dimension or belonging to different performance dimensions and to build a compromise solution. Therefore, we opted for the compromise programming approach based on variables characterising farming practices, such as animal feeding. Compared with multi-objective programming, this approach has advantages over goal programming in that it does not need to know the decision-maker's aspiration level for each indicator and provides a more restrained Pareto efficient solution set (Rehman and Romero, 1993). Pareto efficiency is achieved when it is not possible to improve one indicator without worsening another.

The focus on animal feeding was chosen because of its central role in livestock systems and its pivotal role in the relationship between three performance dimensions—economic performance, environment performance, and animal welfare performance. Our hypothesis is that ratios from intensive systems that use more corn and less pasture grass compared to extensive systems generate higher feed costs, higher GHG emissions (that may, however, be offset by higher animal productivity), and provide less animal welfare. Indeed, from an economic perspective, feeding costs contribute largely to the production costs of cattle farms. Estimations for feeding costs vary considerably because they do not generally consider the same scope. Commonly reported feed costs only include purchased feed, i.e. mainly concentrates. If all costs are included, i.e. not only purchased feed, but also inputs (seeds, fertilisers,

pesticides), rent paid for land and mechanisation costs for on-farm produced feed, feed costs ratioed to total production costs account for 37% for extensive farming systems (grass-based only) up to 43% for more intensive systems (based on grass and corn silage) in the French Massif Central region (Delmas et al., 2021). Feeding is also crucial to environmental performance because crop production generates 26.5% of total GHG emissions in France (Citepa, 2024), and half of the crop production area is used to feed animals (INSEE, 2021), whereas grasslands, which provide most of the suckler cow ration, are associated with many ecosystem services (Bengtsson et al., 2019). Feeding also impacts the four principles—'good feeding', 'good housing', 'good health' and 'appropriate behaviour'—of animal welfare (Welfare Quality, 2009). In the Welfare Quality (2009), good feeding management is captured by the indicator 'body condition score', which is a proxy of the criterion 'absence of prolonged hunger'. In the Welfare Quality protocol, only too-skinny animals are included in the score. In addition, inappropriate feeding with a too-rich diet can lead to health disorders (acidosis, infertility, etc.) and thus impact the 'good health' principle. Furthermore, pasture, which corresponds to a feeding practice, is considered in two criteria of the Welfare Quality protocol: 'ease of movement' (part of the 'good housing' principle) because it provides a large space to animals and 'expression of other behaviours' (part of the 'appropriate behaviour' principle) because it promotes "the expression of species-specific natural behaviours such as foraging" (Welfare Quality, 2009). Pasture not only provides more opportunities to express behaviour (foraging, exploration, walking, social interactions) but also reduces abnormal oral activities and injuries (Demba and Rose, 2023; Palacio et al., 2023). It is thus considered to promote positive experiences, on the conditions that the pasture cover nutritional needs and animals are protected against adverse weather (Mee and Boyle, 2020). In the present paper we thus infer animal welfare from the time they spend at pasture.

In this work, we seek to 1) understand which indicators regarding economic, environmental and animal welfare performance are conflicting for suckler cattle farms and 2) consider how these conflicts can be managed. We first determine the relationships between the different performance indicators via a bioeconomic model focusing on variables impacting feeding (i.e. ration, herd size and composition, and calving period), and analyse the conflicts between performance indicators. We then explore how the trade-offs can be managed via a compromise programming approach.

# 2. Materials and methods

## 2.1. Optimisation models

We developed a general bioeconomic model to which we applied several objective functions (maximisation or minimisation of a performance indicator), each leading to a distinct single-objective optimisation model. At least one objective function was specified for each of the three dimensions — economic performance, environment performance, and animal welfare performance —. A total of seven objective functions were defined: two economic (feed margin in euros and feed margin ratio); four environmental (measuring the impact of climate change and eutrophication, each expressed per hectare and per kilogram of carcass); and one for animal welfare (see Section 2.2).

The decision variables in the bioeconomic model are feed ration per animal, herd composition and size, and calving period (see Section 2.3.1). They were chosen because they impact animal feeding, which plays a central role in livestock systems and is pivotal in the relationship between the three performance dimensions. The scientific and technical literature provides well-established parameters and equations to link feed to economic and environmental performance. The prices of purchased feed can easily be found, and production costs for on-farm-produced feed can be calculated (Bouchard et al., 2023). The AGRIBALYSE programme (AGRIBALYSE, 2024) created a life cycle inventory (LCI) database and offers references on the environmental impacts of
agricultural and food products (Koch and Salou, 2022). Welfare Quality (2009) provides a mathematical link between days at pasture and a welfare score. All this information can be used to construct a bio-economic model that links economic, environmental and animal welfare performance objectives to variables impacting feeding, such as ration, herd size and composition, and calving period (Fig. 1).

The model constraints concern herd demography (assuming no inventory change) and animal nutrition (guaranteeing animal needs are satisfied) (see Section 2.3.2), as well as agronomic potential (with two scenarios — plain and mountain —) and limited available land (see Section 2.3.3) (Fig. 1).

Based on the results of the seven single-objective optimisation models, we used compromise programming to determine compromise solutions, i.e. solutions that are as close as possible to the best performance for each optimised objective. Compromise programming consists of three stages, as described in Romero and Rehman (2003) (Fig. 1):

1) The seven single-objective optimisation models are run. For each model, the indicator used in its objective function is optimised and the indicators used in the objective functions of the six other models are computed.

2) The obtained seven values for each indicator enable the construction of a payoff matrix with the optimised values ('ideal values') and the worst obtained values ('anti-ideal values') for each objective.

3) A distance metric between feasible solutions and the utopian point where all objectives would be optimised, i.e., defined by the ideal values, is minimised to obtain a Pareto efficient compromise solution (see Section 2.4).

## 2.2. Objective functions

### 2.2.1. Optimisation of economic performance

For economic performance, we use two profitability indicators to be maximised: farm feed margin in euros ('Feed margin in €') and farm feed margin ratio ('Feed margin ratio'). The farm feed margin is defined as revenues from livestock sales (Eq. 1) minus feed costs that include purchased feed and on-farm feed production costs (Eq. 2), in euros. The feed margin ratio is the ratio of feed margin to farm revenues (Eq. 4). These two economic indicators allow us to evaluate not only how profitable a farm is relative to its feeding costs (feed margin), but also the feeding-cost effectiveness of a production system (feed margin ratio).

$$Revenues = \sum_{k}^{Q} (Nb(AnimalSold_{k}) \times SalesWeight(AnimalSold_{k}) \times Price(AnimalSold_{k})) \quad (1)$$

$$Feed \ costs = \sum_{i}^{N} \left( \left( \sum_{j}^{M} AFQ(Feed_{i}, Animal_{j}) \right) \times Cost(Feed_{i}) \right) \quad (2)$$

$$Feed \ margin \ in \ \epsilon = Revenues - Feed \ costs \quad (3)$$

$$Feed \ margin \ ratio = \frac{(Revenues - Feed \ costs)}{Revenues} \quad (4)$$

where Nb is the number of animals sold, AnimalSold_k is the type of animal sold, SalesWeight is the liveweight for animals sold alive and carcass weight for animal sold for slaughter, Price is the animal sales price per kg liveweight for animals sold alive and per kilogram carcass (kgc) for animals sold for slaughter, AFQ is the annual feed quantity in kg per animal type and feed type, Feed_i is the feed type, Animal_j is the type of animal in the herd (animals for reproduction and for sales), and Cost is the feed cost that includes both production and purchase costs.

The feed production costs and their respective yields are retrieved from the reference document of INOSYS Réseaux d'élevage by Bouchard

et al. (2023). Feed production costs include mechanisation (machinery and labour), input (fertilisers, pesticides, seeds, furniture) and storage costs. The feed production costs depend on the agronomic potential of the parcels (see Section 2.3.3 and Table A1 in Appendix A). The prices of purchased feed are set to be realistic as of 2021 (Table A1 in Appendix A) because the price index in 2021 is close to the 10-year average price index between 2015 and 2024 according to the purchase price index for agricultural means of production (IPAMPA) of INSEE (French National Institute of Statistics and Economic Studies). We use animal sales prices as of 2021 retrieved from the reference document of INOSYS Réseaux d'élevage by Bougarel et al. (2022).

This leads to the following economic objective functions:

* Model 'ECOEUR': maximising the 'Feed margin in €'

* Model 'ECORATIO': maximising the 'Feed margin ratio'

### 2.2.2. Optimisation of environmental performance

For environmental performance, we use two indicators representing environmental impacts: one indicator for climate change impact because, in France, cattle farming alone is estimated to generate 8.5% of national GHG emissions (Citepa, 2022) and one for freshwater eutrophication because "diffuse run-off from agricultural land continues to be a major phosphorus source in European lakes",<fnref n="1" /> and eutrophication "generally ranks higher in severity of water pollution than the emission of toxic substances" (Goedkoop et al., 2008).

