# Applying Simheuristics to Minimize Overall Costs of an MRP Planned Production System
## 7 Conclusions and Future Work  
This article provides insights into the application of simheuristics in identifying optimal MRP planning parameter values for lot size, planned lead time and safety stock. The aim is to find the minimal overall cost (inventory costs plus backorder costs) computed during the application of the MRP planning algorithm in a simulation environment. This article is a further development of the results based on three different simheuristic versions to identify the minimal overall cost only for the MRP planning parameter safety stock and planned lead time. The first extension is that optimal values for all three MRP planning parameters are searched. A second extension is the development of a SA-based simheuristic extension. The third extension focuses on finding optimal parameters without wasting simulation budget for non-promising iterations. Hence, an intelligent simulation budget management (SBM) is introduced to consume the available replications only for potential best solutions, thus skipping solutions outside the defined percentile range. SBM was combined with the SA extension to additionally explore new areas of the solution space and to escape local minima. The application of the developed SBM and SA extensions, combined with all three planning parameters, allows for a systematic identification of optimal planning parameters with a clear optimization target. The numerical results show that the best performing version for this application is ERR. From a production planning  
Figure 3: Comparison between the best result obtained in each simheuristic. perspective, the developed simheuristic versions, specifically ERR, provides a fast and well performing simulation-based optimization approach which is simple to apply in practical environments. The performed simulation study shows the improvement of the existing simheuristic versions regarding the identification of the minimal overall cost with the joint application of SBM and SA. This finding is supported by the lowest overall cost obtained with the highest simulation budget and the joint application of SBM and SA for all three simheuristic versions. Limitations of this study are related to the application field and the production system within which the simheuristics are tested, i.e., only one application field is evaluated in this study and the respective production system is still rather simple. However, this article provides the foundation for future investigations, to systematically apply the simheuristics concept to more complex production system structures and to other application fields. The developed simheuristics focus on a single objective function, however, for real production systems, it is not always possible to transform all objective dimensions into costs. Therefore, future work could investigate how to extend the simheuristic to a multi-objective approach. A broad sensitivity analysis to prove the promising results of SBM is also planned in future work. Conceptualization, K.A. and A.A.J. ; methodology, K.A. and J.P.; software, W.S. ; validation, K.A., W.S. ; formal analysis, K.A., W.S. and J.C.; investigation, W.S. and J.C.; resources, W.S. ; data curation, W.S. ; writing--original draft preparation, W.S. and J.C.; writing--review and editing, K.A., W.S., J.C. and A.A.J. ; visualization, W.S. and J.C.; supervision, K.A. and J.P.; project administration, K.A. and J.P. All authors have read and agreed to the published version of the manuscript. This work has been partially funded by the Spanish Ministry of Science (PID2019-111100 RB-C21/AEI/10.13039/501100011033 and RED2018-102642-T), the Erasmus+ Program (2019-I-ES01-KA103-062602), and funded by the Austrian Science Fund (FWF): P32954-G.  
Not applicable. The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. The following abbreviations are used in this manuscript: