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A mixed integer nonlinear programming model for biomass production

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Abstract

In this paper, a nonlinear model to maximize biomass production with specific nutritional quality is proposed. The model decides about kind of grasses and legumes to cultivate, quantities of each grasses and legumes chosen, the use of resources, and the proper time of harvest at which the biomass with specific nutritional quality is maximized. Model works with sufficient information about biomass yield, nutrient content, water requirements and fertilizer requirements of several crops, and it can explore all possible harvest times and choose the right time in which biomass production is maximized with desired nutritional quality. Furthermore, the solution gives to the producers additional information on weekly irrigation plan and weekly fertilizers plan for m2 of cultivated grass. The model was tested on six scenarios using GAMS and obtained solutions are the global solution in each scenario.

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References

  • Alexander DL, Morel PC, Wood GR (2006) Feedding strategies for maximising gross margin in pig production. Glob Optim Sci Eng Case Stud 3(1):14–20

    Google Scholar 

  • Aderson A, Earle M (1983) Diet planning in the third world by linear and goal programming. J Oper Res Soc 34:9–16

    Article  Google Scholar 

  • Agrell PJ, Stam A, Fischer G (2004) Interactive multiobjective agro-ecological land use planning: the Bungoma region in Kenya. Eur J Oper Res OR Appl 158:194–217

    Article  Google Scholar 

  • Berroterán J (2000) Modelo de utilización Cereal-pasto en sistemas de Producción de Sabanas Bien Drenadas con suelos Ácidos en Venezuela. Interciencia 25(4):203–209

    Google Scholar 

  • Cab F, Enriquez J, Pérez J, Hernádez A, Herrera J, Ortega E, Quero A (2008) Potencial productivo de tres especies de Brachiaria en monocultivo y asociadas con Arachis Pintoi en Isla, Veracruz. Técnica Pecuaria en México 46(003):317–332

    Google Scholar 

  • Chappel AE (1974) Linear programming cuts costs in production of animal feeds. Oper Res Q 25(1):19–26

    Article  Google Scholar 

  • Cortés ME, Sánchez TM (2008) Modelo lineal multiobjetivo para la toma de decisiones en alimentación del ganado. Revis Investig Oper 29(1):5–9

    Google Scholar 

  • El Sayed Abdel Asís MH (2007) Parametric and multiobjective optimisation applied in agriculture: the study of cropping pattern in the Ameriya region in winter crops. Revis Investig Oper 28(1):17–24

    Google Scholar 

  • Frederiksen J, Kategile J (1980) The effect of nitrogen fertilization and time of cutting in first growth in Brachiaria Brizantha on yield, crude protein content and in vitro digestibility. Trop Anim Prod 5(2):136–143

    Google Scholar 

  • Generic Algebraic Modelling Systems Development Corporation (2008). Generic Algebraic Modelling Systems V. 22.9.2. GAMS Development Corporation, Washington, DC

  • García A, Rodríguez JJ, Ruiz DM (1998) Optimización del engorde de bovinos en pastoreo en la Pampa Argentina mediante programación lineal. Invest Agrar Prod Sanid Anim 13(1, 2 y 3):99–117

    Google Scholar 

  • García B, Vilario D, Fogueroa V, López O, Piloto J (1998) Modelo matemático de optimización para granjas integrales de agricultura sostenible. Revis Comput Investig Porcina 5(1):55–67

    Google Scholar 

  • Garg MR (2012) Balanced feeding for improving livestock productivity—increase in milk production and nutrient use efficiency and decrease in methane emission, FAO Animal Production and Health Paper, No. 173, Rome, Italy

  • Gervásio de Oliveira J, Batista J, Barioni L, Gonçalves G, Braga A, Espellet M (2010) Optimized feed planning for a grazing horse production systems. Revis Bras Zootec 39(4):932–940

    Article  Google Scholar 

  • Glen JJ (1974) A Linear programming model for an integrated crop and intensive beef production enterprise. J Oper Res Soc 37(5):487–494

    Article  Google Scholar 

  • Glover F (1975) Improved linear integer programming formulations of nonlinear integer problems. Manag Sci 22(4):455–460

    Article  Google Scholar 

  • González I, Betancourt A, Fuenmayor A, Lugo M (2011) Producción y composición química de forrajes de dos especies de pasto Elefante (Pennisetum sp.) en el Noroccidente de Venezuela. Zootec Trop 29(1):103–112

    Google Scholar 

  • Grof B, Harding W (1970) Dry matter yields and animal production of Guinea grass (panicum maximun) on the humid tropical Coast of North Queensland. Trop Grassl 40(1):85–95

    Google Scholar 

  • Grossmann I, Viswanathan J, Vecchieti A, Raman R, Kalvelagen E. DICOPT (2008) General Algebraic Modelling Systems GAMS Developtment Corporation, Washington, D.C

  • Guenni O, Gil J, Baruch Z, Mrquez L, Nuez C (2006) Respuestas al déficit hídrico en especies forrajeras de Brachiaria (TRIN.) GRISEB. (POACEAE). Interciencia 31(007):505–511

    Google Scholar 

  • Holman F (2002) El uso de modelos de simulación como herramienta para la toma de decisiones en la promoción de nuevas alternativas forrajeras: el caso de Costa Rica y Perú. Archivos Latinoamericanos de Producción Animal 10(1):35–45

    Google Scholar 

  • Jena S, Poggi M (2013) Harvest planning in the Brazilian sugar cane industry via mixed integer programming. Eur J Oper Res Innov Appl OR 230:374–384

