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International audience; Economic and environmental sustainability is a major concern for pig production systems (PPS). Previous studies showed that formulating low-impact diets using a carbon tax could decrease the climate change (CC) impact of pigfattening units. However, they did not consider the effect of interactions between feed formulas, feeding and shipping strategies (FFSS) on the environmental impacts of pig production. Consequently, the objective of this study was to investigate effects of a carbon tax on economically optimized FFSS and the resulting economic and environmental performances. We used a bi-level optimization model in which the upper level represents a bioeconomic model that simulates the growth of a batch of pigs and optimizes both the amino acid contents in growing and finishing feeds, the level of feed supply, and the shipping strategy. The lower level represents a linear least-cost feed formulation. The model’s behaviour was investigated in four contexts of recent feed and pork prices (low price: L and high price: H; feed: F and pork: P) at different carbon tax level. Optimized FFSS were highly sensitive to both the economic context and the carbon tax level. Without carbon tax, CC impact was lower in LF-LP than in the other economic contexts. With HF, the optimal amino acid contents and feed supply decreased as tax level increased. With LF, the optimal amino acid contents in the finishing diet increased as tax level increased, to improve feed conversion ratio. With increasing tax level, peas and cereal by-products were replaced with cereals and oil meals in pig diets. The highest potential of CC mitigation was obtained with HF-LP context, whereas LF-LP context had the lowest potential of CC mitigation because it resulted in low CC impact, even without application of a carbon tax. Optimizing both levels (FFSS) while applying a carbon tax decreased CC by up to 43% and saved up to 26% of income compared to FFSS optimized without carbon tax. This model provides a valuable tool to investigate the adaptation potential of PPS to the application of a carbon tax.

Economic results of pig farming systems are highly variable and depend on the prices of feed ingredients used toformulate the diets as well as on pig performance and pork price. Thus, feeding strategies in fattening units arecritical factors in the economic outputs of pig production and major levers for improvement. This work aims atimproving the profitability of pig farms by proposing the best compromise between the cost of feeding and theperformance of animals. We rely on an individual-based bioeconomic model, which calculates the average grossmargin per fattened pig and the environmental impacts of the production according to biological traits of each pig,such as feed intake and protein deposition potentials, and the feeding strategy. The objective function maximizesthe average gross margin per pig using an optimization procedure regarding the feeding strategy. The optimizationproblem is solved with an evolutionary algorithm. The behaviour of this process was investigated, in one-phaseand two-phase feeding programs, using two among three feeds A, B, and C, formulated to achieve 110, 90 or 90% of digestible lysine requirements of an average pig at 30, 65 and 120 kg of body weight, respectively. We studied as decision variables the percentage of the two feeds in the blend at each phase and the average live weight of the pen at the end of the first phase. With this optimization strategy, it is possible to optimize simultaneously the feed mixture to be distributed at each phase and the pig weight at feed change. In two-phase feeding program, for the pig population tested, optimal pen average pig weight at diet change was lighter than common practice (50 vs 65 kg), and optimal feed digestible lysine contents amounted 8.5 and 6.3 g/kg in phase 1 and 2, respectively. Further investigations will extend the range of available decision variables and consider multi-objectives optimization to account for environmental impacts.

International audience; Economic results of pig-fattening systems vary greatly and depend in part on prices of pork and feeds, as well as pig growth performance (e.g. slaughter weight, lean percentage). Previous studies revealed that feeding and shipping strategies are critical factors in the economic outputs of pig production. However, they failed to consider both strategies and the variability in pig growth performance simultaneously. Consequently, the objective of this study was to develop a new procedure to improve the profitability of pig farms by estimating the best compromise among feeding costs, pork price, animal performance, and shipping constraints. We considered a bi-level programming problem in which the upper-level represents a bioeconomic model that simulates the growth of each pig according to its biological traits whereas the lower-level represents a linear least-cost feed formulation. Bioeconomic decisions taken at the upper-level are live weight at diet changes, the percentage of mean amino acid requirement to be covered at the start of each phase, and the target weight for slaughter. Maximising the mean gross margin per fattened pig is the objective function at the upper-level. It depends on pork price and feeds cost (the objective function of the lower-level) which results from the proportion of each feed ingredient (the lower-level decision variables) at the lower-level. The optimisation problem at the upper-level is solved using an evolutionary algorithm. We considered three sets of prices: average pork and feed prices, high pork and low feed prices, and low pork and high feed prices. The changes in pork prices had major impacts on shipping decisions while had minor impacts on feeding decisions. Optimising the shipping strategy at the same time modified the optimal feeding strategy. Considering the bi-level optimisation model improved the gross margin by 1.65 €/pig (5.2%) compared to the situation where each model (the bioeconomic model and least-cost feed formulation) was optimised separately, and by 3.59 €/pig (11.2%) compared to the common practice on farms in France.