The impact of climate change is measured as anthropogenic GHG net emissions and the sum of the impacts of feed, enteric fermentation, and effluent storage (Eq. 5). It is expressed in CO₂ equivalents. The climate change impact with respect to feed (Eq. 6) is calculated with the environmental impact data from the AGRIBALYSE database. AGRIBALYSE provides environmental indicators for agricultural products via life cycle assessment (LCA) and sets the system boundaries from cradle to 1) a field gate for on-farm-produced crops, 2) a storage unit for purchased crops, 3) a processing plant for processed feed (e.g., canola meals), and 4) arrival at the French port for imported feed (Wilfart et al., 2017). The functional units of the indicators in AGRIBALYSE are kg of dry matter (DM) for forage and kg of feed for concentrate feed (Koch and Salou, 2022). In AGRIBALYSE, carbon sequestration is considered by applying -170 kgC/ha/year for crops and temporary grasslands and 110 kgC/ha/year for permanent grasslands (Koch and Salou, 2022). The impacts of climate change on enteric fermentation (Eq. 7) and effluent storage (Eq. 8) were calculated via the CAP2ER method, which relies mainly on the methods proposed by the IPCC (2006) (Carbon Agri, 2019).

Freshwater eutrophication is expressed in kg P equivalents (Eq. 9) because P is the limiting factor in the yield of aquatic biomass, which is detrimental to the freshwater ecosystem if it is in excess. In AGRIBALYSE, freshwater eutrophication is calculated via the SALCA-P model (Nemecek and Kägi, 2007; Prasuhn, 2006).

$$ClimateChange = CCFeed + CCEntFerm + CCEffStor \quad (5)$$

with

$$CCFeed = \sum_{i}^{N} \left( \left( \sum_{j}^{M} AFQ(Feed_{i}, Animal_{j}) \right) \times ClimImpact(Feed_{i}) \right) \quad (6)$$

$$CCEntFerm = 45.42 - 6.66 \times IL + 0.75 \times NI^2 + 19.65 \times PCO - 35 \times PCO^2 - 2.69 \times NI \times PCO \times \sum_{i}^{N} \left( \left( \sum_{j}^{M} AFQ(Feed_{i}, Animal_{j}) \right) \times DOM(Feed_{i}) \right) \times 25 \quad (7)$$

<footnote n="1">¹ https://www.eea.europa.eu/en/analysis/indicators/nutrients-in-fresh-water-in-europe, accessed on May 16, 2025.</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. Overview of the modelling approach combining compromise programming with a bioeconomic model. Compromise programming consists of three stages: 1) single-objective optimisation, 2) definition of a payoff matrix consisting of ideal and anti-ideal values for each single objective, and 3) determination of a compromise solution.</figcaption></figure>

$$ CCEffStor = \sum_{i}^{N} \left( \left( \sum_{j}^{M} AFQ(Feed_{i}, Animal_{j}) \right) \times NDOM(Feed_{i}) \times 0.67 \right. \\ \left. \times 0.18 \times \left( \sum_{k}^{2} FCM_{k} \times FM_{k} \right) \right) \times 25 \quad (8) $$

$$ Eutrophication = \sum_{i}^{N} \left( \left( \sum_{j}^{M} AFQ(Feed_{i}, Animal_{j}) \right) \times EutriImpact(Feed_{i}) \right) \quad (9) $$

where AFQ is the annual feed quantity in kg per animal type and feed type, Feedᵢ is the feed type, Animalⱼ is the animal type, CCFeed is the climate change impact due to animal feed, ClimImpact is the climate change impact data from AGRIBALYSE, CCEntFerm is the climate change impact due to enteric fermentation, CCEffStor is the climate change impact due to effluent storage, IL is the ingestion level, PCO is the proportion of concentrates in the ration, DOM is the digestible organic matter, NDOM is the nondigestible organic matter, FCMₖ is the CH₄ conversion factor for the manure management system k, FMₖ is the fraction of manure managed in the manure management system k, 25 is the conversion factor from CH₄ to CO₂ eq, ClimateChange is the total climate change impact, and EutriImpact is the freshwater eutrophication data from AGRIBALYSE; Koch and Salou, 2022).

We express each of these indicators with two functional units: kilogram carcass (kgc) of sold animals and hectare (ha) of land used. The carcass yields are set to 0.53 for cows, 0.55 for heifers and female weanlings, and 0.58 for young bulls and male weanlings (Web-agri, 2019). To estimate the amount of meat produced, expressed in kgc, we also apply these yields to animals sold alive. The idea is to test the impact of the choice regarding the functional unit because, in the scientific literature, the conclusions differ depending on whether the environmental impacts are expressed per quantity produced or per ha (Mysko et al., 2025; Salou et al., 2017). Regarding the land used, we considered the land used on the farm but also included estimates of

hectares of purchased feed via the land occupation data of AGRIBALYSE, which leads to the following four environmental objective functions:

* Model 'ENVCLIMATKGC': minimising the impact of climate change per kgc produced

* Model 'ENVCLIMATHA': minimising the impact of climate change per ha of land used

* Model 'ENVEUTRKGC': minimising eutrophication per kgc produced

* Model 'ENVEUTRHA': minimising eutrophication per ha of land used.

### 2.2.3. Optimisation of animal welfare performance

For animal welfare performance, we choose a proxy representing grazing time to be maximised because grazing is recognised as an important welfare indicator (Welfare Quality, 2009). Under- and over-conditioning are not included in the objective function because they are implicitly considered in the bioeconomic model, where constraints ensure that nutritional needs of animals are satisfied (see Section 2.2.2).

We first estimate how much grass each animal type needs to consume at pasture per day to cover its intake capacity (Eq. 10). From the total amount of grass consumed in kg DM, we calculate the number of grazing days as a percentage of total days on the farm during the year (Eq. 11).

$$ \text{DailyGrassAmount}(Animal_{j}) = \frac{IC(Animal_{j})}{FV('grass')} \quad (10) $$

where Animalⱼ is one of the animal types presented in Section 2.1.1, FV is the fill value in fill units per feed type, and IC is the intake capacity in fill units per animal type. Equations with regard to intake capacities are derived from reference guides (Agabriel et al., 2014; Institut national de la recherche agronomique, 2007; Jarrige, 1989) and are detailed in Fig. A2 in Appendix A. Fill values were extracted from feed tables (Institut national de la recherche agronomique, 2007) (Table A3 in Appendix A).

$$ \text{PercentageGrazingTime}(Animal_{j}) = \frac{\text{TotalFeed('grass', Animal}_{j})}{\text{DailyGrassAmount}(Animal_{j})} \times \frac{1}{\text{DaysOnFarm}(Animal_{j})} \times 100 \quad (11) $$
where TotalFeed is the total amount of a feed type in kg DM (here, ‘grass’) consumed by an animal type Animalj, DailyGrassAmount is the estimated daily consumed grass at pasture in kg DM, and DaysOnFarm is the number of days an animal type stays on the farm during the year as some animal types are sold during the year.

To calculate the average percentage grazing time at the herd level, the percentages of grazing time per animal type are weighted according to the number of animals and days present at the farm during the year. Furthermore, we add the constraint that fattened young bulls are not produced when optimising for animal welfare because of the high amount of concentrate feed needed in their fattening stage (between 50% and 60% of the ration), which may be detrimental to animal welfare owing to the risk of acidosis.

This leads to the following animal welfare objective function:

* Model ‘AW’: maximising the average ‘Percentage grazing time per year’ of the herd.

## 2.3. Bioeconomic model specification

### 2.3.1. Definition of decision variables related to animal feed

Our simulated case studies are based on typical French suckler cattle farms provided by the large livestock network INOSYS - Reseaux d'élevage (https://portail.inosys-reseaux-elevage.fr/FR/). The decision variables — ration per animal, herd composition and size, and calving period — are defined as follows.

For the possible components of the feed rations, we selected standard feed types for French suckler cattle. For forage, we chose permanent grasslands for fresh forage ('grass'), two dried forages - hay from permanent grasslands ('hay') and straw ('straw' if purchased and 'strawOF' if produced on farm) - two silages - one made of permanent grasslands ('grass silage') and one made of corn as a whole plant ('corn silage'). For concentrates, we chose triticale for a cereal ('triticale' if purchased and 'triticaleOF' if produced on farm) and two by-products—canola meal for one produced locally ('canola meal') and soybean meal for one produced abroad ('soybean meal').

For herd composition, we modelled a herd with animal types typically sold by French suckler cattle farms (Bougarel et al., 2022) (Fig. 2). The herd composition and size determine the stocking rate, i.e., the annual average number of livestock units (LU) per hectare of utilised agricultural area (UAA). LUs were calculated via conversion factors according to the Eurostat classification (European Union, 2024).

Regarding the calving season, we tested two variants commonly found: calving at the end of winter/beginning of spring (calving month was set in March) and calving at the end of summer/beginning of autumn (calving month was set in September).

### 2.3.2. Demographic and animal nutrition constraints

We considered a static annual model assuming a farm and a herd at equilibrium, without a change in inventories. The demographic constraints are detailed in Fig. A1 in Appendix A.

