# An improved algorithm for solving profit-maximizing cattle diet problems

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Published online in *Animal*, June 2020. DOI: 10.1017/S1751731120001433

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J. G. O. Marques, R. de O. Silva, L. G. Barioni, J. A. J. Hall, L. O. Tedeschi and D. Moran
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Abstract
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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 (NASEM, 2016). Non-linearity 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, i.e. linear time complexity is achieved through parametric linear programming. Results show the impacts of choosing different objective functions (minimizing cost, maximizing profit, maximizing profit per daily weight gain) may lead to different optimal solutions. In targeting improved ration formulation on feedlot systems, the paper demonstrates how profitability and nutritional constraints can be met as an important part of a sustainable intensification production strategy.

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Key words:
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linear programming, nonlinear programming, ration formulation, optimization, feedlot.

**Text**

Technical report: ERGO-19-016

**History:**

Published online in

*Animal*, June 2020. DOI: 10.1017/S1751731120001433