Optimizing Production Decisions Using a Hybrid Simulation-Genetic Algorithm Approach

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.