Multicriteria Fractional Model for Feed Formulation: Economic, Nutritional and Environmental Criteria

Authors

  • Radu Burlacu University of Agronomic Sciences and Veterinary Medicine-Bucharest
  • Cosmin Niţu University of Agronomic Sciences and Veterinary Medicine-Bucharest

Keywords:

Multi-objective fractional programming, Diet formulation, Pig-nutrition, Environment

Abstract

The traditionally used linear programming model for feed formulation has sought the least- cost combination of ingredients that satisfies a specific level of nutritional requirements. Together with the search for the lowest possible cost, other aspects such as maximising diet efficiency in relation to proposed production objectives and minimising any excess that may lead to unacceptable damage to the environment, are other factors that are gaining in impor- tance in the world of animal nutrition. Taking into account all these factors forces us not only to bear in mind the individual concentrations of each of the nutrients in the feed but also the ratios of these with other nutrients.

In this work we show how a multi-objective fractional programming model is better adapted to current needs in feed design than the traditionally used least cost linear model.

We also show how the model can be solved using the interactive multi-goal programming method with existing linear optimisation software.

References

Logistics Quarterly 9, 181–186. Cole, D.J.A., Van Lunen, T.A., 1994, Ideal amino acid patterns. In: D Mello, J.P.F. (Ed.), Amino Acids in Farm Animal Nutrition. CAB International, pp. 99–112.

Canh, T.T., Aarnink, A.J.A., Schutte, J.B., Sutton, A., Langhout, D.J., Verstegen, M.W.A., Dietary protein affects nitrogen excretion and ammonia emission from slurry of growing-finishing pigs, 1998.

Jean dit Bailleul, P., Rivest, J., Dubeau, F., Pomar, C., Reducing nitrogen excretion in pigs by modifying the traditional least-cost formulation algorithm. Livestock Production Science 2001, 72, 199–211. Kemme, P.A., 1998. Phytate and phytases in pig Nutrition. PhD thesis, Agricultural University Wageningen, Holland.

Lara, P., Multiple objective fractional programming and livestock ration formulation: a case study for dairy cow diets in Spain. Agricultural Systems 1993, 41, 321–334.

Lara, P., Romero, C., An interactive multigoal programming model for determining livestock rations: an application to dairy cows in Andalusia, Spain. Journal Operational Research Society 1992, 43 (3), 945–953.

Lara, P., Romero, C., Relaxation of nutrient requirements on livestock rations through interactive multigoal programming. Agricultural Systems 1994, 45, 443–453.

Spronk, J., Interactive Multi Goal Programming: applications to Financial Planning. Martinus Nijhoff, Boston 1981.

Mitani, K., Nakayama, H., A multiobjective diet planning support system using the satisficing trade-off method. Journal of Multi-Criteria Decision Analysis 1997, 6, 131–139.

Charnes, A., Cooper, W.W., Programming with linear fractional functionals. Naval Research Livestock Production Science 1962, 56 (3), 181–191.

Rehman, T., Romero, C., Multiple-criteria decision-making techniques and their role in livestock ration formulation. Agricultural Systems 15 1984, (1), 23–49.

Schaible, S., Fractional programming I. Duality. Management Science 1976, 22, 858–867.

Tozer, P.R., Stokes, J.R., A multi-objective programming approach to feed ration balancing and nutrient management. Agricultural Systems 2001, 67, 201–215.

Fundacio´ n Espan˜ ola para el Desarrollo de la Nutricio´ n Animal (FEDNA), 1999. Normas FEDNA para la Formulacio´ n de Piensos Compuestos. Madrid.

National Research Council (NRC), 1998. Nutrient Requirements of Swine, 10th ed. National Academy Press, Washington, DC.

Downloads

Published

2023-09-05