This paper considers a real-world production planning problem in which production line failures cause uncertainty regarding the practical implementation of a given production plan. We provide a general formulation of this problem as an extended stochastic knapsack problem, in which uncertainty arises from non-trivial perturbations to the decision variables that cannot be represented in closed form. We then proceed by describing a combination of exact optimization, simulation and a meta-heuristic that can be employed in such a setting. Specifically, a discrete-event simulation (DES) of the production system is developed to estimate solution quality and to model perturbations to the decision variables. A genetic algorithm (GA) can then be used to search for optimal production plans, using a simulation-based optimization approach. To provide effective seeding to the GA, we propose initialization operators that exploit mathematical programming in combination with the DES model. The approach is benchmarked against integer linear programming and chance-constrained programming. We find that our approach significantly outperforms contestant techniques under various levels of uncertainty.