Feed constraints were based on nutritional needs per animal type regarding energy and protein requirements (Eq. 13), and intake capacity (Eq. 14), based on the Inra, 2007 feeding system.

$$ \sum_{i}^{N} (\text{FQ}(\text{Feed}_i, \text{Animal}_i) \times \text{X}(\text{Feed}_i, \text{NutrInd}_k)) \geq \text{DNN}(\text{Animal}_i, \text{NutrInd}_k) \quad (13) $$

$$ \begin{aligned} 0.9 \times \text{IC}(\text{Animal}_i) & \leq \sum_{i}^{N} (\text{FQ}(\text{Feed}_i, \text{Animal}_i) \times \text{FV}(\text{Feed}_i)) \\ & \leq \text{IC}(\text{Animal}_i) \end{aligned} \quad (14) $$

where FQ is the daily feed quantity in kg per animal type and feed type, Feedi is the feed type, Animalj is the animal type, X is the feed value for

each feed type with respect to one of the feed indicators NutrIndk (i.e., energy or protein), DNN is the daily nutrition needs per animal type and feed indicator, FV is the fill value per feed type, and IC is the intake capacity per animal type.

Equations with regard to daily nutritional needs and intake capacities are derived from reference guides (Agabriel et al., 2014; Institut national de la recherche agronomique, 2007; Jarrige, 1989) and are detailed in Fig. A2 in Appendix A. We assumed that each animal type followed a fixed path regarding Average Daily Gain (ADG) (Table A3 in Appendix A). All rations were calculated to reach exactly the requirements for the specified ADGs and, thus, all animals of the same type were sold at the same weight in all optimisation models. Feed values were extracted from feed tables (Institut national de la recherche agronomique, 2007) (Table A4 in Appendix A).

We limited straw feed to a maximum of 5% of the total ration. For the concentrate feed, we set 10% of the total ration as the maximum for non-fattened animals and 60% for fattened animals. Furthermore, we set a minimum of concentrate feed for fattened animals during their fattening stage: 30% of the total ration for fattened heifers, fattened cull cows and heavy weanlings, and 50% for fattened young bulls. We introduced these constraints to be more in line with the recommendations of technical institutes (see, for example, the reference document of INOSYS Réseaux d'élevage by Alexandre et al. (2024)).

### 2.3.3. Agronomic and land constraints

Among the major regions for suckler cattle farming in France are the Massif Central, a mountainous region, and the Charolais region, a grassland area in the plain region (Perrot and Duflot, 2025). Therefore, we consider these two regions with different agronomic potentials, which we designate ‘mountain’ and ‘plain’. All forage feed (except straw) and triticaleOF were produced on the farm, whereas all concentrate feed (except triticaleOF) and straw were purchased. For on-farm-produced feed, yields depend on the region (see Table A1 in Appendix A).

The farm size was set to 100 ha, and all the produced feed was fed, i. e., no fallow land or crop sales. Except for straw, no additional forage feed could be purchased. All parcels could be used to produce corn silage, triticale or grassland as long as the production meets all the feed constraints. If a parcel was used as a grassland, it could be used for gazing only, for grazing and hay production, for grazing and silage production, or for grazing, hay and silage production. The idea of these assumptions is to determine the optimised feed ration at the herd level given an agronomic potential and not to produce a dynamic model where crop rotations are constrained. For both regions, we assumed that the average grazing season ranged from April to October (both months included).<fnref n="2" />

## 2.4. Determination of compromise solutions

To determine a compromise solution, we define the distance metric $L_p$ (Eq. 12) with respect to an ideal point, whose coordinates are the optimum values for the various objectives (each represented by a specific indicator). $L_p$ is a family of distances, called the Minkowski distances, with p varying from 1 to infinity. It is a measure of proximity that generalises the Euclidean distance (where p = 2). $L_1$ represents the longest metric, and $L_\infty$ represents the shortest metric, with all other metrics lying in between. The higher p is, the greater the weight given to the largest deviation (Romero and Rehman, 2003).

<footnote n="2">² This is a simplification because in reality pasture seasons differ between plain and mountain regions. However, this simplification should not substantially affect the results.</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 2. Types of animals raised (in regular characters) and sold (in bold characters).</figcaption></figure>

$$L_p = \left[ \sum_j^T W(Ind_j) \times \left| \frac{Ideal(Ind_j) - x(Ind_j)}{Ideal(Ind_j) - Anti\_ideal(Ind_j)} \right|^p \right]^{1/p} \quad (15)$$

where Ind_j is one of the indicators presented in Sections 2.1.1–2.1.3, Ideal is the optimised (ideal) value of a given indicator j, Anti_ideal is the worst value obtained by a given indicator in the single-objective optimisations, x is the value of a given indicator to be optimised for an efficient compromise solution, and W is the weight representing the importance of the difference between the value of a given indicator and its ideal value. We use distance functions with p equal to 1 and infinity, as these two metrics give the boundaries of the possible distance value. All the weights are set equal.

This leads to the following two compromise objective functions:

* Model ‘COMP’: minimising ‘L₁’

* Model ‘COMPINF’: minimising ‘L∞’

## 2.5. Implementation of the modelling approach

The modelling approach combining compromise programming with the bioeconomic model was run on the general algebraic modelling system mathematical modelling platform (GAMS Development Corporation, Washington, DC, USA) via nonlinear programming and solved with the CONOPT4 solver. When we ran the optimisations, the solver status returned the “Optimal solution. Reduced gradient less than tolerance,” which means that the “solution is a locally optimal interior solution” and that “the value of the objective function is very accurate while the values of the variables can be less accurate due to a flat objective function in the interior of the feasible area.”<fnref n="3" /> In other words, some combination of variables may give very similar values for the optimised indicators. For example, a large herd size with rather non-fattened animals may lead to similar indicator values than a smaller herd size with rather fattened animals because feed rations at the herd

level are similar. In these cases, the optimisation algorithm treats these combinations equally. To stabilise the results, we added a factor proportional to the livestock units and to the number of multiparous cows (set at a minimum of 30 for a uniform starting point) in the single-objective optimisation functions, inciting the algorithm to choose the variable combinations with a larger herd size without impacting the optimised indicator value.

## 3. Results

First, we put forward the conflicts between indicators within a performance dimension and between performance dimensions (Section 3.1). Then, we present the compromise solutions (Section 3.2). Because the results did not differ substantially between the calving seasons, i.e., the end of winter vs. the end of summer, we focused only on the calving season at the end of winter. The results of the calving season at the end of summer can be found in Appendix B.

### 3.1. Conflicting performances

In the model optimising for the feed margin in € (ECOEUR), the indicator feed margin ratio (42% in the plain region and 36% in the mountain region) is lower than its ideal value (ECORATIO) (59% in the plain region and 52% in the mountain region), and in the model optimising for the feed margin ratio (ECORATIO), the indicator feed margin in € (52 k€ in the plain region and 33 k€ in the mountain region) is also lower than its ideal value (ECOEUR) (62 k€ in the plain region and 36 k€ in the mountain region). Thus, optimising for feed margin and optimising for cost-effectiveness lead to conflicting results within the ECO performance dimension. The shortfall in euros that exists when the economic indicator is optimised as a ratio is greater when the agronomic potential is greater (Table 1). In terms of practices, optimising the feed margin ratio (in comparison with feed margin in €) leads to an extension of the system with respect to herd size and/or composition (i. e., fewer animals sold and/or fattened) and to feed rations (i.e., no corn silage and fewer concentrates) (Fig. 3).

With respect to the ENV performance dimension, there are fewer conflicts between the two ENV indicators—climate change impact and

<footnote n="3">³ https://www.gams.com/latest/docs/S_CONOPT4.html, accessed on May 6th, 2025.</footnote>
eutrophication—than between the two different functional units—kgc and ha—for the climate change impact indicator (Table 1). In terms of practices, optimising per ha (in comparison with kgc) leads to an extensification of the system with regard to herd size and/or composition (i.e., fewer animals sold and/or fattened). The minimisation of per ha indicators reduces inputs and animal production per ha. It is associated with a reduction in purchased feed (i.e., canola meals and straw) (Fig. 3). The minimisation of per kgc indicators increases animal production to reduce environmental impacts: fattening animals is a strategy that is optimal for minimising GHG emissions per kgc, and increasing herd size is optimal for minimising both eutrophication and climate change per kgc. Corn silage, grass silage and canola meal are introduced into the diet when optimising for climate change, whereas grass silage is preferred when optimising for eutrophication (Fig. 3).

When indicators belonging to different performance dimensions are compared, optimising for feed margin in € (ECOEUR) and for climate change impact per kgc (ENVCLIMKGC) lead to rather similar values for five out of the seven indicators. We also obtain similar patterns between optimising for the feed margin ratio (ECORATIO), for eutrophication (ENVEUTRKGC and ENVEUTRHA), and for climate change per ha (ENVCLIMHA). In contrast, there is a clear conflict between ECO and AW optimisation, as well as between ENV/kgc and AW optimisation (Table 1). With respect to practices, AW optimisation favours preserved forage where nutritional requirements are met with the least surface area to maximise grazing (given that the total surface area is limited), i.e., corn silage, and it privileges animals that are not fattened. Feeding animals not yet fattened with a high proportion of corn silage is, however, economically and environmentally less attractive than feeding

them with a mainly grass-based ration.

