# A Network-Based Model for Optimization of Container Location Assignment at Inland Terminals
## 6 Validation of the Mathematical Model
### Assessing Model Performance  
The proposed model was validated by comparing the number of manipulations between the simulated inland terminal and the actual data collected for the one terminal used to set up the simulation.  
For the inland terminal used to set up the validation simulation, approximately 60% of container manipulations were unproductive, corresponding to 2.5 unproductive manipulations per container. Among all containers arriving at the inland terminal, 18.4% were 20', 79.9% were 40', and 1.7% were 45'. No 30' containers arrived at the terminal. The retention times of certain types of containers are shown in Tables 12-14. The retention times of criterion categories were unknown for the used terminal, so we used average values for the retention times from our analysis of 11 inland terminals. The occupancy of the terminal was approximately 60%.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Container ID** & **Criterion** & \multicolumn{2}{c}{**TEU**} & \multicolumn{2}{c}{**Retention Time**} & \multicolumn{2}{c}{**Average**} & **Storage Tier** \\ \hline
9 & 0.345 & 0.429 & 0.529 & 1.5 & 5.5 & 5 & 4.25 & 5 & 3 or 2 \\ \hline
10 & 0.329 & 0.511 & 0.922 & 1.5 & 5.5 & 5 & 4.25 &  
A simulation with these input data and model applications was performed for 50 parallel replications, with each replication lasting 720 h. Of all containers, 23.3% were 20\({}^{\prime}\), 74.4% were 40\({}^{\prime}\), and 2.3% were 45\({}^{\prime}\). The average terminal occupancy was 55.6%. The simulated retention times (Figure 6) were lower than the average for the 11 European inland terminals (Table 2) by 17.95% (1.75 days) in the case of 20\({}^{\prime}\) containers, 8.75% (0.7 day) in the case of 40\({}^{\prime}\) containers, and 1.05% (0.5 day) in the case of 45\({}^{\prime}\) containers.  
Figure 5: Container storage processes at the simulated inland terminal (**a**) as observed or (**b**) according to the proposed mathematical model.  
The simulated average number of inbound containers in simulation replications was 29.6 full containers per train per day (Figure 7), similar to what was actually observed. The average simulated retention time of each train was 1.89% (12 min) longer than what was observed for the actual inland terminal, where containers are stored based on the \"first-in, first-out\" principle. Conversely, the model results led to an unloading time that was 8% (12 min) shorter than the time observed for the inland terminal used in the simulation, and 20% (36 min) shorter than the average time across all 11 European inland terminals.  
The average number of container manipulations was 12,908 in the simulation, of which 3845 (38%) were unproductive (Figure 7). This corresponded to 22% fewer unproductive manipulations than observed at the actual inland terminal, and 37% fewer than observed across all 11 European inland terminals (Figure 8). These results suggest that the proposed model can improve container storage processes at inland terminals.  
Figure 6: Simulated container retention times as a function of simulation replication.  
Figure 7: Average train retention time.