# Multi-Criteria Optimization in Operations Scheduling Applying Selected Priority Rules
## 6 Discussion  
The obtained experimental outcomes reflect the dynamical structure of the system determined by applied priority rule. As the precise analytical expression of the transformation of input parameters (time between arrivals for the entry of the parts) to the outputs (production goals) is not known, all objective function values were determined by simulation in a simulation-based optimization process. The results of experiments related to single-objective optimization of production objectives, which are presented in Table 6 and compared in Figures 2 and 3, show that priority rules EDD and STR provided the comparable ideal and worst values for almost all production objectives in the studied model system. That means the daily production limits of the investigated production system according to both rules were similar, therefore the reference points would have to influence the MOP solution only insignificantly. The ideal  
Figure 5: Ranking of applied methods of multi-criteria optimization in the conjunction with selected priority rule. Figure 6: The comparison of coordinates of the ideal point for the EDD priority rule and the best evaluated compromise solution yielded by WSM + EDD. and the worst values were applied in the robust transformation involved in both employed multi-criteria optimization methods in the next step. The following optimization experiments were conducted with the focus on comparing results of multi-criteria optimization with the relation to the evaluation of reached production goals, respecting the implemented specific priority rule. The results presented in Table 9 demonstrate that there does not exist a single dispatching rule that achieves the highest ranking in the connection to applied multicriteria methods according to all observed performance objectives. As can be seen in Figure 5, according to the type of scalar objective function used in the multi-criteria optimization, the best ranking overall was obtained for the WSM when the EDD priority rule was applying. Very similar although slightly worse results were achieved by the WSM using the STR rule. Both scalarization methods in the presence of the FIFO priority rule achieved the worst results with a relatively large loss. The result has confirmed what, e.g., [PERSON] [23] states, that the FIFO rule is not recommended for manufacturing operations since it is usually overcome by any other priority rule. The presented findings point to that employing the EDD and STR rule brought similar production performance results in the context of the complex view to obtained compromise solutions in the studied production system. The relatively long inter-arrival times for EDD rule presented as effective solutions in design space in Table 8 are in consonance with the fact that due date based dispatching rules are expected to work well at low utilization levels [35], and outperformed other rules under light load and smaller job shop configurations [23]. Based on the findings of this investigation, a practical suggestion for production how to set up the input arrival time of each of four entering parts into the system under the specific rule can be proposed. It is determined by design variables presented in Table 8. When utilizing the EDD rule and WSM method, the effective solution is following the values of the design vector (12; 15; 14; 9), determined in minutes. Comparing to the unreachable best results determined by ideal point, the loss of production performance is 2.07% for an average number of manufactured products, 25.26% for an average flow time, 1.52% for average machine utilization, 40.78% for average work in progress, and 0.52% for average cost per part unit, respectively. As for the recommendation of input arrival times when utilizing the STR rule with WSM, it is the design vector (14; 13; 13; 9), determined in minutes.