# Dwell Time Estimation of Import Containers as an Ordinal Regression Problem
###### Abstract  
The optimal stacking of import containers in a terminal reduces the reshuffles during the unloading operations. Knowing the departure date of each container is critical for optimal stacking. However, such a date is rarely known because it depends on various attributes. Therefore, some authors have proposed estimation algorithms using supervised classification. Although supervised classifiers can estimate this dwell time, the variable \"dwell time\" takes ordered values for this problem, suggesting using ordinal regression algorithms. Thus, we have compared an ordinal regression algorithm (selected from 15) against two supervised classifiers (selected from 30). We have set up two datasets with data collected in a container terminal. We have extracted and evaluated 35 attributes related to the dwell time. Additionally, we have run 21 experiments to evaluate both approaches regarding the mean absolute error modified and the reshuffles. As a result, we have found that the ordinal regression algorithm outperforms the supervised classifiers, reaching the lowest mean absolute error modified in 15 (71%) and the lowest reshuffles in 14 (67%) experiments. dwell time estimation; attribute selection; ordinal regression algorithms; performance metrics for ordinal regression +
Footnote †: journal: Medical  
To reduce the reshuffles, operators need to know a priori the dwell time of each arriving container. The dwell time of a container measures the days (hours or weeks) that it shall stay in the yard [7]. We shall refer to dwell time as the dwell time of import containers in a yard of a container terminal. Predominantly, the actual dwell time is unknown because the departure date to its client depends on several attributes [8]. Thus, operators employ their expertise or some algorithms to estimate the dwell time. By reducing the reshuffles, container terminals lessen their operation time and fuel consumption. Two approaches are commonly used for estimating the dwell time. The first is an empirical approach based on the operators' knowledge [9; 10; 11; 12; 13]. The second is an approach based on statistical and machine-learning algorithms [7; 8; 14; 15; 16; 17; 18]. The proposals of machine-learning algorithms to estimate the dwell time have employed supervised classification algorithms [14; 16; 17] and regression algorithms [7; 18]. Nevertheless, the estimation of the dwell time is still considered an open problem because none of these approaches has satisfied the demands of containers yards [6; 7; 17; 19; 20]. Recent studies have solved similar problems with ordinal regressors based on deep neural networks and other machine-learning algorithms, e.g., image ordinal estimation [21], knee osteoarthritis severity [22], degree of building damage [23], and Twitter sentimental analysis [24]. These problems present a class attribute with an ordinal domain, such as the dwell time of import containers in a yard. The algorithms proposed in such studies have improved their accuracies employing ordinal regression methods. In contrast, research works proposing machine-learning algorithms for estimating the dwell time [7; 8; 14; 15; 16; 17; 18], have not explored ordinal regression methods. Thus, we have considered that there is room for improvements estimating the dwell time with ordinal regressors. In this research, we have stated the estimation of the dwell time as an ordinal regression problem. We have considered that modeling and solving this problem using ordinal regression algorithms, instead of as a supervised classification or regression problem, we can reduce the reshuffles compared to those obtained by means of supervised classification algorithms. Additionally, we have performed attribute engineering by extracting, selecting, and evaluating several attributes. Consequently, this work makes the following contributions:  
1.