    Article  Google Scholar 

  • Johnson C, Reiling B, Mislevy P, Hall M (2001) Effects of nitrogen fertilization and harvest date on yield, digestibility, fiber, and protein fractions of tropical grasses. J Anim Sci 79:2439–2448

    Article  Google Scholar 

  • Juárez F, Fox D, Blake R (1999) Evaluation of tropical grasses for milk production by dual-purpose cows in tropical mexico. J Dairy Sci 82:2136–2145

    Article  Google Scholar 

  • Júdez L, de Miguel M, Mas J, Bru R (2002) Modeling crop regional production using positive mathematical programming. Math Comput Model 35:77–86

    Article  Google Scholar 

  • Martínez D, Hernádez A, Enríquez J, Pérez J, González S, Herrera J (2008) Producción de forraje y componentes del Rendimiento del Pasto Brachiaria Humidicola Ciat 6133 con diferente manejo de la defoliación. Técnica Pecuaria en México 46(004):427–438

    Google Scholar 

  • Hj Mohamad N, Said F (2011) A mathematical programming approach to crop mix problem. Técnica Pecuaria en México 46(004):427–438

    Google Scholar 

  • Munford A (1996) The use of iterative linear programming in practical applications of animal diet formulation. Afr J Agric Res 6(1):191–197

    Google Scholar 

  • Oladokun VO, Johnson A (2012) Feed formulation problem in nigerian poultry farms: a mathematical programming approach. Am J Sci Ind Res 3(1):14–20

    Google Scholar 

  • Olivera Y, Machado R, Del Pozo P, Ramírez J, Cepero B (2007) Evaluación de accesiones de Brachiria brizanta en suelos ácidos. Época de máximas precipitaciones, Pastos y Forrajes 30(3):303–313

    Google Scholar 

  • Peralta J, Carrillo S, Hernández H, Porfirio N (2007) Características morfológicas y productivas, en etapa de producción, para ocho gramíneas forrajeras tropicales. APPA-ALPA-Cusco, Cusco

    Google Scholar 

  • Pérez J, García E, Enríquez J, Quero R, Pérez J, Hernández A (2004) Análisis de crecimiento, área foliar específica y concentración de nitrógeno en hojas de pasto “mulato”(Brachiaria hbrido, cv.). Técnica Pecuaria en México 42(003):447–458

    Google Scholar 

  • Prišenk J, Turk J, Rozman Č, Borec A, Zrakić M, Pažek K (2014) Advantages of combining linear programming and weighted goal programming for agriculture application. Oper Res Int J 14(2):253–260

    Article  Google Scholar 

  • Rehman T, Romero C (1987) Goal programming with penalty functions and livestock ration formulation. Agric Syst 23:117–132

    Article  Google Scholar 

  • Rosenthal R (2008) GAMS. A User’s guide. GAMS Development Corporation, Washington, DC

    Google Scholar 

  • Saxena P (2011) Comparision of linear and nonlinear programming techiniques for animal diet. Appl Math 1(2):106–108

    Article  Google Scholar 

  • Saxena P Pathak (2011) Application of nonlinear programming for optimization of nutrient requirements for maximum weight gain in buffaloes. Int J Food Sci Nutr Eng 1(1):8–10

    Article  Google Scholar 

  • Saxena P, Pathak V, Kumar V (2012) Programming techinique for animal diet formulation: a non-linear approach. Int J Food Sci Nutr Eng 2(5):85–88

    Article  Google Scholar 

  • Sevilla G, Pasinato A, García J (2001) Curvas de crecimiento de forrajeras templadas irrigadas. Archivos Latinoamericanos de Produccin Animal 9(2):91–98

    Google Scholar 

  • Tedeschi LO, Fox DG, Sainz RD, Barioni LG, Raposo de Medeiros S, Boin C (2005) Mathematical models in ruminant nutrition. Sci Agric 62(1):76–91

    Article  Google Scholar 

  • Vassalos M, Dillon D, Freshwater D, Karanikolas P (2010) Modeling multifunctionality of agriculture at a farm-level: The case of Kerkini District, Northern Greece, Applied Studies in Agribusiness and Commerce. Budapest (3–4):59–64

    Article  Google Scholar 

  • Waugh FV (1951) The minimum-cost dairy feed. J Farm Econ 33:299–310

    Article  Google Scholar 

  • Westerlund T, Lastusilta T. Alpha ECT (2008) General Algebraic Modelling Systems GAMS Development Corporation, Washington, D.C

  • Žgajnar J, Juvančič L, Kavčič S (2009) Combination of linear and weighted goal pragramming with penalty function in optimisation of a daily cow ration. Agric Econ 55(10):492–500

    Google Scholar 

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Acknowledgements

The work was supported by CDCHT-UCLA-Venezuela under the project 002-DAG-2012.

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Authors and Affiliations

  1. Universidad CentroOccidental Lisandro Alvarado (UCLA), Apdo 400, Barquisimeto, Venezuela

    J. Contreras & H. Lara

  2. Biominbloq CA., Sarare, Venezuela

    G. Nouel-Borges

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  1. J. Contreras
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  2. H. Lara
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  3. G. Nouel-Borges
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Correspondence to J. Contreras.

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Contreras, J., Lara, H. & Nouel-Borges, G. A mixed integer nonlinear programming model for biomass production. Oper Res Int J 19, 39–57 (2019). https://doi.org/10.1007/s12351-016-0283-4

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  • DOI: https://doi.org/10.1007/s12351-016-0283-4

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