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Optimizing Production Decisions Using a Hybrid Simulation–Genetic Algorithm Approach

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  • Oliver Musshoff
  • Norbert Hirschauer

Abstract

Mathematical programming has for a long time been recognized as a powerful tool. Despite its capacity for solving constrained optimization problems under uncertainty, some methodological obstacles have persisted over the years. The main problem is that the eventually complex results of an unbiased statistical analysis (multiple correlated stochastic variables with different distributions and nonadditive links between) cannot be adequately accounted for within minimization of total absolute deviation (MOTAD) or expected value‐variance (EV) models that rely on the algorithmic determination of the variability measure. In this paper, we develop a methodological hybrid consisting of Monte Carlo simulation and genetic algorithms: the Monte Carlo simulation facilitates the easy representation of diverse stochastic processes and correlation, and the genetic algorithm ensures that the optimization procedure remains applicable even in the case of complex stochastic information. This hybrid approach is applied to the production‐planning problem of a German crop farm. Variant calculations are used to account for the unknown risk attitude of the farmer. Model results demonstrate that optimized production programs and expected total gross margins are not only highly sensitive to the risk attitude, but also to the stochastic processes that are estimated (or assumed) for various activities. We furthermore find evidence that the hybrid approach is able to generate considerable improvement in farm‐program decisions and outperforms planning models that assume static distributions. La programmation mathématique est reconnue depuis longtemps comme étant un outil puissant. Malgré sa capacitéà résoudre des problèmes d'optimisation avec contraintes en situation d'incertitude, certains obstacles méthodologiques ont persisté au fil du temps. Le principal problème réside dans le fait que les résultats éventuellement complexes d'une analyse statistique non biaisée (plusieurs variables aléatoires corrélées avec différentes distributions et des liens non additifs entre elles) ne peuvent être adéquatement représentés dans les modèles MOTAD et E‐V qui dépendent de la détermination algorithmique de la mesure de la variabilité. Dans le présent article, nous avons élaboré une méthode hybride à partir d'une simulation de Monte Carlo et d'algorithmes génétiques: la simulation de Monte Carlo facilite la représentation de divers processus stochastiques et de diverses corrélations, et l'algorithme génétique assure que la procédure d'optimisation demeure applicable même dans le cas d'information stochastique complexe. Cette méthode hybride est appliquée au problème de planification de la production auqúel est confrontée une exploitation de cultures en Allemagne. Des calculs de variantes sont utilisés pour tenir compte de l'attitude inconnue du producteur quant au risque. Les résultats du modèle indiquent que les programmes de production optimisés et les marges brutes totales prévues ne sont pas uniquement sensibles à l'attitude face aux risques mais aussi aux processus stochastiques qui sont estimés (ou supposés) pour diverses activités. Nous avons également trouvé que la méthode hybride peut améliorer considérablement les décisions concernant les programmes agricoles et qu'elle est supérieure aux modèles de planification qui supposent des distributions statiques.

Suggested Citation

  • Oliver Musshoff & Norbert Hirschauer, 2009. "Optimizing Production Decisions Using a Hybrid Simulation–Genetic Algorithm Approach," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 57(1), pages 35-54, March.
  • Handle: RePEc:bla:canjag:v:57:y:2009:i:1:p:35-54
    DOI: 10.1111/j.1744-7976.2008.01137.x
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    References listed on IDEAS

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    6. Robert Finger & Nadja El Benni, 2012. "A Note on Price Risks in Swiss Crop Production – Empirical Results and Comparisons with other Countries," Journal of Socio-Economics in Agriculture (Until 2015: Yearbook of Socioeconomics in Agriculture), Swiss Society for Agricultural Economics and Rural Sociology, vol. 5(1), pages 131-151.
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    8. Finger, Robert, 2012. "Modeling the sensitivity of agricultural water use to price variability and climate change—An application to Swiss maize production," Agricultural Water Management, Elsevier, vol. 109(C), pages 135-143.

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