# Proactive Scheduling and Routing of MRP-Based Production with Constrained Resources
## 7 Conclusions  
This study presents an innovative, mathematically grounded approach that addresses critical limitations of traditional MRP/ERP systems in handling proactive production scheduling and routing under resource constraints. By formulating and implementing a mixed-integer linear programming (MILP) model enriched with dynamic routing capabilities, partial resource utilization, and traceability of demand sources, the proposed method significantly enhances the responsiveness and efficiency of MRP-based production environments. The model assumes discrete, deterministic production conditions and is less suited for continuous processes (e.g., chemical plants) without modifications to account for flow dynamics. The integrated PT and PR procedures automate data transformation from MRP/ERP systems and optimize model size, enabling real-time and computationally efficient decision-making. Computational experiments based on real-world production data confirm substantial performance gains: cost reductions of up to 25% and execution time reductions exceeding 50%, depending on the optimization objective. The model also demonstrates high adaptability to operational disruptions such as resource unavailability or equipment failure. In contrast to costly and rigid APS systems, the proposed solution provides a flexible, scalable, and economically viable alternative for manufacturers seeking to modernize production planning while maintaining compatibility with existing MRP infrastructures. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Q**} & \multirow{2}{*}{**O**} & \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**T-FIRST**} & \multicolumn{2}{c}{**T-OPTIM**} & \multicolumn{2}{c}{**T-FIRST**} & \multicolumn{2}{c}{**T-OPTIM**} \\  & & & **(MILP)** & **(MILP)** & **(MILP + PR)** & **(MILP + PR)** \\ \hline Q2 & 2 & 85 & 1.2 & 4.06 & **0.30** & **1.77** \\ Q3 & 2 & 85 & 15.87 & 46.67 & **2.30** & **28.93** \\ Q2 & 5 & 85 & 34.67 & 67.56 & **4.56** & **15.24** \\ Q3 & 5 & 85 & 234.67 & 765.56 & **8.56** & **43.24** \\ Q2 & 10 & 85 & 74.26 & 349.45 & 5.63 & **62.63** \\ Q3 & 10 & 85 & 1587.34 & 3287.11 & **67.34** & **456.34** \\ Q2 & 20 & 150 & 142.34 & 1245.76 & **12.45** & **234.47** \\ Q3 & 20 & 150 & 403.42 & \(>\)5000.00 & **76.45** & **1884.45** \\ Q2 & 50 & 150 & 434.21 & 7834.56 & **15.34** & **345.67** \\ Q3 & 50 & 150 & 6372.45 & \(>\)7500.00 & **143.45** & **2186.56** \\ \hline \hline \end{tabular}  
* \(\bigcirc\)—number of orders, No.—number of execution periods, T-FIRST—time to obtain the first feasible solution, T-OPTIM—time to obtain the optimal solution. MILP—a mathematical programming solver was used to solve the problem, MILP + PR—a mathematical programming solver with a size reduction PR procedure was used for the solution.  
\end{table} 
Table 6: Results of the last stage of experiments (performance experiments). Future research will extend the framework to stochastic environments [16], multi-facility coordination, and AI-based decision support--areas where the current deterministic, single-facility model requires adaptation [17; 18]. In addition, we intend to apply the proposed framework in our other research domains, such as the VRP/CVRP [19] and timetabling problems [20]. We plan in the implementation area that the results will be visualized using Gantt charts (machine/task timelines) and network diagrams (dynamic routing paths). For what-if scenarios (Q1-Q4), dashboards highlight with colors which decisions are acceptable, unacceptable, or optimal. Conceptualization, J.W. and P.S. ; methodology, J.W. and P.S. ; software, J.W. ; validation, P.S. ; formal analysis, P.S. ; investigation, [PERSON]; resources, [PERSON]; data curation, [PERSON]; writing--original draft preparation, P.S. ; writing--review and editing, P.S. ; visualization, [PERSON]; supervision, P.S. ; project administration, P.S. ; funding acquisition, P.S. All authors have read and agreed to the published version of the manuscript. This research was funded by the Polish Ministry of Science and Higher Education.