IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v60y2009i12d10.1057_jors.2008.106.html
   My bibliography  Save this article

Multiobjective stochastic programming for feed formulation

Author

Listed:
  • T Peña

    (University of Valladolid)

  • P Lara

    (University of Córdoba)

  • C Castrodeza

    (University of Valladolid)

Abstract

The minimum cost linear programming model used traditionally for feed formulation does not take account of variability of nutrients in feed ingredients. Therefore, it may be that the nutrient requirements of the animal are not adequately met. In this paper, we show how a multiobjective stochastic model that permits confronting the cost of the ration with the probabilities of meeting the nutrient requirements of the animal can enhance the process of animal diet formulation. The model presented here does not require any a priori information from the decision maker, eliciting his preferences through an interactive process. This is the main advantage in relation to other models found in the literature for treating the problem of nutrient variability, which introduce stochastic constraints in the single objective minimum cost model requiring fixing the level of probability desired for each one of the nutrients in advance.

Suggested Citation

  • T Peña & P Lara & C Castrodeza, 2009. "Multiobjective stochastic programming for feed formulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1738-1748, December.
  • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:12:d:10.1057_jors.2008.106
    DOI: 10.1057/jors.2008.106
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/jors.2008.106
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1057/jors.2008.106?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rehman, Tahir & Romero, Carlos, 1984. "Multiple-criteria decision-making techniques and their role in livestock ration formulation," Agricultural Systems, Elsevier, vol. 15(1), pages 23-49.
    2. Nijkamp, P. & Spronk, J., 1978. "Interactive multiple goal programming," Serie Research Memoranda 0003, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    3. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    4. Castrodeza, Carmen & Lara, Pablo & Pena, Teresa, 2005. "Multicriteria fractional model for feed formulation: economic, nutritional and environmental criteria," Agricultural Systems, Elsevier, vol. 86(1), pages 76-96, October.
    5. Siegfried Schaible, 1976. "Duality in Fractional Programming: A Unified Approach," Operations Research, INFORMS, vol. 24(3), pages 452-461, June.
    6. Sabir A. Rahman & F. E. Bender, 1971. "Linear Programming Approximation of Least-Cost Feed Mixes with Probability Restrictions," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 53(4), pages 612-618.
    7. Siegfried Schaible, 1976. "Fractional Programming. II, On Dinkelbach's Algorithm," Management Science, INFORMS, vol. 22(8), pages 868-873, April.
    8. Siegfried Schaible, 1976. "Fractional Programming. I, Duality," Management Science, INFORMS, vol. 22(8), pages 858-867, April.
    9. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    10. C. van de Panne & W. Popp, 1963. "Minimum-Cost Cattle Feed Under Probabilistic Protein Constraints," Management Science, INFORMS, vol. 9(3), pages 405-430, April.
    11. Leclercq, J. -P., 1982. "Stochastic programming: An interactive multicriteria approach," European Journal of Operational Research, Elsevier, vol. 10(1), pages 33-41, May.
    12. Joyce T. Chen, 1973. "Quadratic Programming for Least-Cost Feed Formulations under Probabilistic Protein Constraints," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 55(2), pages 175-183.
    13. William B. Roush & Robert H. Stock & Terri L. Cravener & Thomas H. D'Alfonso, 1994. "Using Chance-Constrained Programming for Animal Feed Formulation at Agway," Interfaces, INFORMS, vol. 24(2), pages 53-58, April.
    14. Caballero, Rafael & Cerda, Emilio & del Mar Munoz, Maria & Rey, Lourdes, 2004. "Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 158(3), pages 633-648, November.
    15. Lilly M. Lancaster, 1992. "The Evolution of the Diet Model in Managing Food Systems," Interfaces, INFORMS, vol. 22(5), pages 59-68, October.
    16. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
    17. Goedhart, Marc H. & Spronk, Jaap, 1995. "Financial planning with fractional goals," European Journal of Operational Research, Elsevier, vol. 82(1), pages 111-124, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luhandjula, M.K. & Joubert, J.W., 2010. "On some optimisation models in a fuzzy-stochastic environment," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1433-1441, December.
