## 3 Materials and Methods
### Crossover Operator DPPX
To show the influence of Ka on makespan, the authors conducted another series of experiments on instances Mk04, Mk08, and Mk09 that were randomly selected. In these experiments, the authors removed condition Ki \(\leq\) Ka from DPPX crossover and ran the algorithm under the following parameters:

* Population size: 400;
* Number of parents 30% of population size: 120;
* Mutation probability: 50%;
* Number of generations: 100. The results are shown in Table 10.

From the experimental results, it is clearly seen that the makespan decreases compared to the best-known result, but the production costs increase and exceed the average price of 18 monetary units per hour that was entered as an input parameter. It is clear that the condition Ki \(\leq\) Ka is necessary in the algorithm since it gives the decision-maker the opportunity to plan production in accordance with the best possible capacity utilization in the time frame but also with real production costs. It is clear that if the costs of each machine were identical, the relative makespan would not make sense, but in real production, this is not the case, and the model and software solution presented in this paper can be a very useful tool when planning production with cost control. ## 5 Discussion and Conclusions

In this paper, a novel optimization approach for resolving capacity planning difficulties in SMEs is proposed. The approach is based on job shop scheduling for SMEs to simultaneously minimize production time and maximize earnings, which is essential for SMEs' survival on the current market. The proposed approach, unlike most other models in the literature, takes into account the average cost price of production per unit of time and thus gives the possibility of determining the makespan when the production costs are average, i.e., so that there is always a profit. If the cost price of the working hour of the machine is not taken into account, it can happen that the makespan is minimal, but the earnings are minimal or even in extreme cases non-existent, because most of the operations in such a schedule are performed on machines whose working hour cost is high, and thus do not provide financial resources for survival on the market. Through a mathematical model, the offered model defines relative makespan in a theoretical sense and demonstrates its practical applicability in the proposed software solution. Through the idea of relative makespan, the model combines two contradictory aims (minimize makespan and maximize profitability). It solves the P-FJSP issue, but it is \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Problem Instance**} & \multirow{2}{*}{\(\mathbf{n}\times\mathbf{m}\)} & \multirow{2}{*}{**BS**} & **RMRGA with** & **RMRGA without** & \multirow{2}{*}{**AC**} & \multirow{2}{*}{**AC**} \\  & & & \(\mathbf{Ki}\leq\mathbf{Ka}\) & \(\mathbf{Ki}\leq\mathbf{Ka}\) & & & \\ \cline{2-7}  & & \(\mathbf{C_{m}}\) & \(\mathbf{C_{R}}\) & \(\mathbf{C_{M}}\) & **with Ki \(\leq\) Ka** & **without Ki \(\leq\) Ka** \\ \hline Mk04 & \(15\times 8\) & 60 & 61 & 49 & \(18.50\) & 18.71 \\ \hline Mk08 & \(20\times 10\) & 523 & 494 & 412 & 17.25 & 18.31 \\ \hline Mk09 & \(20\times 10\) & 307 & 308 & 304 & 18.37 & 18.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Influence of average hour cost on behavior of RMGA. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Machine** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** \\ \hline
\begin{tabular}{c} Average cost \\ per hour \\ \end{tabular} & 15 & 16 & 18 & 20 & 18 & 19 & 21 & 22 & 21 & 16 & 17 & 18 & 19 & 15 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Example of average cost per hour for every machine. also conceivable to solve the T-FJSP (Total Flexible Job Shop Problem) when any operation may be performed on every machine by only modifying the matrix record input data.