# Dwell Time Estimation of Import Containers as an Ordinal Regression Problem
## 4 Results and Discussion
White arrows indicate container pairs that generate reshuffles. Figure 5 depicts the \(MAE\mu\) (left) obtained by the ordinal regression algorithm and the respective supervised classification algorithm for each optimization instance. Moreover, the figure depicts the number of reshuffles (right) computed by the optimization algorithm using those departure dates estimated with the ordinal regression algorithm and the respective supervised classification algorithm. Black circles indicate those instances where the ordinal regression algorithm lost against the respective supervised classification algorithm. Figure 6 illustrates box plots for both methods, ordinal regression and classification. Both graphs (\(MAE\mu\) and reshuffles) show lower median errors for the ordinal regression approach. The classification method shows lower dispersion in the \(MAE\mu\) than the ordinal regression method, while the ordinal regression method shows the lower quartile values. Likewise, the ordinal regression yielded lower second and third quartiles than the classification method regarding the reshuffles, but the min, max, and first quartile values were similar. These distributions indicate differences between the methods higher concerning the \(MAE\mu\) than the reshuffles because of the effect of the optimization algorithm. Figure 5: Radial graphs with the \(MAE\mu\) (**left**) and reshuffles (**right**) output by each algorithm inferring the dwell time using both datasets split into 21 instances. A black circle encloses each instance where the ordinal regression algorithm lost against the supervised classification algorithm, i.e., six regarding \(MAE\mu\) and seven regarding the reshuffles. Figure 6: Box plots describing the \(MAE\mu\) (**a**) and the reshuffles (**b**) output by the ordinal regression and the classification methods. The ordinal regression algorithm reached a lower \(MAE\mu\) for 15 (71%) instances and a lower number of reshuffles for 14 (67%) instances. Figure 7 depicts the rank sums comparing the ordinal regression against the classification regarding \(MAE\mu\) and reshuffles. The Wilcoxon signed ranks test [47] indicated that there were significant differences between both methods regarding the \(MAE\mu\) (\(p\)-value = 0.009128), but the differences were not significant regarding the reshuffles (\(p\)-value = 0.1393). Nevertheless, the dwell time estimated with the ordinal regression algorithm generated 87 reshuffles less than the estimated with the supervised classifiers in these 21 experiments. Additionally, in 16 of these experiments, a lower \(MAE\mu\) induced a lower number of reshuffles. The other five experiments showed a different behavior due to the influence of the optimization algorithm previously explained. From these results, we conclude that the dwell time of the containers is estimated more accurately as an ordinal regression problem than as a supervised classification problem, at least using these attributes of the containers. Moreover, all the algorithms reached a higher \(MAE\mu\) and number of reshuffles using the examples in the Dataset2_Test than the examples in Dataset1_Test (instances 1, 2, 3, 4, 11, 12, 16, and 17). Since only Dataset1 includes the attribute \"Product\", we recommend including this attribute to improve the algorithms for the dwell time estimation.