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An improved algorithm for solving profit-maximizing cattle diet problems

Published online by Cambridge University Press:  23 June 2020

J. G. O. Marques Open the ORCID record for J. G. O. Marques [Opens in a new window] ,
R. de O. Silva Open the ORCID record for R. de O. Silva [Opens in a new window] ,
L. G. Barioni Open the ORCID record for L. G. Barioni [Opens in a new window] ,
J. A. J. Hall Open the ORCID record for J. A. J. Hall [Opens in a new window] ,
L. O. Tedeschi Open the ORCID record for L. O. Tedeschi [Opens in a new window]  and
D. Moran Open the ORCID record for D. Moran [Opens in a new window]
J. G. O. Marques*
Affiliation:
Global Academy of Agriculture and Food Security, The University of Edinburgh, Edinburgh EH25 9RG, UK
R. de O. Silva
Affiliation:
Global Academy of Agriculture and Food Security, The University of Edinburgh, Edinburgh EH25 9RG, UK
L. G. Barioni
Affiliation:
Embrapa Agricultural Informatics, Campinas 13083-886, Brazil
J. A. J. Hall
Affiliation:
School of Mathematics, The University of Edinburgh, Edinburgh EH9 3FD, UK
L. O. Tedeschi
Affiliation:
Department of Animal Science, Texas A&M University, College Station, TX 77843-2371, USA
D. Moran
Affiliation:
Global Academy of Agriculture and Food Security, The University of Edinburgh, Edinburgh EH25 9RG, UK
*
†E-mail: j.g.o.marques@sms.ed.ac.uk
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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.

Keywords

linear programmingnonlinear programmingration formulationoptimizationfeedlot
Type
Research Article
Information
animal , Volume 14 , Issue S2: 9th Workshop on Modelling Nutrient Digestion and Utilization in Farm Animals (MODNUT) , August 2020 , pp. s257 - s266
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Animal Consortium

