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Minimum-Cost Cattle Feed Under Probabilistic Protein Constraints

Author

Listed:
  • C. van de Panne

    (Econometric Institute, Netherlands School of Economics, Rotterdam)

  • W. Popp

    (Fellow of the NUFFIC (Netherlands University Foundation for International Cooperation), Econometric Institute)

Abstract

The optimal composition of cattle feed, which can be formulated as a linear programming problem in the case of certainty, is considered when compositions of inputs vary. In the corresponding linear programming formulation the coefficients of the constraints are not constant but can be considered as stochastic. Reformulating the constraints as chance constraints, a nonlinear programming problem results. For an illustrative example this problem is solved using one of Zoutendijk's methods of feasible directions.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:9:y:1963:i:3:p:405-430
    DOI: 10.1287/mnsc.9.3.405
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    Cited by:

    1. Wong, Man Hong, 2013. "Investment models based on clustered scenario trees," European Journal of Operational Research, Elsevier, vol. 227(2), pages 314-324.
    2. G. C. Calafiore & L. El Ghaoui, 2006. "On Distributionally Robust Chance-Constrained Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 1-22, July.
    3. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    4. Zare M., Yahia & Daneshmand, Ahmad, 1995. "A linear approximation method for solving a special class of the chance constrained programming problem," European Journal of Operational Research, Elsevier, vol. 80(1), pages 213-225, January.
    5. Singh, Vikas Vikram & Lisser, Abdel, 2019. "A second-order cone programming formulation for two player zero-sum games with chance constraints," European Journal of Operational Research, Elsevier, vol. 275(3), pages 839-845.
    6. 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.
    7. Zheng, Xiaojin & Wu, Baiyi & Cui, Xueting, 2017. "Cell-and-bound algorithm for chance constrained programs with discrete distributions," European Journal of Operational Research, Elsevier, vol. 260(2), pages 421-431.
    8. İhsan Yanıkoğlu & Dick den Hertog, 2013. "Safe Approximations of Ambiguous Chance Constraints Using Historical Data," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 666-681, November.
    9. Avik Pradhan & M. P. Biswal, 2017. "Multi-choice probabilistic linear programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 122-142, March.
    10. Miguel A. Lejeune & François Margot, 2016. "Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities," Operations Research, INFORMS, vol. 64(4), pages 939-957, August.
    11. Kriens, J. & van Lieshout, J.T.H.C. & Roemen, J.H.J. & Verheyen, P.A., 1983. "Management accounting and operational research," Other publications TiSEM da4f2baa-f699-48f2-80b7-8, Tilburg University, School of Economics and Management.
    12. Kunikazu Yoda & András Prékopa, 2016. "Convexity and Solutions of Stochastic Multidimensional 0-1 Knapsack Problems with Probabilistic Constraints," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 715-731, May.
    13. 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.
    14. Semih Atakan & Kerem Bülbül & Nilay Noyan, 2017. "Minimizing value-at-risk in single-machine scheduling," Annals of Operations Research, Springer, vol. 248(1), pages 25-73, January.
    15. Gülşen, Ece & Olivetti, Elsa & Freire, Fausto & Dias, Luis & Kirchain, Randolph, 2014. "Impact of feedstock diversification on the cost-effectiveness of biodiesel," Applied Energy, Elsevier, vol. 126(C), pages 281-296.
    16. 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.
    17. Poojari, Chandra A. & Varghese, Boby, 2008. "Genetic Algorithm based technique for solving Chance Constrained Problems," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1128-1154, March.

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