In brief, the different optimisations lead to more or less intensive production systems in terms of the stocking rate, herd composition (animals sold not yet fattened versus fattened), and off-grazing ration (grass-based versus corn silage/concentrates) (Fig. 4).

## 3.2. Compromise solutions

The values of the two compromise solutions for the seven indicators are similar. Compared with the ideal values obtained with the single-objective optimisation models, the compromise solutions generate foregone feed margins of approximately 20% in the plain region and approximately 15% in the mountain region (Table 1). With respect to practices, the two compromise solutions differ, but they have in common that they both sell a mix of not yet fattened and fattened animals (not fattened males & fattened females or fattened males & not fattened females) and/or have lower stocking rates than the ECOEUR optimisation does. The ratios rely less on corn silage and concentrate feed than do the intensive systems proposed by the ECOEUR and ENVCLIMKGC optimisations (Fig. 3). Overall, the compromise solutions are most similar to the results obtained through the ECORATIO, ENVCLIMHA and ENVEUTRHA optimisations (Fig. 4).

## 4. Discussion

In this work, on French suckler cattle farms, we constructed a bio-economic model that links economic, environmental and animal welfare performance indicators to variables impacting feeding (i.e. ration, herd

<caption>**Table 1**</caption>

Indicator values in each single-objective optimisation model (columns) for the calving season at the end of winter in the mountain (A) and plain (B) regions. COMP and COMPINF are models that optimise a compromise solution, and the other models optimise the indicator with the same number (1–7). Heatmap colours are set for each row, with dark green representing ideal values and dark red representing anti-ideal values for each indicator.

### OPTIMISATION MODELS

<table><thead><tr><th rowspan="3"></th><th rowspan="3">INDICATORS</th><th rowspan="3">UNITS</th><th colspan="2">ECO</th><th colspan="4">ENV</th><th rowspan="3">BEA</th><th rowspan="3">COMP p=1</th><th rowspan="3">COMPINF p=inf</th></tr><tr><th>€</th><th>RATIO</th><th colspan="2">CLIM</th><th colspan="2">EUTR</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th></tr></thead><tbody><tr><td rowspan="7">(A)</td><td>1. Feed margin</td><td>1 000 €</td><td>36</td><td>33</td><td>32</td><td>23</td><td>32</td><td>29</td><td>22</td><td>29</td><td>31</td></tr><tr><td>2. Feed margin</td><td>%</td><td>36</td><td>52</td><td>34</td><td>45</td><td>34</td><td>47</td><td>29</td><td>47</td><td>45</td></tr><tr><td>3. Climate impact</td><td>kg CO2 eq/kgc</td><td>21</td><td>22</td><td>19</td><td>25</td><td>19</td><td>23</td><td>26</td><td>23</td><td>21</td></tr><tr><td>4. Climate impact</td><td>100 kg CO2 eq/ha</td><td>43</td><td>34</td><td>42</td><td>31</td><td>41</td><td>33</td><td>43</td><td>33</td><td>35</td></tr><tr><td>5. Eutrophication</td><td>kg P eq/10<sup>4</sup> kgc</td><td>17</td><td>12</td><td>11</td><td>14</td><td>10</td><td>10</td><td>20</td><td>12</td><td>13</td></tr><tr><td>6. Eutrophication</td><td>kg P eq/100 ha</td><td>34</td><td>18</td><td>23</td><td>17</td><td>22</td><td>15</td><td>34</td><td>17</td><td>21</td></tr><tr><td>7. Grazing time</td><td>% of year</td><td>47</td><td>50</td><td>46</td><td>56</td><td>46</td><td>54</td><td>56</td><td>55</td><td>53</td></tr><tr><td rowspan="7">(B)</td><td>1. Feed margin</td><td>1 000 €</td><td>62</td><td>52</td><td>58</td><td>36</td><td>48</td><td>46</td><td>40</td><td>49</td><td>49</td></tr><tr><td>2. Feed margin</td><td>%</td><td>42</td><td>59</td><td>40</td><td>52</td><td>47</td><td>53</td><td>39</td><td>58</td><td>53</td></tr><tr><td>3. Climate impact</td><td>kg CO2 eq/kgc</td><td>21</td><td>22</td><td>19</td><td>27</td><td>22</td><td>23</td><td>27</td><td>23</td><td>23</td></tr><tr><td>4. Climate impact</td><td>100 kg CO2 eq/ha</td><td>61</td><td>47</td><td>61</td><td>43</td><td>53</td><td>46</td><td>58</td><td>45</td><td>51</td></tr><tr><td>5. Eutrophication</td><td>kg P eq/10<sup>4</sup> kgc</td><td>17</td><td>11</td><td>13</td><td>15</td><td>10</td><td>10</td><td>20</td><td>11</td><td>12</td></tr><tr><td>6. Eutrophication</td><td>kg P eq/100 ha</td><td>49</td><td>24</td><td>42</td><td>24</td><td>23</td><td>21</td><td>43</td><td>22</td><td>26</td></tr><tr><td>7. Grazing time</td><td>% of year</td><td>39</td><td>51</td><td>46</td><td>59</td><td>47</td><td>54</td><td>59</td><td>53</td><td>49</td></tr></tbody></table>

Optimisation models: compromise solutions with 2 different distance metrics defined by the parameter p ('COMP' & 'COMPINF'), maximisation of feed margin in € ('ECOEUR'), maximisation of feed margin ratio ('ECORATIO'), minimisation of climate change impacts per kgc ('ENVCLIMKGC') and per ha of land used ('ENVCLIMHA'), minimisation of eutrophication per kgc ('ENVEUTRKGC') and per hectare of land used ('ENVEUTRHA'), maximisation of grazing time as an animal welfare proxy ('AW').
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Animals sold (upper graph) and feed rations (lower graph) at the herd level for a farm of 100 ha in each optimisation model (rows) with respect to two regions – mountain and plain – for the calving season end of winter. The values in brackets are the average livestock units at the farm.</figcaption></figure>

Optimisation models: compromise solutions with 2 different distance metrics defined by the parameter *p* ('COMP' & 'COMPINF'), maximisation of feed margin in € ('ECOEUR'), maximisation of feed margin ratio ('ECORATIO'), minimisation of climate change impacts per kgc ('ENVCLIMKGC') and per ha of land used ('ENVCLIMHA'), minimisation of eutrophication per kgc ('ENVEUTRKGC') and per hectare of land used ('ENVEUTRHA'), maximisation of grazing time as an animal welfare proxy ('AW').
<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Approximate positioning with respect to herd size/composition (i.e., stocking rate, types of animals sold) and the off-grazing feed ration of the different optimisation models.</figcaption></figure>

Optimisation models: compromise solutions with 2 different distance metrics defined by the parameter p ('COMP' & 'COMPINF'), maximisation of feed margin in € ('ECOEUR'), maximisation of feed margin ratio ('ECORATIO'), minimisation of climate change impacts per kgc ('ENVCLIMKGC') and per ha of land used ('ENVCLIMHA'), minimisation of eutrophication per kgc ('ENVEUTRKGC') and per hectare of land used ('ENVEUTRHA'), maximisation of grazing time as an animal welfare proxy ('AW').

size and composition, and calving period). We then optimised these practices according to each of these indicators, as well as according to a compromise objective. We found that 1) conflicts exist between indicators within the same performance dimensions (e.g., feed margin versus cost-effectiveness for economic performance, indicators expressed per kgc versus ha for environmental performance), 2) conflicts exist between different performance dimensions (e.g., maximising grazing time vs. feed margin), 3) compromise solutions allow substantial improvements in environmental and animal welfare performance compared with feed margin-driven optimisation with foregone feed margins of approximately 15% of the optimum values, and 4) the different optimisations lead to more or less intensive production systems in terms of the stocking rate, herd composition and ration.

## 4.1. Consistency of indicator values

In this section, we discuss whether the constructed models yield consistent results regarding the values of the performance indicators. For the economic indicators, the results obtained can be compared to the average values of the French DIAPASON database managed by INOSYS Réseaux d'élevage, a livestock network operated by the French Livestock Institute and French Chambers of Agriculture (Institut de l'Elevage et Chambres d'Agriculture, 2014). In DIAPASON, the adjusted feed margin<fnref n="4" /> averages in 2021 (the year chosen as the reference in our study) were 64 k€ for the farms located in plain regions and 33 k€ for those located in moderate-mountainous regions. In the model optimising for the feed margin in €, which assumes that farmers act as homo economicus, the feed margin was 62 k€ for the plain region and 36 k€ in the mountain region. Thus, the results are very close to the averages reported in DIAPASON. With respect to the feed margin ratio indicator, those obtained in the model optimising for the feed margin in €—42% for the plain region and 36% for the mountain region—are slightly higher than the averages of 37% for the plain region and 34% for the moderate-mountainous region in DIAPASON.

