Looking at current enterprise resource planning systems shows that material requirements planning (MRP) is one of the main production planning approaches implemented there. The MRP planning parameters lot size, safety stock, and planned lead time, have to be identified for each MRP planned material. With increasing production system complexity, more planning parameters have to be defined. Simulation-based optimization is known as a valuable tool for optimizing these MRP planning parameters for the underlying production system. In this article, a fast and easy-to-apply simheuristic was developed with the objective to minimize overall costs. The simheuristic sets the planning parameters lot size, safety stock, and planned lead time for the simulated stochastic production systems. The developed simheuristic applies aspects of simulation annealing (SA) for an efficient metaheuristic-based solution parameter sampling. Additionally, an intelligent simulation budget management (SBM) concept is introduced, which skips replications of not promising iterations. A comprehensive simulation study for a multi-item and multi-staged production system structure is conducted to evaluate its performance. Different simheuristic combinations and parameters are tested, with the result that the combination of SA and SBM led to the lowest overall costs. The contributions of this article are an easy implementable simheuristic for MRP parameter optimization and a promising concept to intelligently manage simulation budget.