# Design and Evaluation of an Integrated Autonomous Control Method for Automobile Terminals

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State of the Art

#### 2.1. Planning Process of Automobile Terminals

#### 2.2. Autonomous Control for Coping with Dynamics and Complexity

## 3. Materials and Methods

#### 3.1. Generic Terminal Model

#### 3.1.1. Structure and Parameters of the Generic Model

#### 3.1.2. Evaluation of KPIs for the Generic Model

#### 3.1.3. Benchmarks Planning Methods

#### 3.2. Real-World Scenario

#### 3.2.1. Automobile Terminal Scenario and Simulation Model

#### 3.2.2. Evaluation Benchmark for the Real-World Case

#### 3.3. Deriving an Integrated Autonomous Control Method for Automobile Terminals

#### 3.3.1. Pheromone-Based Method for Yard Assignment

#### 3.3.2. Pheromone-Based Method for Berth Assignment

#### 3.4. Experimental Design

^{k}experiments are necessary for investigating k factors. In the case at hand this leads to 64 different factor combinations (six factors and two factor levels). To reduce the computational efforts, several approaches for the design of experiments (DOE) exist (e.g., factorial designs or Taguchi method), which aim at reducing the number of combinations. Compared to classical one-factor-at-time approaches (OFAT), the DOE aims to reduce the computational efforts on the one hand side and to keep the advantages of a systematic analysis on the other side. Therefore, DOE approaches usually use context-based knowledge about factors in order to reduce the number of factors (e.g., for fractional factorial designs) [40]. However, compared to other DOE approaches, FFD is the most potent tool to get insights into the behavior of the system [41]. Compared to other DOE techniques, like fractional factorial designs, an FFD is conceptionally open to investigate the impact of all factors. The relevance of factors has not been known or assumed before conducting the experiments. Thus, an FFD is very suitable for a complete factor screening [41,42]. In the case at hand the impact of all factors of the new pheromone-based methods (i.e., ${\gamma}_{1}-{\gamma}_{4}$, ${\alpha}_{PYA}$ and ${\alpha}_{PBA}$) are unknown in advance, too. Neglecting factors might cause misleading interpretation of the result. To avoid this an FFD is applied. Due to the relative low number of factors and the accuracy of this approach, this paper uses a 2

^{k}FFD and follows the methodical approach introduced by Law, 2017 [43]. It conducts simulation runs for all combinations and calculates the mean main effects and interactions of factors [44].

#### 3.5. Simulation Implementation and Validation

## 4. Results and Discussion

#### 4.1. Performance Evaluation of Generic Scenario

_{PYA}and α

_{PBA}) lead in the case at hand to shorter distances. With smaller evaporation values, the calculation of moving average values in both methods relies on a smaller number of cars. Accordingly, the method can react faster to changing external dynamics. Due to the high dynamics in the arrival and departure rate, the positive effect of smaller evaporation constants seems to dominate. Regarding the sorting degree, Figure 7 shows a different result. For varying evaporation constants, the sorting degree keeps nearly stable. This result can be expected for the berth assignment method (PBA). As described above, all berth allocation methods have conceptually only a small impact on the sorting degree.

#### 4.2. Impact of Methods Parameters in the Generic Scenario

_{1,}the Figure 8 results show an interesting result. It weights the first term of the yard assignment, which comprises the distance as a crucial part. Figure 8 shows that low values lead to short distances and vice versa. Conceptionally, it was expected that a higher weighting decreases the driving distances. This can be explained as follows: a high weighting of this term causes a stronger segmentation of cars with long turnover times. These cars are assigned to areas which are further away from the quayside. The results for the sorting degree confirm this. A high weighting of γ

_{1}seems to cause a stronger segmentation of car groups and better sorting results. In this scenario this effect seems to overrule the originally intended effect. Figure 8 shows that there are effects of the evaporation constant on the driving distance, but it is weaker than the effects of the weighting factors. Especially, the effect of α

_{PBA}seems to be neglectable compared to the remaining factors. Regarding the sorting degrees, factors γ

_{2}, γ

_{3}and γ

_{4}have the largest effect. As conceptionally planned, γ

_{2}(FIFO) and γ

_{3}(storage segmentation) aim at influencing the sorting of cars. Figure 8 shows that higher weighting of these factors improves the sorting. The factor γ

_{4}has a strong impact on the sorting, too. This can be explained by the greedy nature of term weighted by γ

_{4.}It aims at promoting rows with shorter driving distances. For high values rows with shorter distances are preferred, and the sorting is neglected.

_{2}and γ

_{4}has a strong impact on both KPIs. The interaction between γ

_{1}and γ

_{4}is also of relevance. High weightings of γ

_{1}and γ

_{4}improve both KPIs (short distances and high sorting). This effect is conceptionally desired by differentiating groups according to their turnover times, on the one hand. On the other hand, both factors should help to minimize driving distances, which is confirmed by Figure 9 also.

