Optimierung unter Unsicherheit mit Hilfe stochastischer Simulation und Genetischer Algorithmen - dargestellt anhand der Optimierung des Produktionsprogramms eines Brandenburger Marktfruchtbetriebes -

Abstract

Optimization has been recognized as a powerful tool in teaching and research for a long time. In spite of its well known problem solving capacity, some methodological obstacles have persisted over the years. The main problem is that stochastic variables and their correlations cannot be adequately accounted for within traditional optimization procedures. In this paper, we develop a methodological mix of stochastic simulation and a heuristic optimization procedure which has become known as genetic algorithms. The simulation-part of the mix allows for the consideration of complex information such as stochastic processes; the genetic algorithms-part ensures that the method remains manageable in terms of required time and resources. We demonstrate the decision support potential of the approach by optimizing the production program of a Brandenburg crop farm. We account for the risky environment by using existing stochastic information: on the one hand, we model man-days which are available in critical seasons (particularly harvesting) as triangular distributions according to expert estimations. On the other hand, we use empirical time series and estimate stochastic processes for the gross margins of different activities (wheat, barley etc.). Additionally, variant calculations are made in order to take into account different risk attitudes of decision-makers. Model results in terms of optimal production programs and expected total gross margins are highly sensitive both to the risk attitudes of decision-makers and the stochastic processes which are estimated for different activities.