The Application of Fuzzy Models in Dairy Cow Ration Formulation: An Economic-Nutritional Analysis for Herds

Subject Areas :

A. Sargazi ¹ , M. Yousefellahi ²

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Received: 2025-05-28 Accepted : 2025-08-10 Published : 2025-09-01

Keywords: dairy cows, multi-criteria decision-making, ration,

Abstract :

In milk production, the most significant portion of costs is related to animal feed. Therefore, to reduce the final price of milk, it is essential to use rations with the lowest possible cost. In this study, to formulate an optimal ration based on 2024 data from Sistan dairy farms, three methods were employed: simple linear programming, goal programming, and fuzzy-goal programming. The model was optimized for four differ-ent groups: fresh cows, low-yielding cows, mid-yielding cows, and super-yield cows. Additionally, to achieve a flexible ration using the fuzzy-goal method, an initial optimal program was developed using de-terministic linear programming to minimize cost. Then, by adding two more objective functions (maximiz-ing nutrients and minimizing water consumption), the goal programming model was obtained. The results showed that, considering the flexibility in the fuzzy-goal method, in most groups, the lower cost led to the selection of this method over linear programming as the optimal ration. Furthermore, the results indicated that the fuzzy model, by reducing costs by 8% compared to conventional rations, while maintaining energy-protein balance, helps prevent disorders such as ketosis and acidosis. In contrast, the linear model, with a 6% cost reduction, reduces protein to dangerous levels (down by 14%), and the goal model, with an 8-17% cost increase, is only justified for specific animals. The findings confirm the efficiency of the fuzzy model in simultaneously managing costs (average 1280000 IRR/head/day) and herd health. It is recommended that dairy farms combine this model with grouping cows based on milk production to increase profitability by up to 18%.

References:

Asadpour H. and Abazari A. (2014). Determining the optimal cropping pattern of Lalehabad region, Babol County, using goal programming linear model. Agric. Econ. Dev. 20(87), 25-137.
Chakraborty D. and Chaudhary P. (2017). Application of fuzzy logic in agricultural systems: A review. Int. J. Agric. Biol. Eng. 10(4), 1-17.
Chung M. and Hanigan M.D. (2023). A multi-objective optimiza-tion model for dairy feeding management. Comput. Electron. Agric. 204, 107521-107532.
Han Y., Huang Y., Jia S. and Lio J. (2013). An interval-parameter fuzzy linear programming with stochastic vertices model for water resources management under uncertainty. Math. Probl. Eng. 2013, 1-12.
Kılınç B., Kılınç İ., Takma Ç. And Gevrek Y. (2024). The appli-cations of fuzzy logic models on food and marine food prod-ucts. Archiv. Lebensm. Hyg. 75, 52-63.
Naseri S.H., Chameh R. and Paydar M.M. (2020). A two-stage multi-parametric model for solving animal diet formulation with floating price based on a fuzzy flexible linear program-ming model. Iranian J. Optim. 12(1), 1-15.
Notte G., Cangiano C., Pedemonte M., Chilibroste P., Rossing W. and Groot J.C.J. (2023). A multi-objective optimization model for dairy feeding management. Agric. Syst. 204, 107521-107529.
NRC. (2001). Nutrient Requirements of Dairy Cattle. 7th Ed. Na-tional Academy Press, Washington, DC., USA.
Pal B.B., Goswami S.B., Sen S. and Banerjee D. (2012). Using fuzzy goal programming for long-term water resource alloca-tion planning in agricultural system: A case study. Math. Model. Comput. 2012, 170-184.
Pomar C., Pomar J., Dubeau F., Joannopoulos E. and Dussault J. P. (2014). Multi-objective optimization for reducing phospho-rus content in pig feeds. J. Anim. Sci. 92(5), 1853-1862.
Regulwar S. and Gurav R. (2013). Fuzzy multi-objective linear programming for sustainable cropping pattern and irrigation planning in different agro-climatic zones of Delhi. Int. J. Eng. Adv. Technol. 2(3), 123-130.
Ringer H. (2022). The application of nonlinear programming on ration formulation for dairy cattle. J. Dairy Sci. 105(3), 2180-2189.
Saboohi M. (2011). Application of mathematical programming in agricultural economics using Excel software. Zabol University Press, Zabol, Iran.
Saxena P. (2022). Animal diet formulation: Optimization and simulation techniques. MS. Thesis, Gautam Buddha Univer-sity, India.