_{1}contradicts these expectations.

#### 4.3. Performance Evaluation of Real-Word Scenario

_{PYA}and α

_{PBA}values. In contrast to the generic scenario, the driving distances in the real terminal model seem not to be sensitive to variations in the evaporation constant.

_{PBA}value. In general, this scenario seems to offer more potentials concerning the sorting degree. Compared to the generic scenario, the real case comprises a dramatically higher number of rows and vehicle groups. Consequently, this leads to a higher sorting complexity with more optimization potentials. The PYA method can use these potentials and improve the sorting. However, due to the fact discussed above, both evaporation constants do not have a direct impact due to their equations (Equations (2) and (3)). Thus, this effect seems to be caused indirectly by the dynamics induced by the assignment process. Figure 12 indicates that smaller α

_{PBA}values may lead to faster reactions of the method.

#### 4.4. Full Factorial Analysis of Real-Word Scenario

_{1}and α

_{PBA}, all effects are tendentially similar to the observed results in the generic scenario. A significant impact of α

_{PBA}can now be observed in this scenario. Higher values of α

_{PBA}lead to shorter driving distances. Regarding γ

_{1}these results contradict the observation in the generic scenario. High values of γ

_{1}lead to lower driving distances. A possible explanation is that turnover times in the realistic scenario are more heterogeneous than in the generic scenario. There is still a strong separation of cars with longer turnover times, but it leads in this case to more free storage spaces near the quayside, which can be used by high runner cars. This is the originally intended effect of this parameter. However, this finding indicates that the effect of this parameter is sensitive to the scenario and its configuration.

_{1}has stronger interactions with the other factors. As already assumed in the discussion of the generic scenario, this can be explained by more heterogeneous turnover times in this real case. The strongest interaction can still be found for factors γ

_{1}and γ

_{4}. The impact of interactions between weighting factors and evaporation constants seems to remain low. Both figures confirm this. Only the interaction of γ

_{1}and α

_{PYA}has an impact on both KPIs.

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Material flow processes and related terminal planning tasks—based on [13].

**Figure 2.**Generic automobile terminal scenario [12].

OEM | Destination | Ship Group | Avg. Arrival Rate [Cars/Day] | Amplitude [Cars/Day] | Relative Phase Shift [−] | Avg. Turnover Time [d] |
---|---|---|---|---|---|---|

OEM 1 | D1 | R3 | 47.62 | 45.24 | 0 | 10 |

D2 | R3 | 38.10 | 36.20 | 0.2 | 15 | |

D3 | R2 | 28.57 | 27.14 | 0.4 | 20 | |

D4 | R2 | 19.05 | 18.10 | 0.6 | 25 | |

D5 | R1 | 9.52 | 9.04 | 0.8 | 30 | |

D6 | R1 | 57.14 | 54.28 | 1 | 5 | |

OEM 2 | D1 | R3 | 38.10 | 36.20 | 0 | 15 |

D2 | R3 | 28.57 | 27.14 | 0.2 | 20 | |

D3 | R2 | 19.05 | 18.10 | 0.4 | 25 | |

D4 | R2 | 9.52 | 9.04 | 0.6 | 30 | |

D5 | R1 | 57.14 | 54.28 | 0.8 | 5 | |

D6 | R1 | 47.62 | 45.24 | 1 | 10 | |

OEM 3 | D1 | R3 | 28.57 | 27.14 | 0 | 20 |

D2 | R3 | 19.05 | 18.10 | 0.2 | 25 | |

D3 | R2 | 9.52 | 9.04 | 0.4 | 30 | |

D4 | R2 | 57.14 | 54.28 | 0.6 | 5 | |

D5 | R1 | 47.62 | 45.24 | 0.8 | 10 | |

D6 | R1 | 38.10 | 36.20 | 1 | 15 | |

OEM 4 | D1 | R3 | 19.05 | 18.10 | 0 | 25 |

D2 | R3 | 9.52 | 9.04 | 0.2 | 30 | |

D3 | R2 | 57.14 | 54.28 | 0.4 | 5 | |

D4 | R2 | 47.62 | 45.24 | 0.6 | 10 | |

D5 | R1 | 38.10 | 36.20 | 0.8 | 15 | |

D6 | R1 | 28.57 | 27.14 | 1 | 20 | |

OEM 5 | D1 | R3 | 9.52 | 9.04 | 0 | 30 |

D2 | R3 | 57.14 | 54.28 | 0.2 | 5 | |

D3 | R2 | 47.62 | 45.24 | 0.4 | 10 | |

D4 | R2 | 38.10 | 36.20 | 0.6 | 15 | |

D5 | R1 | 28.57 | 27.14 | 0.8 | 20 | |

D6 | R1 | 19.05 | 18.10 | 1 | 25 | |

OEM 6 | D1 | R3 | 57.14 | 54.28 | 0 | 5 |

D2 | R3 | 47.62 | 45.24 | 0.2 | 10 | |

D3 | R2 | 38.10 | 36.20 | 0.4 | 15 | |

D4 | R2 | 28.57 | 27.14 | 0.6 | 20 | |

D5 | R1 | 19.05 | 18.10 | 0.8 | 25 | |

D6 | R1 | 9.52 | 9.04 | 1 | 30 |

Ship Group | Avg. Number of Cars per Journey | Standard Deviation | Destinations |
---|---|---|---|