    2. Borodin, Valeria & Bourtembourg, Jean & Hnaien, Faicel & Labadie, Nacima, 2016. "Handling uncertainty in agricultural supply chain management: A state of the art," European Journal of Operational Research, Elsevier, vol. 254(2), pages 348-359.
    3. Rosshairy Abd. Rahman & Graham Kendall & Razamin Ramli & Zainoddin Jamari & Ku Ruhana Ku-Mahamud, 2017. "Shrimp Feed Formulation via Evolutionary Algorithm with Power Heuristics for Handling Constraints," Complexity, Hindawi, vol. 2017, pages 1-12, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rosshairy Abd. Rahman & Graham Kendall & Razamin Ramli & Zainoddin Jamari & Ku Ruhana Ku-Mahamud, 2017. "Shrimp Feed Formulation via Evolutionary Algorithm with Power Heuristics for Handling Constraints," Complexity, Hindawi, vol. 2017, pages 1-12, November.
    2. Torres-Rojo, J. M., 2001. "Risk management in the design of a feeding ration: a portfolio theory approach," Agricultural Systems, Elsevier, vol. 68(1), pages 1-20, April.
    3. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    4. Javier León & Justo Puerto & Begoña Vitoriano, 2020. "A Risk-Aversion Approach for the Multiobjective Stochastic Programming Problem," Mathematics, MDPI, vol. 8(11), pages 1-26, November.
    5. Abdelaziz, Fouad Ben, 2012. "Solution approaches for the multiobjective stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 1-16.
    6. Jörg Fliege & Huifu Xu, 2011. "Stochastic Multiobjective Optimization: Sample Average Approximation and Applications," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 135-162, October.
    7. Fouad Ben Abdelaziz & Cinzia Colapinto & Davide La Torre & Danilo Liuzzi, 2020. "A stochastic dynamic multiobjective model for sustainable decision making," Annals of Operations Research, Springer, vol. 293(2), pages 539-556, October.
    8. Walter J. Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    9. Mahdi Zarghami, 2010. "Urban Water Management Using Fuzzy-Probabilistic Multi-Objective Programming with Dynamic Efficiency," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(15), pages 4491-4504, December.
    10. Selçuklu, Saltuk Buğra & Coit, David W. & Felder, Frank A., 2020. "Pareto uncertainty index for evaluating and comparing solutions for stochastic multiple objective problems," European Journal of Operational Research, Elsevier, vol. 284(2), pages 644-659.
    11. Mingfa Zheng & Yuan Yi & Zutong Wang & Tianjun Liao, 2017. "Relations among efficient solutions in uncertain multiobjective programming," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 329-357, September.
    12. Frauke Liers & Lars Schewe & Johannes Thürauf, 2022. "Radius of Robust Feasibility for Mixed-Integer Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 243-261, January.
    13. Belaid AOUNI & Cinzia COLAPINTO & Davide LA TORRE, 2008. "Solving stochastic multi-objective programming through the GP model," Departmental Working Papers 2008-18, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    14. Zarghami, Mahdi & Szidarovszky, Ferenc, 2009. "Revising the OWA operator for multi criteria decision making problems under uncertainty," European Journal of Operational Research, Elsevier, vol. 198(1), pages 259-265, October.
    15. Paula Alexandra Amaral & Immanuel M. Bomze, 2019. "Nonconvex min–max fractional quadratic problems under quadratic constraints: copositive relaxations," Journal of Global Optimization, Springer, vol. 75(2), pages 227-245, October.
    16. Chaabane Djamal & Mebrek Fatma, 2014. "Optimization of a linear function over the set of stochastic efficient solutions," Computational Management Science, Springer, vol. 11(1), pages 157-178, January.
    17. Walter Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    18. S. Rangavajhala & A. A. Mullur & A. Messac, 2009. "Equality Constraints in Multiobjective Robust Design Optimization: Decision Making Problem," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 315-337, February.
    19. Wong, Man Hong, 2013. "Investment models based on clustered scenario trees," European Journal of Operational Research, Elsevier, vol. 227(2), pages 314-324.
    20. Sophie N. Parragh & Fabien Tricoire & Walter J. Gutjahr, 2022. "A branch-and-Benders-cut algorithm for a bi-objective stochastic facility location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 419-459, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pal:jorsoc:v:60:y:2009:i:12:d:10.1057_jors.2008.106. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave-journals.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.