With respect to the climate change indicator, the net global warming potential (GWP) is estimated to be approximately 18 CO₂ eq/kgc for beef production systems in Berton et al. (2017) and between 27 and 33 CO₂ eq/kgc for cull cows of conventional suckler cow systems in AGRIBALYSE (version 3.1.1). The values in our models range from 19 to

27 kg CO₂ eq/kgc. Other studies report GWP values that do not consider carbon sequestration: GWPs are between 11 and 25 kg CO₂ eq/kgc in De Vries and De Boer (2010) and between 22 and 32 CO₂ eq/kgc in Taylor et al. (2020).<fnref n="5" /> These large variations reported in the literature may result from differences in the calculation methods used and may also reflect differences in beef production systems. With respect to the freshwater eutrophication indicator for beef production systems, assuming a conversion factor of 0.55 from liveweight to carcass weight, the values are between 9 and 16 kg P eq/10⁴ kgc for cull cows of conventional suckler cow systems in AGRIBALYSE (version 3.1.1). The values in our models range from 10 to 20 kg P eq/10⁴ kgc.

In terms of average grazing time, the estimated proportion of grazed feed to total forage, which can serve as a proxy for grazing time, ranges from 49 to 57% for the DIAPASON sample described at the beginning of this section. The values in our models range from 44 to 60%.

From the comparisons above, we can conclude that our models give realistic values for the various indicators used.

## 4.2. Trade-offs and compromise solutions

This section discusses the results of the compromise programming approach, which revealed conflicts between different performance dimensions. The negative relationship between economic performance and environmental performance was clearly demonstrated in previous studies for various environmental indicators, such as GES, erosion, N-leaching and biodiversity (Bamière et al., 2023; Kennedy et al., 2016; Klein et al., 2013; Mosnier et al., 2019). Our study also made clear that conflicts exist within a performance dimension: Optimising for eutrophication and for climate change impact showed conflicting outcomes. This type of intra-dimension conflicts was observed in other studies. For instance, trade-offs between biodiversity and freshwater quality were detected when optimising land use in Brazil (Kennedy et al., 2016).

In our study, the choice of functional unit had a greater impact on the discord between environmental indicators than the type of environmental impact addressed. The models optimising environmental indicators per hectare led to less intensive systems in terms of feed rations and animal sales strategies than those expressed per kgc produced. This is in line with the general observation that farms that are more intensive in terms of productivity per animal—which is the case for fattening farms whose diet relies on concentrate feed—have better environmental performance per kgc produced, whereas extensive farms have better performance per hectare of land used (Joly et al., 2024; Van Der Werf et al., 2020). The results may also be affected by the type of production-related metric used. In Doyle et al. (2023), opting for GHG emissions per net human edible food privileged a forage-only production system while opting for GHG emissions per animal, meat weight gain or per essential amino acids gain privileged systems relying on concentrates.

The choice of metrics is thus crucial. The question that arises is which functional units make the most sense. The answer depends on the objectives pursued. For example, if the objective is to produce a specific quantity of meat (e.g., driven by demand), the functional unit to be prioritised is the quantity of meat produced. However, when the objective is to ensure sufficient edible proteins (Bang et al., 2025), no matter the product (meat, milk, crop, ...), or to not to exceed certain environmental impact thresholds per hectare, the quantity of meat produced becomes the adjustable variable. The choice of objectives will have an impact on the degree of intensification of the resulting system.

The choice between absolute and relative values for indicators will also affect results. Optimising for cost-effectiveness enables the simultaneous achievement of rather good performance in all indicators. In our model optimising for feed margin ratio to revenues, the ration is

<footnote n="4">⁴ The adjusted feed margin was calculated as: animal sales revenues (minus the costs of purchased animals) minus feed and mechanisation costs stemming from beef cattle, scaled to a farm of 100 ha.</footnote>

<footnote n="5">⁵ As the references use different functional units, we assume the following conversion factors: 0.55 from liveweight to carcass weight, 0.43 from liveweight to edible product.</footnote>
mainly grass-based, and the sales strategy consists of not fattening male animals; this is in accordance with the findings of Mysko et al. (2024), where suckler farms with the highest cost-effectiveness rely principally on grass-based feed and sell preferably not yet fattened animals. Choosing an economic indicator in the form of a ratio (as in Mysko et al., 2024) favours synergies between performance dimensions. Although choosing feed margin leads to more conflicts with environmental and animal welfare objectives, “small loss-big gain opportunities” (Kennedy et al., 2016) are nonetheless possible. Depending on the farm circumstances (e.g. agronomic potential), a forgone feed margin of less than 15% can lead to a reduction of eutrophication per ha of almost 40% in our study. It is still necessary to verify whether the changes in absolute values have a substantial effect.

Although reducing environmental impact comes at a cost (Bamière et al., 2023; Mosnier et al., 2019), practices exist that positively impact economic and environmental indicators. In Bang et al. (2025), increased animal production can simultaneously improve gross margin and GHG emissions expressed per different production units (e.g. protein, beef). This is in line with our results where the models optimising for feed margin and for climate change impacts per kgc give similar results.

Despite the bioeconomic model being simplified, the proposed approach highlights potential pitfalls in interpretation arising from choices relating to indicators, functional units and absolute versus relative values. For instance, it may give insights into the ambiguous results in the literature regarding recommendations of intensification versus extensification to achieve sustainability. This makes the rationale behind decisions regarding the implementation of practices more transparent.

### 4.3. Relevance and limitations of the optimising approach

In this section, we discuss the benefits and drawbacks of the modelling approach we chose. One advantage of the compromise programming approach used is that it allows one to see how far each single-objective optimisation is from the attainable ideal value of all considered indicators. The weighting of the various indicators in the distance function has an effect on the compromise solution. Privileging some performance indicators more than others would lead to intermediate results between those of the compromise identified in the present paper (where weights are the same for all indicators) and those of the optimisation according to the preferred performance indicators. Thus, in a compromise programming approach, determining the weights is not essential for drawing conclusions about managing trade-offs between several performance dimensions, because the stepwise construction — first the ideal solution for each objective, then the compromise solution — makes the trade-offs transparent. In contrast, methods that aim to optimise a composite indicator that integrates the different performance dimensions into one value are more sensitive to the choice of weights and raise questions about compensation between indicators, leading to solutions that are regarded as not always satisfying the idea of sustainability (Mosnier et al., 2023).

Furthermore, the compromise programming approach does not necessitate specifying targets, as in the case for goal programming. Although multi-objective programming does not explicitly require such a specification, in practice, the approach needs criteria to select among the large number of optimum solutions (Klein et al., 2013). Determining additional parameters may introduce uncertainty into the results.

In addition to multi-objective optimisations, there are other approaches for determining compromise solutions. For example, models optimising for profit might include increasing taxes on environmental impacts in their profit definition and, thus, explore different cost-effective impact abatement strategies. This was done in a study comparing four bioeconomic models integrating a carbon tax to mitigate GHG emissions (Mosnier et al., 2019). Another approach is to calculate the impact abatements for a set of practices and to calculate the implementation costs (Bamière et al., 2023). These approaches,

however, do not permit the identification of the magnitude of conflicts in the presence of several performance indicators as is the case for compromise programming.

The approach used in this study nevertheless has shortcomings. The indicators chosen only partially cover the three performance concepts. In terms of economic performance, the study is limited to livestock sales revenues and feed costs. Costs related to labour (other than for feed production) and housing are not included. These omissions may overestimate the benefits of fattening, which requires more housing capacity and labour than grazing animals do. In terms of environmental performance, only climate change impacts and eutrophication were considered. We did not include phosphorus consumption, non-renewable fossil and nuclear energy, acidification, or land competition. Furthermore, in addition to negative impacts, one should consider the ecosystem services and the impacts on biodiversity provided by different production systems; such a consideration would favour less intensive agroecological systems, which are misrepresented in current LCA studies (Van Der Werf et al., 2020). In this respect, cattle grazing systems appear to have favourable characteristics (Joly et al., 2024). Thus, the environmental impact per kgc would improve for cattle relative to other production systems, such as intensive poultry and pig systems. Choosing these indicators of positive environmental impacts as optimisation objectives would most likely favour extensive systems for both functional units (ha and kgc).

In terms of animal welfare, grazing is the only indicator used in the welfare objective function and good feeding management is considered in the model constraints. Access to outdoor is of particular importance to improve animal welfare, e.g. it has more impact than improving indoor housing (Palacio et al., 2023). In addition, in a previous study, we found that cattle farms that prioritised grazing also obtained better results for other welfare indicators related to health (calf and other animals' mortality, pregnancy rate) and housing (comfort inferred from building costs) (Mysko et al., 2024). Despite this pivotal role of grazing in the welfare of ruminants, we acknowledge that considering the conditions in which animals are maintained indoors during the season when grazing is not possible, would strengthen our analysis.