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References

Anele, UY, Domby, EM and Galyean, ML 2014. Predicting dry matter intake by growing and finishing beef cattle: evaluation of current methods and equation development. Journal of Animal Science 92, 2660–2667.CrossRefGoogle ScholarPubMed
ANUALPEC 2017. Anuário da pecuária brasileira. FNP Consultoria/Agros Comunicação, São Paulo, SP, Brasil.Google Scholar
Cannas, A, Tedeschi, LO, Atzori, AS and Lunesu, MF 2019. How can nutrition models increase the production efficiency of sheep and goat operations? Animal Frontiers 9, 33–44.CrossRefGoogle ScholarPubMed
CEPEA 2018. PIB do Agronegócio Brasileiro. Piracicaba, SP, Brasil.Google Scholar
Cortez-Arriola, J, Groot, JCJ, Rossing, WAH, Scholberg, JMS, Améndola Massiotti, RD and Tittonell, P 2016. Alternative options for sustainable intensification of smallholder dairy farms in North-West Michoacán, Mexico. Agricultural Systems 144, 22–32.CrossRefGoogle Scholar
Dantzig, GB 1998. Linear programming and extensions. Princeton University Press, Princeton, NJ, USA.Google Scholar
Eggleston, HS, Buendia, L, Miwa, K, Ngara, T and Tanabe, K 2006. 2006 IPCC guidelines for national greenhouse gas inventories. Institute for Global Environmental Strategies, Hayama, Japan.Google Scholar
Fox, DG, Sniffen, CJ, O’Connor, JD, Russell, JB and Van Soest, PJ 1992. A net carbohydrate and protein system for evaluating cattle diets: III. Cattle requirements and diet adequacy. Journal of Animal Science 70, 3578–3596.CrossRefGoogle ScholarPubMed
Galyean, ML and Tedeschi, LO 2014. Predicting microbial protein synthesis in beef cattle: relationship to intakes of total digestible nutrients and crude protein. Journal of Animal Science 92, 5099–5111.CrossRefGoogle ScholarPubMed
Garcia-Launay, F, Dusart, L, Espagnol, S, Laisse-Redoux, S, Gaudré, D, Méda, B and Wilfart, A 2018. Multiobjective formulation is an effective method to reduce environmental impacts of livestock feeds. British Journal of Nutrition 120, 1298–1309.CrossRefGoogle ScholarPubMed
de Gouvello Filho, C and Hissa, B 2011. Brazil low carbon case study: technical synthesis report. The World Bank Group, Washington, DC, USA.Google Scholar
Hadrich, JC, Wolf, CA and Harsh, SB 2005. Optimal livestock diet formulation with farm environmental compliance consequences. In American Agricultural Economics Association Annual Meeting, Providence, RI, USA, p. 15.Google Scholar
Hertzler, G, Wilson, DE, Loy, DD and Rouse, GH 1988. Optimal beef cattle diets formulated by nonlinear programming. Journal of Animal Science 66, 1115.CrossRefGoogle ScholarPubMed
Huangfu, Q and Hall, JAJ 2018. Parallelizing the dual revised simplex method. Mathematical Programming Computation 10, 119–142.CrossRefGoogle Scholar
Kaimowitz, D and Angelsen, A 2008. Will livestock intensification help save Latin America’s tropical forests? Journal of Sustainable Forestry 27, 6–24.CrossRefGoogle Scholar
Mackenzie, SG, Leinonen, I, Ferguson, N and Kyriazakis, I 2016. Towards a methodology to formulate sustainable diets for livestock: accounting for environmental impact in diet formulation. British Journal of Nutrition 115, 1860–1874.CrossRefGoogle ScholarPubMed
Marques, JGO 2020. MaxProfitFeeding/README.md at master BlackNellore/MaxProfitFeeding. Retrieved on 1 December 2019 from https://github.com/BlackNellore/MaxProfitFeeding/blob/master/README.mdGoogle Scholar
Marques, JGO, Silva, RdO, Barioni, LG, Hall, JAJ and Moran, D 2019. An improved algorithm for solving nonlinear profit maximizing animal diet problems. Advances in Animal Biosciences 10, 290.Google Scholar
Moraes, LE and Fadel, JG 2013. Minimizing environmental impacts of livestock production using diet optimization models. In Sustainable animal agriculture (ed. Kebreab, E.), pp. 67–82. CABI, Boston, MA, USA.CrossRefGoogle Scholar
Moraes, LE, Fadel, JG, Castillo, AR, Casper, DP, Tricarico, JM and Kebreab, E 2015. Modeling the trade-off between diet costs and methane emissions: A goal programming approach. Journal of Dairy Science 98, 5557–5571.CrossRefGoogle ScholarPubMed
Moraes, LE, Wilen, JE, Robinson, PH and Fadel, JG 2012. A linear programming model to optimize diets in environmental policy scenarios. Journal of Dairy Science 95, 1267–1282.CrossRefGoogle ScholarPubMed
NASEM 2016. Nutrient requirements of beef cattle, 8th revised edition. National Academies Press, Washington, D.C.Google Scholar
Nicholson, CF, Lee, DR, Boisvert, RN, Blake, RW and Urbina, CI 1994. An optimization model of the dual-purpose cattle production system in the humid lowlands of Venezuela. Agricultural Systems 46, 311–334.CrossRefGoogle Scholar
NRC 1984. Nutrient requirements of beef cattle. National Academies Press, Washington, D.C., USA.Google Scholar
O’Connor, JD, Sniffen, CJ, Fox, DG and Chalupa, W 1993. A net carbohydrate and protein system for evaluating cattle diets: IV. Predicting amino acid adequacy. Journal of Animal Science 71, 1298–1311.CrossRefGoogle ScholarPubMed
Oishi, K, Kato, Y, Ogino, A and Hirooka, H 2013. Economic and environmental impacts of changes in culling parity of cows and diet composition in Japanese beef cow-calf production systems. Agricultural Systems 115, 95–103.CrossRefGoogle Scholar
Oishi, K, Kumagai, H and Hirooka, H 2011. Application of the modified feed formulation to optimize economic and environmental criteria in beef cattle fattening systems with food by-products. Animal Feed Science and Technology 165, 38–50.CrossRefGoogle Scholar
Pashaei Kamali, F, van der Linden, A, Meuwissen, MPM, Malafaia, GC, Oude Lansink, AGJM and de Boer, IJM 2016. Environmental and economic performance of beef farming systems with different feeding strategies in southern Brazil. Agricultural Systems 146, 70–79.CrossRefGoogle Scholar
Pomar, C, Dubeau, F, Létourneau-Montminy, M-P, Boucher, C and Julien, P-O 2007. Reducing phosphorus concentration in pig diets by adding an environmental objective to the traditional feed formulation algorithm. Livestock Science 111, 16–27.CrossRefGoogle Scholar
Press, WH, Teukolsky, SA, Vetterling, WT and Flannery, BP 2007. Numerical recipes: the art of scientific computing. Cambridge University Press, New York, NY, USA.Google Scholar
Russell, JB, O’Connor, JD, Fox, DG, Van Soest, PJ and Sniffen, CJ 1992. A net carbohydrate and protein system for evaluating cattle diets: I. Ruminal fermentation. Journal of Animal Science 70, 3551–3561.CrossRefGoogle ScholarPubMed
Sartorello, GL, Bastos, JPST and Gameiro, AH 2018. Development of a calculation model and production cost index for feedlot beef cattle. Revista Brasileira de Zootecnia 47.CrossRefGoogle Scholar
Sniffen, CJ, O’Connor, JD, Van Soest, PJ, Fox, DG and Russell, JB 1992. A net carbohydrate and protein system for evaluating cattle diets: II. Carbohydrate and protein availability. Journal of Animal Science 70, 3562–3577.CrossRefGoogle ScholarPubMed
Soto, C and Reinoso, V 2012. Modelo de formulación de raciones al mínimo costo para ganado de carne basado en el sistema NRC 2000. Archivos de Zootecnia 61, 255–266.CrossRefGoogle Scholar
Tedeschi, LO 2019. ASN-ASAS symposium: future of data analytics in nutrition: mathematical modeling in ruminant nutrition: approaches and paradigms, extant models, and thoughts for upcoming predictive analytics. Journal of Animal Science 97, 1921–1944.CrossRefGoogle Scholar
Tedeschi, LO and Fox, DG 2020. The Ruminant Nutrition System: Volume I - An Applied Model for Predicting Nutrient Requirements and Feed Utilization in Ruminants. (3rd ed.). XanEdu, Ann Arbor, MI, USA.Google Scholar
Tedeschi, LO, Fox, DG, Chase, LE and Wang, SJ 2000. Whole-herd optimization with the Cornell net carbohydrate and protein system. I. Predicting Feed Biological Values for Diet Optimization with Linear Programming. Journal of Dairy Science 83, 2139–2148.CrossRefGoogle ScholarPubMed
Tedeschi, LO, Fox, DG, Sainz, RD, Barioni, LG, de Medeiros, SR and Boin, C 2005. Mathematical models in ruminant nutrition. Scientia Agricola 62, 76–91.CrossRefGoogle Scholar
Wang, SJ, Fox, DG, Cherney, DJR, Chase, LE and Tedeschi, LO 2000a. Whole-herd optimization with the Cornell net carbohydrate and protein system. III. Application of an optimization model to evaluate alternatives to reduce nitrogen and phosphorus mass balance. Journal of Dairy Science 83, 2160–2169.CrossRefGoogle ScholarPubMed
Wang, SJ, Fox, DG, Cherney, DJR, Chase, LE and Tedeschi, LO 2000b. Whole-herd optimization with the Cornell net carbohydrate and protein system. II. Allocating homegrown feeds across the herd for optimum nutrient use. Journal of Dairy Science 83, 2149–2159.CrossRefGoogle ScholarPubMed
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