Application of Fuzzy Optimization in Diet Formulation

Volume 2, Issue 3, pp 459--468 http://dx.doi.org/10.22436/jmcs.02.03.09

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2899 Downloads
• 4060 Views

Authors

D. Darvishi Salookolayi - Department of Mathematics, Payeme Noor University, Bandpey branch, Babol, Iran A. Teimouri Yansari - Department of Animal Science, University of Agriculture and Bioresource of Sari, Sari, Mazandaran, Iran S. H. Nasseri - Department of Mathematics and Computer Sciences, Mazandaran University, Babolsar, Iran

Abstract

Feeding cost comprised about 65 to 75 percentage of dairy cattle production systems. Reduction feed cost and consideration seasonal or regional limitation of feed sources especially some forages increased necessity of the optimization of feed formulation in dairy caws. However, without a positive answer and accrue methods based on linear models those used on ration formulation, application of new mathematical models as fuzzy models seems to be very useful to taken account and meeting nutrient requirements and formulation based on ration least cost and composition in different levels. Fuzzy models promise to be a valuable tool as they link measurable information to linguistic interpretation using membership functions. The objective of this paper was using linear fuzzy model in formulation of dairy cow ration in early lactation and compare to linear programming models. Using linear programming models, the final cost of one kilogram of total mixed ration was 1333.5 Rails, and at this level cow nutrients requirements were met. Using fuzzy model and applying all restriction, the least cost for one kilogram of total mixed ration was 1222.5 Rails, and at this level cow nutrients requirements were met. Using fuzzy model in compare to linear programming models, feed cost was reduced about 8 percentages. The result of this experiment guarantees the formulation of ration using fuzzy models can be used to reduce feed cost and obtain different ration that they may met dairy cow nutrients requirements over different situations. In addition, because of the results in an illustrative example, it is concluded that the procedure outlined in this paper suitably deals with ration formulation and, therefore, enables a practical implementation of fuzzy evaluation of agricultural production systems.

Share and Cite

Keywords

• ration formulation
• linear fuzzy model
• dairy cow.

MSC

•  90B22
•  90C70

References

• [1] T. H. D'Alfonso, W. B. Roush, J. A. Ventura, Least cost poultry rations with nutrient variability: a comparison of linear programming with a margin of safety and stochastic programming models, Poult. Sci., 71 (1992), 255--262
  • View Article
  • Google Scholar


• [2] National Research Council (NRC), Nutrient Requirements of Dairy Cattle, National Academies Press, Washington (2001)
  • View Article
  • Google Scholar


• [3] W. B. Roush, T. L. Cravener, F. Zhang, Computer formulation observations and caveats, J. Appl. Poultry. Res., 5 (1996), 116--125
  • View Article
  • Google Scholar


• [4] N. R. St. Pierre, W. R. Harvey, Incorporation of uncertainty in composition of feeds into least-cost ration models. 1. Single-chance constrained programming, J. Dairy Sci., 69 (1986), 3051--3062
  • View Article
  • Google Scholar


• [5] C. J. Sniffen, R. W. Beverly, C. S. Mooney, M. B. Roe, A. L. Skidmore, J. R. Black, Nutrient requirements versus supply in the dairy cow: strategies to account for variability, J. Dairy Sci., 76 (1993), 3160--3178
  • View Article
  • Google Scholar


• [6] C. C. Stallings, M. L. McGilliard, Lead factors for total mixed ration formulation, J. Dairy Sci., 67 (1984), 902--907
  • View Article
  • Google Scholar


• [7] P. R. Tozer, Least-cost ration formulations for Holstein dairy heifers by using linear and stochastic programming, J. Dairy Sci., 83 (2000), 443--451
  • View Article
  • Google Scholar


• [8] N. Owen-Smith, Assessing the constraints for optimal diet models, Evolutionary Ecology, Vol. 7, 530--531 (1993)
  • View Article
  • Google Scholar


• [9] I. Morag, Y. Edan, E. Maltz, IT--information technology: an individual feed allocation decision support system for the dairy farm, Journal of agricultural engineering research, 79 (2001), 167--176
  • View Article
  • Google Scholar


• [10] R. E. Bellman, L. A. Zadeh, Decision making in a fuzzy environment, Management Science, 17 (1970), 141--164
  • View Article
  • Google Scholar


• [11] J. M. Cadenas, D. A. Pelta, H. R. Pelta, J. L. Verdegay, Application of fuzzy optimization to diet problems in Argentienan farms, Eur. J. Oper. Res., 158 (2004), 218--228
  • View Article
  • Google Scholar


• [12] Y. L. Chang, R. S. Sullivan, Quantitative systems for business: QSB, Prentice Hall, Upper Saddle River (1986)
  • View Article
  • Google Scholar


• [13] T. Itoh, H. Ishii, T. Nanseki, A model of crop planning under uncertainty in agricultural management, Int. J. Prod. Econ., 81/82 (2003), 555--558
  • View Article
  • Google Scholar


• [14] D. G. Luenberger, Y. Ye, Linear and nonlinear programming, Addison-Wesley, Canada (1984)
  • View Article
  • Google Scholar


• [15] D. A. Pelta, J. L. Verdegay, J. M. Cadenas, Introducing SACRA: A decision support system for the construction of cattle diets, in: Applied Decision Support with Soft Computing, 2003 (2003), 391--401
  • View Article
  • Google Scholar


• [16] T. Shoacheng, Interval number and fuzzy number linear programming, Fuzzy Sets and Systems, 66 (1994), 301--306
  • View Article
  • Google Scholar


• [17] H. J. Zimmermann, Fuzzy Set Theory--and Its Applications, Kluwer Academic Publishers, Boston (1991)
  • View Article
  • Google Scholar