Further, we considered some decision variables as fixed, such as yield, production life of cows, age at first calving and age at slaughter. These variables are cited as economic-climatic win-win strategies (Bang et al., 2025). However, increased efficiency due to yield improvement, which shortens the time to slaughter for a specific target weight, has its limits. Breeding goals based solely on growth performance have been shown to lead to health issues (e.g., fertility problems) and animal welfare concerns (Van Marle-Köster and Visser, 2021). Furthermore, Bang et al. (2025) demonstrate that the effectiveness of these practices depends heavily on the operational circumstances of farms, such as land availability, stall capacity, production restrictions (e.g., quotas) and government payments. Progress at the animal level (e.g., genetics, feed efficiency) over the last decades has also not, on average, translated into improvements in the efficiencies of farm systems (Veysset et al., 2015).

## 5. Conclusion

This study investigated possible conflicts between the competing objectives of economic, environmental and animal welfare performance on suckler cattle farms. The trade-offs shown in this paper demonstrate that if farmers act as *homo economicus* and optimise feed margin only, important opportunities for improving the environment and animal welfare at low cost may be missed. In contrast, if economic objectives are ignored when optimising for environmental and animal welfare objectives, the farms may not be able to stay in business due to their low economic performance. The compromise solutions presented here show that, compared with feed margin-driven optimisation, environmental and animal welfare performance can be substantially enhanced, with foregone feed margins of approximately 15% of the optimum values. This is achieved by reducing herd size and animal fattening, increasing
the share of grassland in farmland and reducing the purchase of concentrate feed. Our study did not consider possible efficiency improvements that could have induced more synergies between economic and environmental performance. However, efficiency improvements related to better growth performance should be approached with caution, as beyond a certain level, they are likely to deteriorate animal welfare.

The question of who pays the costs of compromise solutions is crucial. Farmers express doubts about taxpayers' willingness to pay for the public goods they expect from agriculture, such as environmental and animal welfare performance (Cusworth and Dodsworth, 2021). The adoption of compromise solutions is therefore highly dependent on political will. Further studies should explore the best ways to incentivise farmers to adopt strategies that go beyond the economic considerations inherent in the production process and improve performance in terms of environmental and animal welfare indicators. In addition, this work could be extended with compromise-risk programming to reduce the risk and uncertainty of the models (Romero et al., 1988).

Another question concerns the generalisability of our results. The models in our study provide an optimised solution for a specific objective within a particular context. It is worth noting that, breeders will be unable to adapt instantaneously if the context changes. For instance, housing is designed for a specific number of animals. Consequently, only marginal changes to the number of livestock are possible in the short term. Nevertheless, exploring the validity of the models under different soil and climate conditions, as well as the effect of domestic and international markets on the robustness of the solutions they generate, would be important.

Another extension of this work could involve investigating other types of livestock farming besides suckler cattle, such as dairy farming and monogastric animal farming. The environmental and animal welfare issues are likely to be even more centred on feed for these types of farming.

## Funding agency

This work was supported by the metaprogramme "SANté et Bien-être des Animaux en élevage" (SANBA) of INRAE; and the international research centre on sustainable agroecosystems IRC-SAE of 16-IDEX-0001 (CAP 20-25).

## Credit authorship contribution statement

**Larissa Mysko:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Project administration, Methodology, Formal analysis, Conceptualization. **Claire Mosnier:** Writing – review & editing, Validation, Software, Methodology, Conceptualization. **Patrick Veysset:** Writing – review & editing, Writing – original draft, Supervision, Conceptualization. **Isabelle Veissier:** Writing – review & editing, Writing – original draft, Supervision, Funding acquisition, Conceptualization. **Jean-Joseph Minviel:** Writing – review & editing, Writing – original draft, Supervision, Methodology, Funding acquisition, Conceptualization.

## Declaration of competing interest

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.

## Acknowledgements

The authors thank the French Livestock Institute and French Chambers of Agriculture for kindly allowing us access to their data collected via the *Dispositif INOSYS Réseaux d'élevage* (Institut de l'Elevage/Chambres d'Agriculture), as well as American Journal Experts for English-language proof-editing support.

# Appendix A. Appendix

<caption>Table A1</caption>

Production yields and costs for on-farm produced feed and prices for purchased feed as of 2021 (Bouchard et al., 2023).

<table><thead><tr><th rowspan="3">Feed type</th><th colspan="2">Yield</th><th colspan="2">Production cost</th><th rowspan="3">Purchase price<br>(in €/t)</th></tr><tr><th colspan="2">(in tDM/ha)</th><th colspan="2">(in €/tDM)</th></tr><tr><th>Mountain</th><th>Plain</th><th>Mountain</th><th>Plain</th></tr></thead><tbody><tr><td>Grass</td><td>5.0</td><td>7.0</td><td>36</td><td>29</td><td></td></tr><tr><td>Grass & hay</td><td>5.0</td><td>7.0</td><td>124</td><td>97</td><td></td></tr><tr><td>Grass</td><td>1.0</td><td>2.0</td><td>50</td><td>27</td><td></td></tr><tr><td>Hay</td><td>4.0</td><td>5.0</td><td>74</td><td>70</td><td></td></tr><tr><td>Grass & grass silage</td><td>5.0</td><td>7.0</td><td>140</td><td>116</td><td></td></tr><tr><td>Grass</td><td>1.5</td><td>2.5</td><td>39</td><td>27</td><td></td></tr><tr><td>Grass silage</td><td>3.5</td><td>4.5</td><td>101</td><td>89</td><td></td></tr><tr><td>Corn silage</td><td>8.0</td><td>12.0</td><td>121</td><td>93</td><td></td></tr><tr><td>Straw</td><td>2.4</td><td>3.6</td><td>0</td><td>0</td><td>50</td></tr><tr><td>Triticale</td><td>4.0</td><td>6.0</td><td>210</td><td>177</td><td>230</td></tr><tr><td>Canola meal</td><td>-</td><td>-</td><td>-</td><td>-</td><td>300</td></tr><tr><td>Soybean meal</td><td>-</td><td>-</td><td>-</td><td>-</td><td>400</td></tr></tbody></table>
<table><caption>**Table A2**
Environmental impact values (AGRIBALYSE).</caption><thead><tr><th>Feed type</th><th>Feed description</th><th>Climate change impact</th><th>Freshwater eutrophication</th></tr></thead><tbody><tr><td>Grass</td><td>Grazed grass, permanent meadow, without clover, Auvergne, on field</td><td>-0.051691</td><td>0.000021</td></tr><tr><td>Hay</td><td>Baled hay, permanent meadow, without clover, Auvergne, at farm</td><td>0.117577</td><td>0.000036</td></tr><tr><td>Grass silage</td><td>Grass silage, horizontal silo, permanent meadow, without clover, Auvergne, at farm</td><td>0.162630</td><td>0.000037</td></tr><tr><td>Corn silage</td><td>Silage maize, conventional, France, at field</td><td>0.233676</td><td>0.000083</td></tr><tr><td>Straw</td><td>Triticale straw, France, at field</td><td>0.061331</td><td>0.000005</td></tr><tr><td>TriticaleOF</td><td>Triticale grain, conventional, France, at field</td><td>0.613453</td><td>0.000195</td></tr><tr><td>Tritiale</td><td>Triticale grain, conventional, France, at storage agency</td><td>0.624232</td><td>0.000196</td></tr><tr><td>Canola meal</td><td>Rapeseed meal, France, at plant</td><td>0.437539</td><td>0.000116</td></tr><tr><td>Soybean meal</td><td>Soybean meal, Brazil, average deforestation, crushing in France, at plant</td><td>2.596390</td><td>0.000824</td></tr></tbody></table>

**For the female track:**

The calves are sold at 9 months as weanlings ('calfFW') or remain in the herd ('calfFH') to become heifers (Eq. 1). The male proportion of total births ('SEXRATIO') is set to 0.5 and the numerical productivity, i.e., the number of calves alive per cow per year, ('NUMPROD') to 0.9.

$$N('calf\_FW') + N('calf\_FH') = NUMPROD \times (1 - SEXRATIO) \times (N('multipare') + N('primipare')) \quad (1)$$

The heifers aged 1 to <2 years are sold at 18 months as heifers to be fattened ('heifer_NF') or remain in the herd ('heifer_1') (Eq. 2).

$$N('calf\_FH') = N('heifer\_NF') + N('heifer\_1') \quad (2)$$

The heifers aged 2 to <3 years are sold at 28 months as fattened heifers ('heifer_F') or remain in the herd to become heifers for renewal ('heifer_renew') (Eq. 3).

$$N('heifer\_1') = N('heifer\_F') + N('heifer\_renew') \quad (3)$$

First calving occurs at 36 month and, thus, primiparous cows are aged 3 to < 4 years ('primipare') (Eq. 4) and replace cull cows that are sold either to be fattened ('cull_NF') or fattened ('cull_F') (Eq. 5).

$$N('heifer\_renew') = N('primipare') \quad (4)$$

$$N('cull\_NF') + N('cull\_F') = N('primipare') \quad (5)$$

Renewal rate ('RENEW') of cows was set at 0.2, corresponding to an average between what is commonly used for a hardy and a high-performing breed (Eq. 6).

