## 6 Conclusions and Future Work  
This study introduces a novel scheduling problem, the job-shop scheduling problem with variable machine efficiency and maintenance activities (JSSP-VME-MT). The paper also includes machine efficiency decay and maintenance activities, providing a more realistic depiction of scheduling challenges in real-world manufacturing environments. To solve this problem, we presented a memetic algorithm, incorporating a variable neighborhood descent for local search and various specialized genetic operators. We analyzed the algorithm's performance on different test instances, showing encouraging results. Notably, the algorithm's performance was not the article's primary focus. Instead, the emphasis was on the introduction of the new problem. However, the algorithm's results improved over the initial solutions, emphasizing the effectiveness of the memetic approach and the incorporated local search. The findings of this study offer several valuable insights for managers and practitioners in industries reliant on efficient job scheduling. By incorporating variable machine efficiency and maintenance activities into the scheduling framework, the proposed MA enables a more realistic representation of operational constraints. This approach provides managers with the ability to:  
* Optimize production schedules by balancing efficiency decay and maintenance needs, reducing the risk of machine breakdowns. * Improve resource utilization by aligning maintenance activities with operational requirements, minimizing downtime while maintaining production flow. * Adapt scheduling strategies dynamically in response to changes in machine performance, enabling better handling of uncertainties in the production environment. Several avenues hold potential for further exploration. Fine-tuning the memetic algorithm's parameters and exploring new neighborhood structures for the variable neighborhood descent could lead to significant improvements. While the running times for the algorithm were relatively low, there remains a substantial computational budget for more complex or intensive methods. Thus, more advanced local search techniques or entirely new algorithm designs could be employed. Figure 14: Mean running times aggregated by the number of machines and jobs. Beyond improvements to the existing approach, we also encourage investigating alternative models for efficiency decay, exploring beyond the linear model used in this study. Different industrial contexts may call for more complex or other decay models, and these could offer valuable new perspectives on the problem. Validating the algorithm using exact solvers such as CPLEX/PuLP/Gurobi: While the current study focused on larger problem instances where exact solvers face scalability issues, future work will include comparisons on smaller problem instances to benchmark the quality of solutions against the optimal results provided by exact solvers. This will provide additional validation of the proposed algorithm's performance and highlight trade-offs between computational efficiency and solution optimality. While the performance improvement of the proposed algorithm is incremental, the primary novelty of this work lies in the introduction of the JSSP-VME-MT problem and its solution framework. Future studies can build upon this foundation to further enhance algorithmic performance  
We hope that introducing the JSSP-VME-MT sparks further research in this area, enriching the literature on scheduling problems and offering new tools and methods for tackling these complex, real-world challenges. Conceptualization, D.F. and A.E. ; methodology, D.F. and A.E. ; software, D.F. ; validation, D.F. and A.E. ; formal analysis, D.F. and A.E. ; investigation, D.F. and A.E. ; data curation, D.F. and A.E. ; writing--original draft preparation, D.F. and A.E. ; writing--review and editing, D.F. and A.E. ; All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.