# Multi-Criteria Optimization in Operations Scheduling Applying Selected Priority Rules
## 6 Discussion
The loss when comparing the compromise solution to the best values in case of setting relating to the WSM+STR rule, is 0.84% for an average number of manufactured products, 25.98% for an average flow time, 1.58% for average machine utilization, 45.06% for average work in progress, and 1.48% for average cost per part unit. For the setup of design variables going up from the WPM + STR rule, the suggested design vector is (15; 12; 15; 10), determined in minutes. The corresponding loss is 5.01% for an average number of manufactured products, 3.25% for average flow time, 5.74% for average machine utilization, 1.12% for average work in progress, and 2.26% for average cost per part unit, respectively, all in the relation to the values of ideal point. Despite the weights in scalar objective function were the same, we can notice that in contrast to WSM methods that prioritized some of the production objectives, the compromise solution yielded by WPM is in a relative evaluation more balanced. In this context, the results confirmed that the scalarization methods applying in a priori arrangement bring the problem with the precise reflection of the weights to desired Pareto optimal solutions [24]. The coordinates of the weight vector serve as the model parameters in a multi-objective function and influence the location of Pareto front points. When exploring the compromise solutions found in the objective space from the perspective of the production goals control, we can see a noticeable impact of the applied scalarization method on the evaluation of production results. The comparison of the reached results in Figure 4a-e shows that all production goals that we wish to maximize, such as the number of products and machine utilization, were substantially higher in the case of the WSM method employed, regardless of the applied priority rule. On the contrary, the WPM method provided better results for production goal values that need to be minimized. As we can see in Figure 4, the production objectives, such as the average flow time and the average work in progress, achieved smaller values in comparison to results yielded by the WSM method. Finally, in the case of the average costs per part unit, we can notice very similar and comparable results for all applied methods. Working with many contradictory objectives assumes that they are not completely independent, and a correlation can appear between some of them. As can be noticed in the results introduced in Figure 4, there exist two pairs of objectives which are correlated. We can observe the positive correlation between the number of products and machine utilization (Figure 4a,b), as well as between flow time and work-in-progress (Figure 4c,d). We supposed that correlations, applied transformation of production objectives, and different expressions defining the structure of objective function themselves could explain the obtained results significantly. To evaluate the direct influence of correlations on optimization results will need further experiments with a reduced set of objectives. The rankings of priority rules strongly depend on selected performance measures involved in evaluation and the structure of the production system model itself. The interesting different approach, how to optimize multiple objectives in flexible job shop system, is introduced in a comparative study in the work of [PERSON] et al. [48]. They conducted single-objective optimizations for five individual objectives in the presence of 30 priority rules consequently to evaluate the individual performance objective with respect to the scheduling principle. The observed objectives were makespan, mean flow time, proportion of tardy jobs, mean tardiness, and maximum tardiness. As for ranking of rules, each priority rule's performance was measured as the percentage deviation from the best performing priority rule. Based on the best results via ranking, they constructed the hybrid scheduling rule to ensure optimization of all five objectives simultaneously.