$$N('cull\_NF') + N('cull\_F') = RENEW * (N('multipare') + N('primipare')) \quad (6)$$

**For the male track:**

The calves are sold at 9 months as lean weanlings ('calf_MWL'), as heavy weanlings ('calf_MWH') or remain in the herd as lean ('calf_ML') or heavy ('calf_MH') weanlings (Eq. 7).

$$\begin{aligned} N('calf\_ML') + N('calf\_MH') + N('calf\_MWL') + N('calf\_MWH') \\ = NUMPROD \times SEXRATIO \times (N('multipare') + N('primipare')) \end{aligned} \quad (7)$$

Lean weanlings become young bulls sold at 14 months to be fattened ('youngbull_NF') (Eq. 8) and heavy weanlings become fattened young bulls sold at 18 months ('youngbull_F') (Eq. 9).

$$N('calf\_ML') = N('youngbull\_NF') \quad (8)$$

$$N('calf\_MH') = N('youngbull\_F') \quad (9)$$

<caption>**Fig. A1.** Demographic constraints to maintain constant herd inventories.</caption>
For heifers not to be fattened/for renewal:

$$DNN\_UFL(maintenance) = (0.024 + 0.0454 \times \left(\frac{ADG}{1000}\right)^{1.4}) \times LW^{0.75}$$

$$DNN\_PDI(maintenance) = DNN\_UFL(maintenance) \times 90 \qquad IC\_FU = I_{type} \times LW^{0.9}$$

For cows (primiparous and multiparous):

$$DNN\_UFL(maintenance) = [(I_s \times I_a) + (0.0068 \times (BCS - 2.5))] \times LW^{0.75} \quad DNN\_UFL(milk) = 0.45 \times MilkProd$$

$$DNN\_UFL(gain) = 1 \text{ for primiparous and 0 otherwise} \qquad DNN\_UFL(pregnancy) = \frac{DNN\_PDI(pregnancy)}{90}$$

$$DNN\_PDI(maintenance) = 3.25 \times LW^{0.75} \qquad DNN\_PDI(pregnancy) = 0.07 \times LWC \times e^{0.111 \times PregWeek}$$

$$DNN\_PDI(gain) = 90 \times UFV(gain) \qquad DNN\_PDI(milk) = 53 \times MilkProd \qquad IC\_FU = I_{IC} \times \frac{LW}{100}$$

For calves, weanlings, heifers to be fattened and young bulls:

$$DNN\_UFV(maintenance) = MF \times 0.549 \times 0.834 \times I_a \times LW^{0.75} \qquad DNN\_UFV(gain) = g1 \times \frac{ADG}{1000} + g2$$

$$DNN\_PDI(maintenance) = 3.25 \times LW^{0.75} \qquad DNN\_PDI(gain) = d1 \times \frac{ADG}{1000} + d2 \qquad IC\_FU = a \times LW^{b}$$

For fattened culled cows:

$$DNN\_UFV(maintenance and gain) = (g1 \times \frac{ADG}{1000} + g2 + g3 \times BCS + g4 \times LW) \times 0.996$$

$$DNN\_PDI(maintenance and gain) = 0.9 \times DNN\_UFV(maintenance and gain) \qquad IC\_FU = a \times LW^{b}$$

Where ADG is the average daily gain in g, LW the liveweight in kg, Itype is 0.0346 for Charolais and hardy breeds, Is depends on the physiological stage (0.041 for suckling stage, 0.037 otherwise), Ia depends on the activity (1.1 for loose house, 1.2 for pasture), BCS is the body condition score target, MilkProd is the average daily milk production in kg during the suckling stage (for Charolais: 7.2 for multiparous, 6.4 for primiparous), LWC is the expected calf liveweight at birth, PregWeek is the week of pregnancy, IIC depends on the physiological stage (for pregnancy stage: 1.9 for multiparous and 1.8 for primiparous, for suckling stage: 2.1 for multiparous, 2.0 for primiparous, MF is the maintenance factor (which varies from 0.075 to 0.102 depending on the animal type), 0.549 is the conversion rate from Mcalories to UFV and 0.834 is the conversion rate from net energy for maintenance to UFV, Is depends on the activity (1 for tie-stall, 1.1 for loose house, 1.2 for pasture), g1, g2, g3, g4, d1, and d2 are factors depending on liveweight and animal type, a and b are factors depending on animal type. 0.996 is a factor for medium frame size.

**Fig. A2.** Daily nutrition needs (DNN) with regard to energy (expressed in UFV – a feed unit for lactation – or UFV – a feed unit for maintenance and meat production –) and protein (expressed in PDI – gram of protein digested in the small intestine –) requirements and intake capacity (IC) (expressed in FU – a fill unit –).
<caption>**Table A3**</caption>

Assumed yearly beginning liveweight and monthly Average Daily Gains (ADG) for the calving season at the end of winter (upper table) and at the end of summer (lower table).

<table><thead><tr><th rowspan="3">Animal type</th><th>Liveweight</th><th colspan="14">Average Daily Gain (ADQ) in g</th></tr><tr><th>in kg</th><th colspan="12">months</th></tr><tr><th>Mar</th><th>Mar</th><th>Apr</th><th>May</th><th>Jun</th><th>Jul</th><th>Aug</th><th>Sep</th><th>Oct</th><th>Nov</th><th>Dec</th><th>Jan</th><th>Feb</th></tr></thead><tbody><tr><td>calf_FH</td><td>45</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>600</td><td>600</td><td>600</td><td>600</td></tr><tr><td>calf_ML</td><td>45</td><td>1000</td><td>1000</td><td>1000</td><td>1000</td><td>1000</td><td>1000</td><td>1000</td><td>1000</td><td>720</td><td>720</td><td>720</td><td>720</td></tr><tr><td>calf_MH</td><td>45</td><td>1130</td><td>1139</td><td>1139</td><td>1139</td><td>1374</td><td>1374</td><td>1374</td><td>1130</td><td>1130</td><td>1130</td><td>1500</td><td>1500</td></tr><tr><td>calf_FW</td><td>45</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>600</td><td>sold</td><td></td><td></td></tr><tr><td>calf_MWL</td><td>45</td><td>1000</td><td>1000</td><td>1000</td><td>1000</td><td>1000</td><td>1000</td><td>1000</td><td>1000</td><td>720</td><td>sold</td><td></td><td></td></tr><tr><td>calf_MWH</td><td>45</td><td>1130</td><td>1139</td><td>1139</td><td>1139</td><td>1374</td><td>1374</td><td>1374</td><td>1130</td><td>1130</td><td>sold</td><td></td><td></td></tr><tr><td>heifer_1</td><td>374</td><td>900</td><td>900</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td></tr><tr><td>heifer_renew</td><td>541</td><td>1050</td><td>1050</td><td>500</td><td>500</td><td>500</td><td>500</td><td>500</td><td>500</td><td>500</td><td>500</td><td>700</td><td>700</td></tr><tr><td>youngbull_NF</td><td>376</td><td>720</td><td>720</td><td>535</td><td>535</td><td>535</td><td>535</td><td>535</td><td>535</td><td>535</td><td>420</td><td>420</td><td>420</td></tr><tr><td>youngbull_F</td><td>503</td><td>1500</td><td>1500</td><td>1500</td><td>1387</td><td>1330</td><td>1330</td><td>1374</td><td>1374</td><td>1374</td><td>1374</td><td>1374</td><td>1374</td></tr><tr><td>heifer_NF</td><td>374</td><td>900</td><td>900</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td><td>400</td></tr><tr><td>heifer_F</td><td>541</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td></tr><tr><td>cull_NF</td><td>700</td><td>sold</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>cull_F</td><td>750</td><td>1000</td><td>1000</td><td>1000</td><td>sold</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>primipare*</td><td>675</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>multipare</td><td>750</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table><table><thead><tr><th rowspan="3"></th><th>months</th><th>Sep</th><th>Oct</th><th>Nov</th><th>Dec</th><th>Jan</th><th>Feb</th><th>Mar</th><th>Apr</th><th>May</th><th>Jun</th><th>Jul</th><th>Aug</th></tr></thead><tbody><tr><td>calf_FH</td><td>45</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>550</td><td>550</td><td>550</td><td>550</td></tr><tr><td>calf_ML</td><td>45</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>600</td><td>650</td><td>650</td></tr><tr><td>calf_MH</td><td>45</td><td>1130</td><td>1139</td><td>1139</td><td>1139</td><td>1374</td><td>1374</td><td>1374</td><td>1130</td><td>1130</td><td>1130</td><td>1500</td></tr><tr><td>calf_FW</td><td>45</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>550</td><td>sold</td><td></td></tr><tr><td>calf_MWL</td><td>45</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>1050</td><td>sold</td><td></td></tr><tr><td>calf_MWH</td><td>45</td><td>1130</td><td>1139</td><td>1139</td><td>1139</td><td>1374</td><td>1374</td><td>1374</td><td>1130</td><td>1130</td><td>sold</td><td></td></tr><tr><td>heifer_1</td><td>368</td><td>550</td><td>550</td><td>550</td><td>550</td><td>550</td><td>550</td><td>950</td><td>950</td><td>400</td><td>400</td><td>400</td></tr><tr><td>heifer_renew</td><td>565</td><td>400</td><td>400</td><td>400</td><td>600</td><td>350</td><td>350</td><td>350</td><td>950</td><td>950</td><td>700</td><td>700</td></tr><tr><td>youngbull_NF</td><td>391</td><td>650</td><td>650</td><td>650</td><td>650</td><td>570</td><td>570</td><td>570</td><td>570</td><td>570</td><td>570</td><td>700</td></tr><tr><td>youngbull_F</td><td>503</td><td>1500</td><td>1500</td><td>1500</td><td>1387</td><td>1330</td><td>1330</td><td>1374</td><td>1374</td><td>1374</td><td>1374</td><td>1374</td></tr><tr><td>heifer_NF</td><td>368</td><td>550</td><td>550</td><td>550</td><td>550</td><td>550</td><td>550</td><td>950</td><td>950</td><td>400</td><td>400</td><td>400</td></tr><tr><td>heifer_F</td><td>565</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td><td>1220</td></tr><tr><td>cull_NF</td><td>700</td><td>sold</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>cull_F</td><td>765</td><td>1000</td><td>1000</td><td>1000</td><td>sold</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>primipare*</td><td>689</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>multipare</td><td>765</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