Les résultats économiques des élevages porcins dépendent des prix du porc et des matières premièresalimentaires, ainsi que des performances techniques des ateliers de production. Les coûts d'alimentation, ainsique le poids d'abattage et le taux de muscle des pièces de chaque porc interviennent dans la construction de lamarge brute. Les stratégies alimentaires et de gestion des abattages des porcs à l'engrais sont donc des facteurs clés des résultats économiques. Différents modèles et outils ont été précédemment développés pour prédire les effets des stratégies alimentaires sur les performances techniques et les résultats économiques (lnraPorc, MOGADOR ... ). Ils ont montré qu'il est nécessaire de prédire la trajectoire de croissance de chaque porc pour estimer correctement les résultats de l'atelier. Ils ne permettent cependant pas d'identifier la stratégied'alimentation optimale dans un contexte économique donné. L'objectif de ce travail était de développer un outilcapable de maximiser la rentabilité de l'atelier d'engraissement dans différents contextes économiques, enproposant le meilleur compromis entre coût d'alimentation et niveau de performance des animaux.L'outil associe un modèle bioéconomique de l'atelier d'engraissement et une procédure d'optimisation de lamarge brute moyenne par porc. Le modèle bioéconomique simule la croissance de chaque porc selon sonpotentiel d'ingestion et de croissance et selon la stratégie d'alimentation. Il calcule la marge brute moyenne parporc engraissé et les impacts environnementaux de la production (par Analyse de Cycle de Vie).La procédure d'optimisation maximise la marge brute moyenne par porc en trouvant le poids cible à l'abattage(PVa), la durée maximale d'engraissement (Dmax) et la meilleure stratégie d'alimentation biphase (BP) en termesde composition de la ration (pourcentages de deux aliments A et B formulés pour couvrir respectivement 110% et90% du besoin en lysine digestible du porc moyen à 30 kg et 120 kg de poids vif) et de poids vif moyen auchangement de phase. Cette procédure utilise un algorithme évolutionnaire adapté à la résolution de problèmesnon linéaires et discontinus (CMA-ES, Covariance Matrix Adaptation Evolution Strategy). Après une phase devalidation des conditions d'utilisation de l'outil, différents scénarios ont été explorés. Dans le contexte économique retenu pour les simulations, l'outil permet d'augmenter la marge brute de 1,33€/porc en cherchant la meilleure BP, en comparaison à un scénario de référence (SR) représenta nt les pratiques habituelles. En ajoutant PVa et Dmax aux variables de décision, l'outil propose une solution qui améliore la marge brute de 2,81 €/porc par rapport à SR. L'outil permet de maximiser le résultat économique de l'atelier d'engraissement en cherchant la meilleure séquence alimentaire biphase et la meilleure gestion des abattages. Les futurs travaux viseront à réaliser une optimisation économique et environnementale conjointe de l'atelier d'engraissement.

Animal production is responsible for several environmental impacts, to which feed production has usually themajor contribution. However, the traditional least-cost feed formulation (LCF) method minimizes the cost withoutconsideration of its environmental impacts. Multi-objective feed formulation has already been proposed to reduce the environmental impacts of pig feeds. It includes an objective function which is a weighted sum (WS) of the normalised values of feed cost, and four environmental impacts of the feed (climate change, land occupation, phosphorus demand and cumulated energy demand) calculated by Life Cycle Assessment. Normalised values are calculated dividing them by their reference value (REF) obtained with LCF (method Norm1). An additional factor α, ranging from 0 to 1 to explore the space of optimal solutions, is then used to weight the relative influence of feed cost and environmental impacts. The aim of this study was to explore potential improvements of the multi-objective method, with applications to pig feeds. We compared WS method with the ϵ-constraint method, which consists in minimizing a single objective while setting a maximum constraint for another one. In our case, the objective function was the weighted sum of the environmental impacts and the constraint was applied on feed cost. Then, we compared the behaviour of the model with Norm1 and with a new normalization method (Norm2), which subtracts the minimum criterion value to the criterion calculated and divides it by the difference between the REF and the minimum criterion values. WS and ϵ-constraint methods produced some common optimal solutions but only ϵ-constraint method allowed to obtain all the solutions of the Pareto front of the problem. Norm2 allowed defining solutions, which reduce consistently all environmental impacts whereas Norm1 allowed compensations between the impacts, which can potentially lead to increase of some impacts. Multi-objective feed formulation method can be substantially improved by implementing Norm2 to avoid possible compensations between impacts, and by applying the ϵ-constraint method to have access to the whole set of feasible optimal solutions.