An improved algorithm for solving profit-maximizing cattle diet problems

Abstract

Feeding cattle with on-pasture supplementation or feedlot diets can increase animal efficiency and system profitability while minimizing environmental impacts. However, cattle system profit margins are relatively small and nutrient supply accounts for most of the costs. This paper introduces a nonlinear profit-maximizing diet formulation problem for beef cattle based on well-established predictive equations. Nonlinearity in predictive equations for nutrient requirements poses methodological challenges in the application of optimization techniques. In contrast to other widely used diet formulation methods, we develop a mathematical model that guarantees an exact solution for maximum profit diet formulations. Our method can efficiently solve an often-impractical nonlinear problem by solving a finite number of linear problems, that is, linear time complexity is achieved through parametric linear programming. Results show the impacts of choosing different objective functions (minimizing cost, maximizing profit and maximizing profit per daily weight gain) and how this may lead to different optimal solutions. In targeting improved ration formulation on feedlot systems, this paper demonstrates how profitability and nutritional constraints can be met as an important part of a sustainable intensification production strategy.

Evaluating environmental and economic trade-offs in cattle feed strategies using multiobjective optimization

“…The ε-constrained is a MO technique, which overcomes convexity issues in nonlinear programming, in contrast to the weighted sum technique (Bérubé et al, 2009). We use the nonlinear profit-maximizing diet model proposed by Marques et al (2020), which is based on the predictive equations of nutrient requirements from NASEM (2016) and Tedeschi and Fox (2020). Using the NASEM ( 2016) system, the NLPMD was shown to be effectively solved through parametric linear programming, i.e., we can obtain the optimal solution by solving a finite number of linear programming models.…”

“…We obtained the nutritional properties of feedstuffs from NASEM ( 2016), which has a library with over 200 feeding ingredients. The mathematical model developed by Marques et al, (2020) requires the following properties to evaluate the nutritional requirements: metabolizable protein (MP), physically effective neutral detergent fiber (peNDF), fat content (FAT), ruminally degradable protein (RDP), crude protein (CP), net energy for maintenance and gain (CNEm and CNEg), and dry matter (DM) to "as fed" (AF) conversion for each ingredient. We obtained LCA information of each ingredient from the ECOALIM database (Wilfart et al, 2016).…”

“…Second, it does not tackle profit maximization in the feed formulation, a reasonable objective. One possible reason is that these factors can imply a hard-to-solve nonlinear programming model, which has recently been addressed by Marques et al (2020) in relation to optimal cattle diet formulation. The latter highlighted significant differences between the use of a nonlinear profitmaximizing diet (NLPMD) model versus least-cost for feed formulation.…”

“…The NLPMD model can be efficiently solved through parametric linear programming, i.e., by optimizing the least-cost model for the range of feasible shrunk weight gain (SWG), i.e., animal weight gain in terms of shrunk bodyweight, approximately 96% of live weight. By integrating the contributions from Marques et al (2020) and Garcia-Launay et al (2018) and computing CH4 and N2O production from enteric fermentation and manure decomposition, it is possible to derive a more comprehensive analysis of the environmental-economic trade-offs in feedlot beef production systems. This paper uses a multiobjective method based on a nonlinear profitmaximizing diet model to assess the economic and environmental trade-offs in diet formulation for feedlots in France.…”

Parameter fitting for individual growth through data assimilation applied to beef cattle

“…NASEM [40], Valadares Filho et al [56]). After established the price of purchased animal, growth rate, feed (dry matter) intake and cost of feed (dry matter) are the most important variables associated with profitability for the stocking and finishing phases of livestock operations [37].…”