<footnote>* For primiparous cows, nutrition needs for weight gains related to growth are considered in the nutrition need equations.</footnote>
<table><caption>**Table A4**
Feed values (Institut national de la recherche agronomique, 2007).</caption><thead><tr><th rowspan="2">Feed type</th><th rowspan="2">Reference</th><th colspan="2">Energy</th><th>Protein</th><th>Intake capacity</th><th>Dry matter</th></tr><tr><th>UFL</th><th>UFV</th><th>PDI</th><th>FU</th><th>%</th></tr></thead><tbody><tr><td>Grass</td><td>FV0160</td><td>0.99</td><td>0.96</td><td>101.22</td><td>0.93</td><td>16.70</td></tr><tr><td>Grass (when parcel also used for hay and silage production)</td><td>FV0110</td><td>0.88</td><td>0.82</td><td>99.11</td><td>1.03</td><td>18.80</td></tr><tr><td>Hay</td><td>FF0520</td><td>0.83</td><td>0.75</td><td>116.32</td><td>0.95</td><td>85.00</td></tr><tr><td>Grass silage</td><td>FE0740</td><td>0.92</td><td>0.86</td><td>85.21</td><td>1.04</td><td>20.00</td></tr><tr><td>Corn silage</td><td>FE4720</td><td>0.91</td><td>0.81</td><td>42.36</td><td>1.05</td><td>35.00</td></tr><tr><td>Straw</td><td>FP0010</td><td>0.42</td><td>0.31</td><td>22.00</td><td>1.60</td><td>88.00</td></tr><tr><td>Triticale</td><td>CC0100</td><td>1.16</td><td>1.17</td><td>71.77</td><td>0.17</td><td>87.30</td></tr><tr><td>Canola-meal</td><td>CT0240</td><td>0.96</td><td>0.90</td><td>173.38</td><td>0.35</td><td>88.70</td></tr><tr><td>Soybean-meal</td><td>CT0280</td><td>1.21</td><td>1.20</td><td>276.01</td><td>0.27</td><td>87.80</td></tr></tbody></table>

## Appendix B. Appendix

<caption>**Table B1**</caption>

Indicator values in each single-objective optimisation model (columns) for the calving season at the end of summer in the mountain (A) and plain (B) regions. COMP and COMPINF are models that optimise a compromise solution, and the other models optimise the indicator with the same number (1–7). Heatmap colours are set for each row, with dark green representing ideal values and dark red representing anti-ideal values for each indicator.

<table><thead><tr><th rowspan="3"></th><th rowspan="3">INDICATORS</th><th rowspan="3">UNITS</th><th colspan="7">OPTIMISATION MODELS</th><th colspan="2">COMP</th></tr><tr><th colspan="2">ECO</th><th colspan="4">ENV</th><th rowspan="2">BEA</th><th rowspan="2">COMP p=1</th><th rowspan="2">COMPINF p=inf</th></tr><tr><th>€</th><th>RATIO</th><th>CLIM</th><th colspan="3">EUTR</th></tr><tr><th></th><th></th><th></th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th></th><th></th></tr></thead><tbody><tr><td rowspan="8">(A)</td><td>1. Feed margin</td><td>1 000 €</td><td>37</td><td>35</td><td>33</td><td>22</td><td>33</td><td>28</td><td>23</td><td>31</td><td>33</td></tr><tr><td>2. Feed margin</td><td>%</td><td>45</td><td>54</td><td>34</td><td>44</td><td>43</td><td>46</td><td>30</td><td>49</td><td>48</td></tr><tr><td>3. Climate impact</td><td>kg CO2 eq/kgc</td><td>22</td><td>22</td><td>19</td><td>26</td><td>22</td><td>24</td><td>25</td><td>23</td><td>21</td></tr><tr><td>4. Climate impact</td><td>100 kg CO2 eq/ha</td><td>40</td><td>33</td><td>42</td><td>31</td><td>38</td><td>33</td><td>42</td><td>33</td><td>34</td></tr><tr><td>5. Eutrophication</td><td>kg P eq/10<sup>4</sup> kgc</td><td>14</td><td>11</td><td>10</td><td>15</td><td>10</td><td>11</td><td>19</td><td>11</td><td>10</td></tr><tr><td>6. Eutrophication</td><td>kg P eq/100 ha</td><td>26</td><td>17</td><td>23</td><td>17</td><td>17</td><td>15</td><td>33</td><td>16</td><td>16</td></tr><tr><td>7. Grazing time</td><td>% of year</td><td>45</td><td>48</td><td>41</td><td>52</td><td>44</td><td>50</td><td>54</td><td>47</td><td>49</td></tr><tr><td rowspan="8">(B)</td><td>1. Feed margin</td><td>1 000 €</td><td>62</td><td>55</td><td>59</td><td>40</td><td>48</td><td>41</td><td>44</td><td>50</td><td>52</td></tr><tr><td>2. Feed margin</td><td>%</td><td>53</td><td>60</td><td>50</td><td>54</td><td>49</td><td>50</td><td>42</td><td>57</td><td>51</td></tr><tr><td>3. Climate impact</td><td>kg CO2 eq/kgc</td><td>22</td><td>22</td><td>21</td><td>25</td><td>22</td><td>25</td><td>26</td><td>22</td><td>21</td></tr><tr><td>4. Climate impact</td><td>100 kg CO2 eq/ha</td><td>56</td><td>47</td><td>57</td><td>43</td><td>52</td><td>46</td><td>59</td><td>45</td><td>51</td></tr><tr><td>5. Eutrophication</td><td>kg P eq/10<sup>4</sup> kgc</td><td>15</td><td>11</td><td>13</td><td>14</td><td>10</td><td>11</td><td>20</td><td>11</td><td>14</td></tr><tr><td>6. Eutrophication</td><td>kg P eq/100 ha</td><td>38</td><td>24</td><td>34</td><td>24</td><td>23</td><td>21</td><td>45</td><td>22</td><td>33</td></tr><tr><td>7. Grazing time</td><td>% of year</td><td>44</td><td>48</td><td>45</td><td>52</td><td>44</td><td>45</td><td>53</td><td>51</td><td>48</td></tr></tbody></table>

Optimisation models: compromise solutions with 2 different distance metrics defined by the parameter p ('COMP' & 'COMPINF'), maximisation of feed margin in € ('ECOEUR'), maximisation of feed margin ratio ('ECORATIO'), minimisation of climate change impacts per kgc ('ENVCLIMKGC') and per ha of land used ('ENVCLIMHA'), minimisation of eutrophication per kgc ('ENVEUTRKGC') and per hectare of land used ('ENVEUTRHA'), maximisation of grazing time as an animal welfare proxy ('AW').
<figure><img src="image_9.png" /></figure>

**Fig. B1.** Animals sold (upper graph) and feed rations (lower graph) at the herd level for a farm of 100 ha in each optimisation model (rows) with respect to two regions – mountain and lain – for the calving season end of winter. The values in brackets are average livestock units at the farm. Optimisation models: compromise solutions with 2 different distance metrics defined by the parameter p ('COMP' & 'COMPINF'), maximisation of feed margin in € ('ECOEUR'), maximisation of feed margin ratio ('ECORATIO'), minimisation of climate change impacts per kgc ('ENVCLIMKGC') and per ha of land used ('ENVCLIMHA'), minimisation of eutrophication per kgc ('ENVEUTRKGC') and per hectare of land used ('ENVEUTRHA'), maximisation of grazing time as an animal welfare proxy ('AW').

## Data availability

For the modelling, only public data was used (e.g., Agribalyse, INRA feed tables) and displayed in the Appendix. Diapason data are confidential.

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