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Weighted Goal Programming and Penalty Functions: Whole-farm Planning Approach Under Risk


  • Zgajnar, Jaka
  • Kavcic, Stane


The paper presents multiple criteria approach to deal with risk in farmer’s decisions. Decision making process is organised in a framework of spreadsheet tool. It is supported by deterministic and stochastic mathematical programming techniques applying optimisation concept. Decision making process is conceptually divided into seven autonomous modules that are mutually linked up. Beside the common maximisation of expected income through linear programming it enables also reconstruction of current production practice. Income risk modelling is based on portfolio theory resting on expected value, variance (E,V) paradigm. Modules dealing with risk are therefore supported with quadratic and constrained quadratic programming. Non-parametric approach is utilised to estimate decision maker’s risk attitude. It is measured with coefficient of risk aversion, needed to maximise certainty equivalent for analysed farms. Multiple criteria paradigm is based on goal programming approach. In contribution focus is put on benefits and possible drawbacks of supporting weighted goal programming with penalty functions. Application of the tool is illustrated with three dairy farm cases. Obtained results confirm advantage of utilizing penalty function system. Beside greater positiveness it proves as useful approach for fine tuning of the model enabling imitation of farmer’s behaviour, which is due to his/her conservative nature not perfect or rational. Results confirm hypothesis that single criteria decision making, based on maximisation of expected income, might be biased and does not necessary lead to the best - achievable option for analysed farm.

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  • Zgajnar, Jaka & Kavcic, Stane, 2011. "Weighted Goal Programming and Penalty Functions: Whole-farm Planning Approach Under Risk," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 118033, European Association of Agricultural Economists.
  • Handle: RePEc:ags:eaae11:118033

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    References listed on IDEAS

    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. Chang, Ching-Ter & Lin, Teng-Chiao, 2009. "Interval goal programming for S-shaped penalty function," European Journal of Operational Research, Elsevier, vol. 199(1), pages 9-20, November.
    3. Lien, Gudbrand, 2002. "Non-parametric estimation of decision makers' risk aversion," Agricultural Economics, Blackwell, vol. 27(1), pages 75-83, May.
    4. Gomez-Limon, Jose A. & Arriaza, Manuel & Riesgo, Laura, 2003. "An MCDM analysis of agricultural risk aversion," European Journal of Operational Research, Elsevier, vol. 151(3), pages 569-585, December.
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    goal programming; risk modelling; risk aversion; production planning; Risk and Uncertainty;

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