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An Alternative Solution To Linear Programming Problems With Stochastic Input-Output Coefficients

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  • Wicks, John A.
  • Guise, John W.B.

Abstract

Deriving acceptable farm plans where input-output coefficients are stochastic is a complex problem. Previous formulations have required many simplifying assumptions about the stochastic variables in the analysis. This paper presents an alternative approach based on the mean absolute deviation, which permits solution by a conventional linear programming algorithm whilst avoiding some of those assumptions previously required. The formulation also incorporates a stochastic objective function. Examples are provided using the situation of stochastic feed supply with reference to representative sheep-grain farms on the Northern Tablelands of New South Wales. Results from these suggest that this alternative approach is a distinct improvement on earlier stochastic formulations which utilize linear programming algorithms.

Suggested Citation

  • Wicks, John A. & Guise, John W.B., 1978. "An Alternative Solution To Linear Programming Problems With Stochastic Input-Output Coefficients," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 22(1), pages 1-19, April.
    • Handle: RePEc:ags:ajaeau:22495
    DOI: 10.22004/ag.econ.22495
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    References listed on IDEAS

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    1. P. B. R. Hazell, 1971. "A Linear Alternative to Quadratic and Semivariance Programming for Farm Planning under Uncertainty," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 53(1), pages 53-62.
    2. P. B. R. Hazell, 1971. "A Linear Alternative to Quadratic and Semivariance Programming for Farm Planning under Uncertainty: Reply," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 53(4), pages 664-665.
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    4. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June.
    5. B. Curtis Eaves, 1971. "On Quadratic Programming," Management Science, INFORMS, vol. 17(11), pages 698-711, July.
    6. Anderson, Jock R. & Dillon, John L. & Hardaker, Brian, 1977. "Agricultural Decision Analysis," Monographs: Applied Economics, AgEcon Search, number 288652, July.
    7. Barry, Christopher B, 1974. "Portfolio Analysis under Uncertain Means, Variances, and Covariances," Journal of Finance, American Finance Association, vol. 29(2), pages 515-522, May.
    8. Anderson, Jock R. & Feder, Gershon, 2007. "Agricultural Extension," Handbook of Agricultural Economics, in: Robert Evenson & Prabhu Pingali (ed.), Handbook of Agricultural Economics, edition 1, volume 3, chapter 44, pages 2343-2378, Elsevier.
    9. 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.
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    Cited by:

    1. Parkinson, Simon C. & Djilali, Ned, 2015. "Long-term energy planning with uncertain environmental performance metrics," Applied Energy, Elsevier, vol. 147(C), pages 402-412.
    2. El-Shazly, Fawzy A. & Mansour, Mahmoud E. E. & Ahmed, Mousa A. & Shehata, Emad A., 2009. "التركيب المحصولى المصرى فى ظل المخاطرة والمتغيرات المحلية والدولية [Egyptian Cropping Pattern Under Risk and Varying Domestic and International Circumstances]," MPRA Paper 42634, University Library of Munich, Germany, revised 04 Oct 2009.
    3. Kingwell, Ross, 1996. "Programming models of farm supply response: The impact of specification errors," Agricultural Systems, Elsevier, vol. 50(3), pages 307-324.
    4. Pannell, David J., 1988. "Modelling Risk in Linear Programming Using Direct Solution of Linearly Segmented Approximations of the Utility Function," Discussion Papers 315423, University of Western Australia, School of Agricultural and Resource Economics.

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