R1 | 1000 | 150 | D5, D6 |

R2 | 1000 | 150 | D3, D4 |

R3 | 1000 | 150 | D1, D2 |

Generic Scenario | Real-World Scenario | |
---|---|---|

Annual volume | 456,202 | 1,765,787 |

Number of parking rows | 1692 | 18,825 |

Terminal capacity | 21,996 | 104,478 |

Annual ship arrivals | 447 | 1245 |

Groups of cars | 36 | 7073 |

Number berth | 5 | 11 |

Parameter Value | Factor Level | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

# | Runs | γ_{1} | γ_{2} | γ_{3} | γ_{4} | α_{f} | α_{s} | γ_{1} | γ_{2} | γ_{3} | γ_{4} | α_{f} | α_{s} |

1 | 10 | 0.05 | 0.05 | 0.05 | 0.05 | 500 | 200 | −1 | −1 | −1 | −1 | −1 | −1 |

2 | 10 | 0.95 | 0.05 | 0.05 | 0.05 | 500 | 200 | 1 | −1 | −1 | −1 | −1 | −1 |

3 | 10 | 0.05 | 0.95 | 0.05 | 0.05 | 500 | 200 | −1 | 1 | −1 | −1 | −1 | −1 |

4 | 10 | 0.95 | 0.95 | 0.05 | 0.05 | 500 | 200 | 1 | 1 | −1 | −1 | −1 | −1 |

5 | 10 | 0.05 | 0.05 | 0.95 | 0.05 | 500 | 200 | −1 | −1 | 1 | −1 | −1 | −1 |

6 | 10 | 0.95 | 0.05 | 0.95 | 0.05 | 500 | 200 | 1 | −1 | 1 | −1 | −1 | −1 |

7 | 10 | 0.05 | 0.95 | 0.95 | 0.05 | 500 | 200 | −1 | 1 | 1 | −1 | −1 | −1 |

8 | 10 | 0.95 | 0.95 | 0.95 | 0.05 | 500 | 200 | 1 | 1 | 1 | −1 | −1 | −1 |

9 | 10 | 0.05 | 0.05 | 0.05 | 0.95 | 500 | 200 | −1 | −1 | −1 | 1 | −1 | −1 |

10 | 10 | 0.95 | 0.05 | 0.05 | 0.95 | 500 | 200 | 1 | −1 | −1 | 1 | −1 | −1 |

11 | 10 | 0.05 | 0.95 | 0.05 | 0.95 | 500 | 200 | −1 | 1 | −1 | 1 | −1 | −1 |

12 | 10 | 0.95 | 0.95 | 0.05 | 0.95 | 500 | 200 | 1 | 1 | −1 | 1 | −1 | −1 |

13 | 10 | 0.05 | 0.05 | 0.95 | 0.95 | 500 | 200 | −1 | −1 | 1 | 1 | −1 | −1 |

14 | 10 | 0.95 | 0.05 | 0.95 | 0.95 | 500 | 200 | 1 | −1 | 1 | 1 | −1 | −1 |

15 | 10 | 0.05 | 0.95 | 0.95 | 0.95 | 500 | 200 | −1 | 1 | 1 | 1 | −1 | −1 |

16 | 10 | 0.95 | 0.95 | 0.95 | 0.95 | 500 | 200 | 1 | 1 | 1 | 1 | −1 | −1 |

17 | 10 | 0.05 | 0.05 | 0.05 | 0.05 | 2500 | 200 | −1 | −1 | −1 | −1 | 1 | −1 |

… | |||||||||||||

64 | 10 | 0.95 | 0.95 | 0.95 | 0.95 | 2500 | 1500 | 1 | 1 | 1 | 1 | 1 | 1 |

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**MDPI and ACS Style**

Görges, M.; Freitag, M.
Design and Evaluation of an Integrated Autonomous Control Method for Automobile Terminals. *Logistics* **2022**, *6*, 73.
https://doi.org/10.3390/logistics6040073

**AMA Style**

Görges M, Freitag M.
Design and Evaluation of an Integrated Autonomous Control Method for Automobile Terminals. *Logistics*. 2022; 6(4):73.
https://doi.org/10.3390/logistics6040073

**Chicago/Turabian Style**

Görges, Michael, and Michael Freitag.
2022. "Design and Evaluation of an Integrated Autonomous Control Method for Automobile Terminals" *Logistics* 6, no. 4: 73.
https://doi.org/10.3390/logistics6040073